Research ArticleThermodynamic Modeling of Surface Tension ofAqueous Electrolyte Solution by Competitive Adsorption Model
Mohamad Javad Kamali1 Zakarya Kamali2 and Gholamhossein Vatankhah1
1Department of Chemical Engineering Islamic Azad University Bushehr Branch Bushehr 751961955 Iran2National Iranian Gas Company (NIGC) Fajr-e Jam Gas Company Bushehr Iran
Correspondence should be addressed to Mohamad Javad Kamali kamalimjgmailcom
Received 14 August 2015 Accepted 4 October 2015
Academic Editor Marc D Donohue
Copyright copy 2015 Mohamad Javad Kamali et alThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited
Thermodynamic modeling of surface tension of different electrolyte systems in presence of gas phase is studied Using thesolid-liquid equilibrium Langmuir gas-solid adsorption and ENRTL activity coefficient model the surface tension of electrolytesolutions is calculatedThe newmodel has two adjustable parameters which could be determined by fitting the experimental surfacetension of binary aqueous electrolyte solution in single temperature Then the values of surface tension for other temperatures inbinary and ternary system of aqueous electrolyte solution are predicted The average absolute deviations for calculation of surfacetension of binary and mixed electrolyte systems by new model are 198 and 170 respectively
1 Introduction
For studying the aqueous electrolyte solution in porousmedia distillation extraction process and liquid-liquiddispersion the calculation of surface tension of aqueoussolutions is required [1] So different equations have beendeveloped to calculate surface tension of mineral saltsAriyama [2] Lorenz [3] Young and Grinstead [4] andGleim and Shelomov [5] formulated useful equations asgroup contribution method for calculation of surface tensionof some limited binary electrolyte-water systems Oka [6]proposed an equation for calculation of surface tension basedon the concentration of solution electronic charge dielectricconstant of water ionic charge and Avogadrorsquos constantLater Hovarth [7] developed this equation by introducing theionic strength and degree of dissociation into Okarsquos model[6] Onsager and Samaras [8] obtained a relation based on thetemperature dielectric constant of water and concentrationof solution for calculation of surface tension of electrolytesolution Schmutzer [9] considered the osmotic coefficientas an important factor for calculation of surface tension ofelectrolyte solution Adding a proportional factor of anionconcentration to the surface tension of water the surfacetension of aqueous electrolyte solution was determined by
Abramazon and Gaukhberg [10] This parameter was con-sidered as a function of the inverse of square of ionic radiusand anion charge Li et al [1] developed a new model forcalculation of surface tension of single and mixed electrolytesolution In this model the surface layer is considered asa distinct phase where the electrolytes could be enteredinto it from other phases The surface tension was obtainedusing the proportion of molality of salt in surface layer toliquid bulk phase While this model had satisfactory resultsin low concentration of electrolytes in high concentrationthe calculated surface tension was not in good agreementwith experimental data Yu et al [11] combined Li et al [1]model with modified mean spherical approximation (MSA)as osmotic coefficient model The results showed that thecalculated surface tension in highly concentrated regions wasimproved Furthermore the Langmuir gas-solid adsorptionmodel was used at equilibrium condition for calculation ofsurface tension of mineral salts by Li and Lu [12] The resultsindicated the satisfactory agreement with experimental dataSadeghi et al [13] used the combination of MSA model [14]with the Ghotbi and Vera [15] and the Mansoori et al [16]equations of state for correlation of the surface tension ofsingle aqueous solution Also the surface tension of differentmixed aqueous solutions was predicted by this approachThe
Hindawi Publishing CorporationJournal of ermodynamicsVolume 2015 Article ID 319704 8 pageshttpdxdoiorg1011552015319704
2 Journal of Thermodynamics
Bulk vapor phase(V)
Surface phase
(S)
Bulk liquid phase
(L)
= H2O + electrolytes
= H2O + electrolytes
Figure 1 Different phases in aqueous electrolyte solution-vaporsystem [1]
results indicate the satisfactory agreement between calculatedand experimental data [13]
In this paper a new model for calculation of surfacetension of the electrolyte systems is developed using theLangmuir adsorption equation and E-NRTL [17] modelThe adjustable parameters of this model are obtained byexperimental data of surface tension at single temperatureThen the model is verified by prediction of surface tension of65 binary electrolyte-water systems and 17 ternary electrolytesystems
2 Thermodynamic Modeling
For calculation of surface tension of electrolyte system theaqueous electrolyte solution-vapor system is supposed asthree different phases bulk vapor phase surface phase andbulk liquid phase (Figure 1) The surface phase is consideredas distinct layer for adsorption of electrolyte from liquidphase In this system the chemical potential of water in liquidbulk phase and surface would be defined as follows [1]
120583119871
119908= 1205831198710
119908+ 119877119879 ln 119886119871
119908
120583119878
119908= 1205831198780
119908+ 119877119879 ln 119886119878
119908minus 119860119908120590sol
(1)
where 120583 119886 119860 and 120590sol represent the chemical potentialactivity partial molar area and surface tension of solutionThe subscripts 119908 119871 119878 119871
0 and 119878
0refer to water liquid phase
surface phase reference state of liquid phase and referencestate of surface phase respectively
At equilibrium condition the chemical potential of waterin surface and liquid phase is equal So we have
1205831198780
119908minus 1205831198710
119908+ 119877119879 ln 119886119878
119908minus 119877119879 ln 119886119871
119908= 119860119908120590sol (2)
Rewriting the above equation for pure water it yields thefollowing equation
120590119908119860119908= 1205831198780
119908minus 1205831198710
119908 (3)
It would be worth noting that the activity of pure water isunity and the partial molar area for pure water is equal to themolar area
Substituting the above equation into (2) results in thefollowing equation
120590sol = 120590119908 +119877119879
119860119908
ln119886119878
119908
119886119871119908
(4)
It is assumed that in the above equation the partial molar areaand molar area of water are equal The molar area of water iscalculated by [18]
119860119908= 119860119908= (119881119908)23
(119873119860)13
(5)
where 119881119908and 119873
119860are molar volume of water and Avogadro
numberUsing the osmotic definition (120601) instead of activity of
water (4) converts to the following equation
120590sol = 120590119908 +V119877119879
5551119860119908
(119898119871120593119871minus 119898119878120593119878) (6)
where 119898 is molality of electrolyte in aqueous solution and Vis stoichiometric coefficient For calculation of the molalityof electrolyte in surface phase (119898119878) the fraction of adsorbedelectrolyte (120579) on the interface between vapor and liquidphases could be related to the excess area (Γ) as [12]
120579 =Γ
Γ0 (7)
where superscript 0means saturated condition On the otherhand the excess area is defined as moles of electrolyte insurface per area of surface [19] So
120579 =119899119878119860119904
1198990119860119904
=119899119878
1198990=119898119878
1198980 (8)
where 119899 is mole number and superscript 119878 indicates thesurface phase The saturated molality of surface phase isconsidered as fraction of molality of liquid bulk phase or
1198980= 1198700119898119871 (9)
where 119871 is liquid bulk phase and1198700 is a constantUsing the Langmuir gas-solid adsorption [20] and equal-
ity of adsorption and desorption rate for an electrolyte insurface phase [21] the adsorbed fraction of electrolyte on thesurface phase is obtained as [12]
120579 =119870119886
1 + 119870119886 (10)
Combining (6)ndash(8) the molality of electrolyte in surfacephase would be obtained as
119898119878=
119870lowast119886
1 + 119870119886119898119871 (11)
where119870lowast = 1198700119870So substituting (11) into (6) the surface tension of pure
aqueous electrolyte solution is calculated It ismentioned thatthe two adjustable parameters 119870lowast and 119870 are obtained from
Journal of Thermodynamics 3
fitting the experimental surface tension data to the calculatedvalues (see (6)) at single temperature
For mixed electrolyte solution the surface tension wouldbe calculated by the following equation
120590sol = 120590119908 +119877119879
5551119860119908
(120593119871sum
119894
V119894119898119871
119894minus 120593119878sum
119894
V119894119898119878
119894) (12)
Assuming competitive adsorption between electrolytes insurface phase [12] the molality of surface phase is
119898119878
119894=
119870lowast
119894119886119894
1 + sum119895119870119895119886119895
119898119871
119894 (13)
3 Result and Discussion
For studying the surface tension of electrolyte solution 65binary electrolyte systems and 17 ternary electrolyte sys-tems are selected The surface tension of these electrolytesolutions is obtained by competitive adsorption model (see(6) or (12)) In this model for calculation of osmotic andactivity coefficients E-NRTL [17] model is used Using theregression of model with experimental surface tension ofbinary electrolyte-water system the adjustable parameters ofcompetitive adsorption model (119870lowast 119870) are optimized Theobjective function is defined as follows
AAD =100
119873119901
119873119901
sum
119894=1
10038161003816100381610038161003816120590calsol minus 120590
expsol10038161003816100381610038161003816
120590expsol
(14)
where AAD 119873119901 and superscripts cal and exp are average
absolute deviation number of data points and calculated andexperimental data of surface tension respectivelyThe resultsfor different binary electrolyte system are given in Table 1 Soat single temperature for each salt which is given in Table 1the surface tension is correlated
As it is shown in Table 1 when the first adjustableparameter (119870lowast) tends to zero or small positive value or thesecond adjustable parameter (119870) becomes a large numberthe molality of electrolyte system in surface phase is closeto zero Moreover when 119870
lowast is lower than unity and 119870 isnot moderately large number the molality of electrolyte insurface phase decreases with respect to the liquid bulk phaseIn these cases which point out to themineral salts the rate ofadsorption in surface layer would be lower than desorptionrate and surface tension of electrolyte solution is increasedwith respect to the surface tension of water Strong inorganicacids organic acetates and propionates which have highvapor pressure tend to escape from liquid phase to surfacephase and consequently the concentration of these compo-nents in surface phase would be greater than liquid phase [11]For these electrolytes the first adjustable parameter is higherthan unity and so the molality of electrolyte in surface phasebecomes greater than the liquid bulk phase and consequentlythe surface tension of aqueous electrolyte solution increaseswith respect to the liquid bulk phase
For other temperatures the value of surface tension ofelectrolyte aqueous solution is predicted and the results are
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 8 10 12 140AgNO3 molality
Figure 2 Prediction of surface tension of AgNO3-water binary
system at 28315 K using the competitive adsorption model Experi-mental data are taken from [10]
60
62
64
66
68
70
72
74
76
78
80Su
rface
tens
ion
(mN
m)
02 04 06 08 1 12 14 16 180BaCl2 molality
Figure 3 Prediction of surface tension of BaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29815 K 998771 119879 = 32315 K and ◼ 119879 =35315 K)
given in Table 2 Using the competitive adsorption modelthe experimental and predicted values of surface tension ofaqueous binary electrolyte system are illustrated in Figures2ndash8 These figures indicate the agreement between predictedand experimental values of surface tension values for AgNO
3
BaCl2 CaCl
2 KBr HNO
3 NaCl andUO
2SO4using E-NRTL
[17] modelFor ternary systems the surface tension of the aqueous
solutions is predicted in vast range of temperatures andmolalities The values of AAD for prediction of surfacetension of 16 ternary systems by competitive adsorptionmodel are shown in Table 3 The overall AAD for predictionof surface tension of mixed electrolyte solutions is 17
4 Journal of Thermodynamics
55
60
65
70
75
80
85
90
95
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 80CaCl2 molality
Figure 4 Prediction of surface tension of CaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (◼ 119879 = 28315 K 998771 119879 = 33315 K and ⧫ 119879 =37315 K)
40
45
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
10 20 30 40 500HNO3 molality
Figure 5 Prediction of surface tension of HNO3-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 30315 K 998771 119879 = 32315 K and ◼ 119879 =34315 K)
The predicted values of surface tension of NH4NO3-
KNO3-water KBr-KCl-water and NH
4Cl-(NH
4)2SO4-water
systems by new surface tension model and experimentalvalues are illustrated in Figures 9 10 and 11 respectivelyThe agreement between predicted and experimental valuesin these figures represents the satisfactory results of thecompetitive adsorption model
55
60
65
70
75
80
85
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60KBr molality
Figure 6 Prediction of surface tension of KBr-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (⧫119879=28315 K998771119879=32315 K and◼119879=36315 K)
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 6 7 8 9 100NaCl molality
Figure 7 Prediction of surface tension of NaCl-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (998771 119879 = 29115 K ◼ 119879 = 31315 K e 119879 = 33315 K⧫ 119879 = 39315 K ◻ 119879 = 42315 K and I 119879 = 44315 K)
4 Conclusion
Based on the Gibbs thermodynamic and distinct area forsurface phase a new model for calculation of surface tensionof single and mixture electrolyte is developed The molalityin surface phase is calculated using Langmuir gas-solidadsorption theory for electrolytes The osmotic coefficientmodel in the competitive adsorption model is E-NRTLmodel The adjustable parameters of the model are obtained
Journal of Thermodynamics 5
60
62
64
66
68
70
72
74
76
78
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 2 250UO2SO4 molality
Figure 8 Prediction of surface tension of UO2SO4-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29315 K ◼ 119879 = 31815 K 998771 119879 = 33315 Kand e 119879 = 34815 K)
70
72
74
76
78
80
82
84
86
88
90
Surfa
ce te
nsio
n (m
Nm
)
5 10 15 20 250NH4NO3 molality
E-NRTL modelExp data (T = 30
∘C)Exp data (T = 25
∘C)Exp data (T = 18
∘C)
Figure 9 Prediction of surface tension of NH4NO3-KNO
3-water
ternary system using the competitive adsorption model with non-competitive approach (KNO
3molality = 052) Experimental data
are taken from [10] (⧫ 119879 = 29115 K ◼ 119879 = 29815 K and 998771 119879 =30315 K)
by correlating the experimental values of surface tension ofbinary electrolyte solution in single temperature For othertemperatures and ternary systems competitive adsorptionmodel could predict the surface tension of aqueous solutionThe agreement between experimental and calculated values
73
74
75
76
77
78
79
80
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 20KCl molality
Figure 10 Prediction of surface tension of KBr-KCl-water ternarysystem using the competitive adsorption model at 29115 K (KBrmolalityKCl molality = 1) Experimental data are taken from [10]
74
76
78
80
82
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60NH4Cl + (NH4)2SO4 molality
Figure 11 Prediction of surface tension of NH4Cl-(NH
4)2SO4-
water ternary system using the competitive adsorption model at29115 K (NH
4Cl molality(NH
4)2SO4molality = 15) Experimental
data are taken from [10]
of the competitive adsorption model could introduce thisnew model as effective one
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
6 Journal of Thermodynamics
Table 1 The optimized values for adjustable parameters (119870lowast 119870) of competitive adsorption model Experimental data are from [10]
System 119879 (∘C) 119873119901
119870lowast
119870 AADAgNO
320 4 699 times 10minus2 616 times 1014 023
Al2(SO4)3
30 12 895 times 10minus1 393 times 1022 046BaCl2
30 5 0 453 times 104 061CaCl2
30 11 660 times 10minus1 427 times 104 081CdCl2
20 5 734 times 10minus1 219 times 101 008CdSO
420 2 747 times 10minus1 362 times 10minus2 915 times 10minus7
CoCl2
20 2 620 times 10minus1 751 times 10minus5 105 times 10minus4
CsCl 25 15 130 times 10minus1 165 times 1016 043CsI 25 11 191 times 10minus6 191 times 10minus6 045CuSO
430 3 783 times 10minus1 564 times 1014 022
HBr 18 2 109 times 100 186 times 1016 007HCl 20 7 105 times 100 153 times 101 094HClO
425 10 106 times 100 286 times 1014 213
HNO3
20 7 142 times 100 603 times 1014 238KBr 20 5 236 times 10minus1 602 times 1014 021KC2H3O2
30 3 114 times 100 927 times 10minus2 040KCNS 25 12 936 times 10minus1 471 times 100 034KCl 20 10 107 times 10minus1 196 times 1016 033K2CrO4
30 15 249 times 10minus1 114 times 1018 035K3Fe(CN)
625 16 191 times 10minus6 191 times 10minus6 067
KI 25 12 191 times 10minus6 191 times 10minus6 317KNO
325 6 166 times 10minus1 273 times 1015 038
KOH 20 4 307 times 10minus1 846 times 1015 035K2SO4
25 12 191 times 10minus6 191 times 10minus6 072LiBr 30 4 640 times 10minus1 999 times 10minus2 034LiCl 25 7 470 times 10minus1 131 times 101 061LiI 18 2 654 times 10minus1 131 times 100 299 times 10minus6
LiOH 20 4 128 times 10minus1 596 times 1014 040Li2SO4
18 2 436 times 10minus1 357 times 10minus2 015MgCl
220 12 728 times 10minus1 250 times 10minus1 113
MgSO4
10 12 831 times 10minus1 543 times 10minus3 075MnCl
218 6 644 times 10minus1 720 times 10minus3 023
NH4Cl 25 6 290 times 10minus1 568 times 1014 010
NH4NO3
20 9 520 times 10minus1 642 times 10minus2 032(NH4)2SO4
30 4 577 times 10minus1 608 times 100 048NaBr 20 4 485 times 10minus1 177 times 10minus2 021NaCHO
230 12 371 times 10minus1 186 times 1016 029
NaC2H3O2
30 12 112 times 100 204 times 1016 104NaC3H5O2
30 12 191 times 100 127 times 1018 026NaC4H7O2
30 12 328 times 100 194 times 1016 077NaCl 20 9 222 times 10minus1 205 times 1016 066NaClO
315 2 138 times 100 431 times 10minus1 003
NaClO4
25 3 861 times 10minus1 216 times 1016 017Na2CrO4
30 4 423 times 10minus1 159 times 10minus2 027NaI 25 8 615 times 10minus1 907 times 1014 016NaNO
320 4 259 times 10minus1 116 times 1015 021
NaOH 18 6 347 times 10minus1 246 times 10minus3 046Na2SO4
30 3 150 times 10minus1 563 times 1017 022Na2S2O3
40 4 448 times 10minus1 900 times 10minus3 021
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
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2 Journal of Thermodynamics
Bulk vapor phase(V)
Surface phase
(S)
Bulk liquid phase
(L)
= H2O + electrolytes
= H2O + electrolytes
Figure 1 Different phases in aqueous electrolyte solution-vaporsystem [1]
results indicate the satisfactory agreement between calculatedand experimental data [13]
In this paper a new model for calculation of surfacetension of the electrolyte systems is developed using theLangmuir adsorption equation and E-NRTL [17] modelThe adjustable parameters of this model are obtained byexperimental data of surface tension at single temperatureThen the model is verified by prediction of surface tension of65 binary electrolyte-water systems and 17 ternary electrolytesystems
2 Thermodynamic Modeling
For calculation of surface tension of electrolyte system theaqueous electrolyte solution-vapor system is supposed asthree different phases bulk vapor phase surface phase andbulk liquid phase (Figure 1) The surface phase is consideredas distinct layer for adsorption of electrolyte from liquidphase In this system the chemical potential of water in liquidbulk phase and surface would be defined as follows [1]
120583119871
119908= 1205831198710
119908+ 119877119879 ln 119886119871
119908
120583119878
119908= 1205831198780
119908+ 119877119879 ln 119886119878
119908minus 119860119908120590sol
(1)
where 120583 119886 119860 and 120590sol represent the chemical potentialactivity partial molar area and surface tension of solutionThe subscripts 119908 119871 119878 119871
0 and 119878
0refer to water liquid phase
surface phase reference state of liquid phase and referencestate of surface phase respectively
At equilibrium condition the chemical potential of waterin surface and liquid phase is equal So we have
1205831198780
119908minus 1205831198710
119908+ 119877119879 ln 119886119878
119908minus 119877119879 ln 119886119871
119908= 119860119908120590sol (2)
Rewriting the above equation for pure water it yields thefollowing equation
120590119908119860119908= 1205831198780
119908minus 1205831198710
119908 (3)
It would be worth noting that the activity of pure water isunity and the partial molar area for pure water is equal to themolar area
Substituting the above equation into (2) results in thefollowing equation
120590sol = 120590119908 +119877119879
119860119908
ln119886119878
119908
119886119871119908
(4)
It is assumed that in the above equation the partial molar areaand molar area of water are equal The molar area of water iscalculated by [18]
119860119908= 119860119908= (119881119908)23
(119873119860)13
(5)
where 119881119908and 119873
119860are molar volume of water and Avogadro
numberUsing the osmotic definition (120601) instead of activity of
water (4) converts to the following equation
120590sol = 120590119908 +V119877119879
5551119860119908
(119898119871120593119871minus 119898119878120593119878) (6)
where 119898 is molality of electrolyte in aqueous solution and Vis stoichiometric coefficient For calculation of the molalityof electrolyte in surface phase (119898119878) the fraction of adsorbedelectrolyte (120579) on the interface between vapor and liquidphases could be related to the excess area (Γ) as [12]
120579 =Γ
Γ0 (7)
where superscript 0means saturated condition On the otherhand the excess area is defined as moles of electrolyte insurface per area of surface [19] So
120579 =119899119878119860119904
1198990119860119904
=119899119878
1198990=119898119878
1198980 (8)
where 119899 is mole number and superscript 119878 indicates thesurface phase The saturated molality of surface phase isconsidered as fraction of molality of liquid bulk phase or
1198980= 1198700119898119871 (9)
where 119871 is liquid bulk phase and1198700 is a constantUsing the Langmuir gas-solid adsorption [20] and equal-
ity of adsorption and desorption rate for an electrolyte insurface phase [21] the adsorbed fraction of electrolyte on thesurface phase is obtained as [12]
120579 =119870119886
1 + 119870119886 (10)
Combining (6)ndash(8) the molality of electrolyte in surfacephase would be obtained as
119898119878=
119870lowast119886
1 + 119870119886119898119871 (11)
where119870lowast = 1198700119870So substituting (11) into (6) the surface tension of pure
aqueous electrolyte solution is calculated It ismentioned thatthe two adjustable parameters 119870lowast and 119870 are obtained from
Journal of Thermodynamics 3
fitting the experimental surface tension data to the calculatedvalues (see (6)) at single temperature
For mixed electrolyte solution the surface tension wouldbe calculated by the following equation
120590sol = 120590119908 +119877119879
5551119860119908
(120593119871sum
119894
V119894119898119871
119894minus 120593119878sum
119894
V119894119898119878
119894) (12)
Assuming competitive adsorption between electrolytes insurface phase [12] the molality of surface phase is
119898119878
119894=
119870lowast
119894119886119894
1 + sum119895119870119895119886119895
119898119871
119894 (13)
3 Result and Discussion
For studying the surface tension of electrolyte solution 65binary electrolyte systems and 17 ternary electrolyte sys-tems are selected The surface tension of these electrolytesolutions is obtained by competitive adsorption model (see(6) or (12)) In this model for calculation of osmotic andactivity coefficients E-NRTL [17] model is used Using theregression of model with experimental surface tension ofbinary electrolyte-water system the adjustable parameters ofcompetitive adsorption model (119870lowast 119870) are optimized Theobjective function is defined as follows
AAD =100
119873119901
119873119901
sum
119894=1
10038161003816100381610038161003816120590calsol minus 120590
expsol10038161003816100381610038161003816
120590expsol
(14)
where AAD 119873119901 and superscripts cal and exp are average
absolute deviation number of data points and calculated andexperimental data of surface tension respectivelyThe resultsfor different binary electrolyte system are given in Table 1 Soat single temperature for each salt which is given in Table 1the surface tension is correlated
As it is shown in Table 1 when the first adjustableparameter (119870lowast) tends to zero or small positive value or thesecond adjustable parameter (119870) becomes a large numberthe molality of electrolyte system in surface phase is closeto zero Moreover when 119870
lowast is lower than unity and 119870 isnot moderately large number the molality of electrolyte insurface phase decreases with respect to the liquid bulk phaseIn these cases which point out to themineral salts the rate ofadsorption in surface layer would be lower than desorptionrate and surface tension of electrolyte solution is increasedwith respect to the surface tension of water Strong inorganicacids organic acetates and propionates which have highvapor pressure tend to escape from liquid phase to surfacephase and consequently the concentration of these compo-nents in surface phase would be greater than liquid phase [11]For these electrolytes the first adjustable parameter is higherthan unity and so the molality of electrolyte in surface phasebecomes greater than the liquid bulk phase and consequentlythe surface tension of aqueous electrolyte solution increaseswith respect to the liquid bulk phase
For other temperatures the value of surface tension ofelectrolyte aqueous solution is predicted and the results are
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 8 10 12 140AgNO3 molality
Figure 2 Prediction of surface tension of AgNO3-water binary
system at 28315 K using the competitive adsorption model Experi-mental data are taken from [10]
60
62
64
66
68
70
72
74
76
78
80Su
rface
tens
ion
(mN
m)
02 04 06 08 1 12 14 16 180BaCl2 molality
Figure 3 Prediction of surface tension of BaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29815 K 998771 119879 = 32315 K and ◼ 119879 =35315 K)
given in Table 2 Using the competitive adsorption modelthe experimental and predicted values of surface tension ofaqueous binary electrolyte system are illustrated in Figures2ndash8 These figures indicate the agreement between predictedand experimental values of surface tension values for AgNO
3
BaCl2 CaCl
2 KBr HNO
3 NaCl andUO
2SO4using E-NRTL
[17] modelFor ternary systems the surface tension of the aqueous
solutions is predicted in vast range of temperatures andmolalities The values of AAD for prediction of surfacetension of 16 ternary systems by competitive adsorptionmodel are shown in Table 3 The overall AAD for predictionof surface tension of mixed electrolyte solutions is 17
4 Journal of Thermodynamics
55
60
65
70
75
80
85
90
95
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 80CaCl2 molality
Figure 4 Prediction of surface tension of CaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (◼ 119879 = 28315 K 998771 119879 = 33315 K and ⧫ 119879 =37315 K)
40
45
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
10 20 30 40 500HNO3 molality
Figure 5 Prediction of surface tension of HNO3-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 30315 K 998771 119879 = 32315 K and ◼ 119879 =34315 K)
The predicted values of surface tension of NH4NO3-
KNO3-water KBr-KCl-water and NH
4Cl-(NH
4)2SO4-water
systems by new surface tension model and experimentalvalues are illustrated in Figures 9 10 and 11 respectivelyThe agreement between predicted and experimental valuesin these figures represents the satisfactory results of thecompetitive adsorption model
55
60
65
70
75
80
85
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60KBr molality
Figure 6 Prediction of surface tension of KBr-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (⧫119879=28315 K998771119879=32315 K and◼119879=36315 K)
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 6 7 8 9 100NaCl molality
Figure 7 Prediction of surface tension of NaCl-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (998771 119879 = 29115 K ◼ 119879 = 31315 K e 119879 = 33315 K⧫ 119879 = 39315 K ◻ 119879 = 42315 K and I 119879 = 44315 K)
4 Conclusion
Based on the Gibbs thermodynamic and distinct area forsurface phase a new model for calculation of surface tensionof single and mixture electrolyte is developed The molalityin surface phase is calculated using Langmuir gas-solidadsorption theory for electrolytes The osmotic coefficientmodel in the competitive adsorption model is E-NRTLmodel The adjustable parameters of the model are obtained
Journal of Thermodynamics 5
60
62
64
66
68
70
72
74
76
78
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 2 250UO2SO4 molality
Figure 8 Prediction of surface tension of UO2SO4-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29315 K ◼ 119879 = 31815 K 998771 119879 = 33315 Kand e 119879 = 34815 K)
70
72
74
76
78
80
82
84
86
88
90
Surfa
ce te
nsio
n (m
Nm
)
5 10 15 20 250NH4NO3 molality
E-NRTL modelExp data (T = 30
∘C)Exp data (T = 25
∘C)Exp data (T = 18
∘C)
Figure 9 Prediction of surface tension of NH4NO3-KNO
3-water
ternary system using the competitive adsorption model with non-competitive approach (KNO
3molality = 052) Experimental data
are taken from [10] (⧫ 119879 = 29115 K ◼ 119879 = 29815 K and 998771 119879 =30315 K)
by correlating the experimental values of surface tension ofbinary electrolyte solution in single temperature For othertemperatures and ternary systems competitive adsorptionmodel could predict the surface tension of aqueous solutionThe agreement between experimental and calculated values
73
74
75
76
77
78
79
80
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 20KCl molality
Figure 10 Prediction of surface tension of KBr-KCl-water ternarysystem using the competitive adsorption model at 29115 K (KBrmolalityKCl molality = 1) Experimental data are taken from [10]
74
76
78
80
82
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60NH4Cl + (NH4)2SO4 molality
Figure 11 Prediction of surface tension of NH4Cl-(NH
4)2SO4-
water ternary system using the competitive adsorption model at29115 K (NH
4Cl molality(NH
4)2SO4molality = 15) Experimental
data are taken from [10]
of the competitive adsorption model could introduce thisnew model as effective one
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
6 Journal of Thermodynamics
Table 1 The optimized values for adjustable parameters (119870lowast 119870) of competitive adsorption model Experimental data are from [10]
System 119879 (∘C) 119873119901
119870lowast
119870 AADAgNO
320 4 699 times 10minus2 616 times 1014 023
Al2(SO4)3
30 12 895 times 10minus1 393 times 1022 046BaCl2
30 5 0 453 times 104 061CaCl2
30 11 660 times 10minus1 427 times 104 081CdCl2
20 5 734 times 10minus1 219 times 101 008CdSO
420 2 747 times 10minus1 362 times 10minus2 915 times 10minus7
CoCl2
20 2 620 times 10minus1 751 times 10minus5 105 times 10minus4
CsCl 25 15 130 times 10minus1 165 times 1016 043CsI 25 11 191 times 10minus6 191 times 10minus6 045CuSO
430 3 783 times 10minus1 564 times 1014 022
HBr 18 2 109 times 100 186 times 1016 007HCl 20 7 105 times 100 153 times 101 094HClO
425 10 106 times 100 286 times 1014 213
HNO3
20 7 142 times 100 603 times 1014 238KBr 20 5 236 times 10minus1 602 times 1014 021KC2H3O2
30 3 114 times 100 927 times 10minus2 040KCNS 25 12 936 times 10minus1 471 times 100 034KCl 20 10 107 times 10minus1 196 times 1016 033K2CrO4
30 15 249 times 10minus1 114 times 1018 035K3Fe(CN)
625 16 191 times 10minus6 191 times 10minus6 067
KI 25 12 191 times 10minus6 191 times 10minus6 317KNO
325 6 166 times 10minus1 273 times 1015 038
KOH 20 4 307 times 10minus1 846 times 1015 035K2SO4
25 12 191 times 10minus6 191 times 10minus6 072LiBr 30 4 640 times 10minus1 999 times 10minus2 034LiCl 25 7 470 times 10minus1 131 times 101 061LiI 18 2 654 times 10minus1 131 times 100 299 times 10minus6
LiOH 20 4 128 times 10minus1 596 times 1014 040Li2SO4
18 2 436 times 10minus1 357 times 10minus2 015MgCl
220 12 728 times 10minus1 250 times 10minus1 113
MgSO4
10 12 831 times 10minus1 543 times 10minus3 075MnCl
218 6 644 times 10minus1 720 times 10minus3 023
NH4Cl 25 6 290 times 10minus1 568 times 1014 010
NH4NO3
20 9 520 times 10minus1 642 times 10minus2 032(NH4)2SO4
30 4 577 times 10minus1 608 times 100 048NaBr 20 4 485 times 10minus1 177 times 10minus2 021NaCHO
230 12 371 times 10minus1 186 times 1016 029
NaC2H3O2
30 12 112 times 100 204 times 1016 104NaC3H5O2
30 12 191 times 100 127 times 1018 026NaC4H7O2
30 12 328 times 100 194 times 1016 077NaCl 20 9 222 times 10minus1 205 times 1016 066NaClO
315 2 138 times 100 431 times 10minus1 003
NaClO4
25 3 861 times 10minus1 216 times 1016 017Na2CrO4
30 4 423 times 10minus1 159 times 10minus2 027NaI 25 8 615 times 10minus1 907 times 1014 016NaNO
320 4 259 times 10minus1 116 times 1015 021
NaOH 18 6 347 times 10minus1 246 times 10minus3 046Na2SO4
30 3 150 times 10minus1 563 times 1017 022Na2S2O3
40 4 448 times 10minus1 900 times 10minus3 021
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
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ThermodynamicsJournal of
Journal of Thermodynamics 3
fitting the experimental surface tension data to the calculatedvalues (see (6)) at single temperature
For mixed electrolyte solution the surface tension wouldbe calculated by the following equation
120590sol = 120590119908 +119877119879
5551119860119908
(120593119871sum
119894
V119894119898119871
119894minus 120593119878sum
119894
V119894119898119878
119894) (12)
Assuming competitive adsorption between electrolytes insurface phase [12] the molality of surface phase is
119898119878
119894=
119870lowast
119894119886119894
1 + sum119895119870119895119886119895
119898119871
119894 (13)
3 Result and Discussion
For studying the surface tension of electrolyte solution 65binary electrolyte systems and 17 ternary electrolyte sys-tems are selected The surface tension of these electrolytesolutions is obtained by competitive adsorption model (see(6) or (12)) In this model for calculation of osmotic andactivity coefficients E-NRTL [17] model is used Using theregression of model with experimental surface tension ofbinary electrolyte-water system the adjustable parameters ofcompetitive adsorption model (119870lowast 119870) are optimized Theobjective function is defined as follows
AAD =100
119873119901
119873119901
sum
119894=1
10038161003816100381610038161003816120590calsol minus 120590
expsol10038161003816100381610038161003816
120590expsol
(14)
where AAD 119873119901 and superscripts cal and exp are average
absolute deviation number of data points and calculated andexperimental data of surface tension respectivelyThe resultsfor different binary electrolyte system are given in Table 1 Soat single temperature for each salt which is given in Table 1the surface tension is correlated
As it is shown in Table 1 when the first adjustableparameter (119870lowast) tends to zero or small positive value or thesecond adjustable parameter (119870) becomes a large numberthe molality of electrolyte system in surface phase is closeto zero Moreover when 119870
lowast is lower than unity and 119870 isnot moderately large number the molality of electrolyte insurface phase decreases with respect to the liquid bulk phaseIn these cases which point out to themineral salts the rate ofadsorption in surface layer would be lower than desorptionrate and surface tension of electrolyte solution is increasedwith respect to the surface tension of water Strong inorganicacids organic acetates and propionates which have highvapor pressure tend to escape from liquid phase to surfacephase and consequently the concentration of these compo-nents in surface phase would be greater than liquid phase [11]For these electrolytes the first adjustable parameter is higherthan unity and so the molality of electrolyte in surface phasebecomes greater than the liquid bulk phase and consequentlythe surface tension of aqueous electrolyte solution increaseswith respect to the liquid bulk phase
For other temperatures the value of surface tension ofelectrolyte aqueous solution is predicted and the results are
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 8 10 12 140AgNO3 molality
Figure 2 Prediction of surface tension of AgNO3-water binary
system at 28315 K using the competitive adsorption model Experi-mental data are taken from [10]
60
62
64
66
68
70
72
74
76
78
80Su
rface
tens
ion
(mN
m)
02 04 06 08 1 12 14 16 180BaCl2 molality
Figure 3 Prediction of surface tension of BaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29815 K 998771 119879 = 32315 K and ◼ 119879 =35315 K)
given in Table 2 Using the competitive adsorption modelthe experimental and predicted values of surface tension ofaqueous binary electrolyte system are illustrated in Figures2ndash8 These figures indicate the agreement between predictedand experimental values of surface tension values for AgNO
3
BaCl2 CaCl
2 KBr HNO
3 NaCl andUO
2SO4using E-NRTL
[17] modelFor ternary systems the surface tension of the aqueous
solutions is predicted in vast range of temperatures andmolalities The values of AAD for prediction of surfacetension of 16 ternary systems by competitive adsorptionmodel are shown in Table 3 The overall AAD for predictionof surface tension of mixed electrolyte solutions is 17
4 Journal of Thermodynamics
55
60
65
70
75
80
85
90
95
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 80CaCl2 molality
Figure 4 Prediction of surface tension of CaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (◼ 119879 = 28315 K 998771 119879 = 33315 K and ⧫ 119879 =37315 K)
40
45
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
10 20 30 40 500HNO3 molality
Figure 5 Prediction of surface tension of HNO3-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 30315 K 998771 119879 = 32315 K and ◼ 119879 =34315 K)
The predicted values of surface tension of NH4NO3-
KNO3-water KBr-KCl-water and NH
4Cl-(NH
4)2SO4-water
systems by new surface tension model and experimentalvalues are illustrated in Figures 9 10 and 11 respectivelyThe agreement between predicted and experimental valuesin these figures represents the satisfactory results of thecompetitive adsorption model
55
60
65
70
75
80
85
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60KBr molality
Figure 6 Prediction of surface tension of KBr-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (⧫119879=28315 K998771119879=32315 K and◼119879=36315 K)
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 6 7 8 9 100NaCl molality
Figure 7 Prediction of surface tension of NaCl-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (998771 119879 = 29115 K ◼ 119879 = 31315 K e 119879 = 33315 K⧫ 119879 = 39315 K ◻ 119879 = 42315 K and I 119879 = 44315 K)
4 Conclusion
Based on the Gibbs thermodynamic and distinct area forsurface phase a new model for calculation of surface tensionof single and mixture electrolyte is developed The molalityin surface phase is calculated using Langmuir gas-solidadsorption theory for electrolytes The osmotic coefficientmodel in the competitive adsorption model is E-NRTLmodel The adjustable parameters of the model are obtained
Journal of Thermodynamics 5
60
62
64
66
68
70
72
74
76
78
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 2 250UO2SO4 molality
Figure 8 Prediction of surface tension of UO2SO4-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29315 K ◼ 119879 = 31815 K 998771 119879 = 33315 Kand e 119879 = 34815 K)
70
72
74
76
78
80
82
84
86
88
90
Surfa
ce te
nsio
n (m
Nm
)
5 10 15 20 250NH4NO3 molality
E-NRTL modelExp data (T = 30
∘C)Exp data (T = 25
∘C)Exp data (T = 18
∘C)
Figure 9 Prediction of surface tension of NH4NO3-KNO
3-water
ternary system using the competitive adsorption model with non-competitive approach (KNO
3molality = 052) Experimental data
are taken from [10] (⧫ 119879 = 29115 K ◼ 119879 = 29815 K and 998771 119879 =30315 K)
by correlating the experimental values of surface tension ofbinary electrolyte solution in single temperature For othertemperatures and ternary systems competitive adsorptionmodel could predict the surface tension of aqueous solutionThe agreement between experimental and calculated values
73
74
75
76
77
78
79
80
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 20KCl molality
Figure 10 Prediction of surface tension of KBr-KCl-water ternarysystem using the competitive adsorption model at 29115 K (KBrmolalityKCl molality = 1) Experimental data are taken from [10]
74
76
78
80
82
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60NH4Cl + (NH4)2SO4 molality
Figure 11 Prediction of surface tension of NH4Cl-(NH
4)2SO4-
water ternary system using the competitive adsorption model at29115 K (NH
4Cl molality(NH
4)2SO4molality = 15) Experimental
data are taken from [10]
of the competitive adsorption model could introduce thisnew model as effective one
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
6 Journal of Thermodynamics
Table 1 The optimized values for adjustable parameters (119870lowast 119870) of competitive adsorption model Experimental data are from [10]
System 119879 (∘C) 119873119901
119870lowast
119870 AADAgNO
320 4 699 times 10minus2 616 times 1014 023
Al2(SO4)3
30 12 895 times 10minus1 393 times 1022 046BaCl2
30 5 0 453 times 104 061CaCl2
30 11 660 times 10minus1 427 times 104 081CdCl2
20 5 734 times 10minus1 219 times 101 008CdSO
420 2 747 times 10minus1 362 times 10minus2 915 times 10minus7
CoCl2
20 2 620 times 10minus1 751 times 10minus5 105 times 10minus4
CsCl 25 15 130 times 10minus1 165 times 1016 043CsI 25 11 191 times 10minus6 191 times 10minus6 045CuSO
430 3 783 times 10minus1 564 times 1014 022
HBr 18 2 109 times 100 186 times 1016 007HCl 20 7 105 times 100 153 times 101 094HClO
425 10 106 times 100 286 times 1014 213
HNO3
20 7 142 times 100 603 times 1014 238KBr 20 5 236 times 10minus1 602 times 1014 021KC2H3O2
30 3 114 times 100 927 times 10minus2 040KCNS 25 12 936 times 10minus1 471 times 100 034KCl 20 10 107 times 10minus1 196 times 1016 033K2CrO4
30 15 249 times 10minus1 114 times 1018 035K3Fe(CN)
625 16 191 times 10minus6 191 times 10minus6 067
KI 25 12 191 times 10minus6 191 times 10minus6 317KNO
325 6 166 times 10minus1 273 times 1015 038
KOH 20 4 307 times 10minus1 846 times 1015 035K2SO4
25 12 191 times 10minus6 191 times 10minus6 072LiBr 30 4 640 times 10minus1 999 times 10minus2 034LiCl 25 7 470 times 10minus1 131 times 101 061LiI 18 2 654 times 10minus1 131 times 100 299 times 10minus6
LiOH 20 4 128 times 10minus1 596 times 1014 040Li2SO4
18 2 436 times 10minus1 357 times 10minus2 015MgCl
220 12 728 times 10minus1 250 times 10minus1 113
MgSO4
10 12 831 times 10minus1 543 times 10minus3 075MnCl
218 6 644 times 10minus1 720 times 10minus3 023
NH4Cl 25 6 290 times 10minus1 568 times 1014 010
NH4NO3
20 9 520 times 10minus1 642 times 10minus2 032(NH4)2SO4
30 4 577 times 10minus1 608 times 100 048NaBr 20 4 485 times 10minus1 177 times 10minus2 021NaCHO
230 12 371 times 10minus1 186 times 1016 029
NaC2H3O2
30 12 112 times 100 204 times 1016 104NaC3H5O2
30 12 191 times 100 127 times 1018 026NaC4H7O2
30 12 328 times 100 194 times 1016 077NaCl 20 9 222 times 10minus1 205 times 1016 066NaClO
315 2 138 times 100 431 times 10minus1 003
NaClO4
25 3 861 times 10minus1 216 times 1016 017Na2CrO4
30 4 423 times 10minus1 159 times 10minus2 027NaI 25 8 615 times 10minus1 907 times 1014 016NaNO
320 4 259 times 10minus1 116 times 1015 021
NaOH 18 6 347 times 10minus1 246 times 10minus3 046Na2SO4
30 3 150 times 10minus1 563 times 1017 022Na2S2O3
40 4 448 times 10minus1 900 times 10minus3 021
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
Submit your manuscripts athttpwwwhindawicom
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ThermodynamicsJournal of
4 Journal of Thermodynamics
55
60
65
70
75
80
85
90
95
Surfa
ce te
nsio
n (m
Nm
)
2 4 6 80CaCl2 molality
Figure 4 Prediction of surface tension of CaCl2-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (◼ 119879 = 28315 K 998771 119879 = 33315 K and ⧫ 119879 =37315 K)
40
45
50
55
60
65
70
75
Surfa
ce te
nsio
n (m
Nm
)
10 20 30 40 500HNO3 molality
Figure 5 Prediction of surface tension of HNO3-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 30315 K 998771 119879 = 32315 K and ◼ 119879 =34315 K)
The predicted values of surface tension of NH4NO3-
KNO3-water KBr-KCl-water and NH
4Cl-(NH
4)2SO4-water
systems by new surface tension model and experimentalvalues are illustrated in Figures 9 10 and 11 respectivelyThe agreement between predicted and experimental valuesin these figures represents the satisfactory results of thecompetitive adsorption model
55
60
65
70
75
80
85
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60KBr molality
Figure 6 Prediction of surface tension of KBr-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (⧫119879=28315 K998771119879=32315 K and◼119879=36315 K)
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 6 7 8 9 100NaCl molality
Figure 7 Prediction of surface tension of NaCl-water binary systemusing the competitive adsorption model Experimental data aretaken from [10] (998771 119879 = 29115 K ◼ 119879 = 31315 K e 119879 = 33315 K⧫ 119879 = 39315 K ◻ 119879 = 42315 K and I 119879 = 44315 K)
4 Conclusion
Based on the Gibbs thermodynamic and distinct area forsurface phase a new model for calculation of surface tensionof single and mixture electrolyte is developed The molalityin surface phase is calculated using Langmuir gas-solidadsorption theory for electrolytes The osmotic coefficientmodel in the competitive adsorption model is E-NRTLmodel The adjustable parameters of the model are obtained
Journal of Thermodynamics 5
60
62
64
66
68
70
72
74
76
78
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 2 250UO2SO4 molality
Figure 8 Prediction of surface tension of UO2SO4-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29315 K ◼ 119879 = 31815 K 998771 119879 = 33315 Kand e 119879 = 34815 K)
70
72
74
76
78
80
82
84
86
88
90
Surfa
ce te
nsio
n (m
Nm
)
5 10 15 20 250NH4NO3 molality
E-NRTL modelExp data (T = 30
∘C)Exp data (T = 25
∘C)Exp data (T = 18
∘C)
Figure 9 Prediction of surface tension of NH4NO3-KNO
3-water
ternary system using the competitive adsorption model with non-competitive approach (KNO
3molality = 052) Experimental data
are taken from [10] (⧫ 119879 = 29115 K ◼ 119879 = 29815 K and 998771 119879 =30315 K)
by correlating the experimental values of surface tension ofbinary electrolyte solution in single temperature For othertemperatures and ternary systems competitive adsorptionmodel could predict the surface tension of aqueous solutionThe agreement between experimental and calculated values
73
74
75
76
77
78
79
80
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 20KCl molality
Figure 10 Prediction of surface tension of KBr-KCl-water ternarysystem using the competitive adsorption model at 29115 K (KBrmolalityKCl molality = 1) Experimental data are taken from [10]
74
76
78
80
82
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60NH4Cl + (NH4)2SO4 molality
Figure 11 Prediction of surface tension of NH4Cl-(NH
4)2SO4-
water ternary system using the competitive adsorption model at29115 K (NH
4Cl molality(NH
4)2SO4molality = 15) Experimental
data are taken from [10]
of the competitive adsorption model could introduce thisnew model as effective one
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
6 Journal of Thermodynamics
Table 1 The optimized values for adjustable parameters (119870lowast 119870) of competitive adsorption model Experimental data are from [10]
System 119879 (∘C) 119873119901
119870lowast
119870 AADAgNO
320 4 699 times 10minus2 616 times 1014 023
Al2(SO4)3
30 12 895 times 10minus1 393 times 1022 046BaCl2
30 5 0 453 times 104 061CaCl2
30 11 660 times 10minus1 427 times 104 081CdCl2
20 5 734 times 10minus1 219 times 101 008CdSO
420 2 747 times 10minus1 362 times 10minus2 915 times 10minus7
CoCl2
20 2 620 times 10minus1 751 times 10minus5 105 times 10minus4
CsCl 25 15 130 times 10minus1 165 times 1016 043CsI 25 11 191 times 10minus6 191 times 10minus6 045CuSO
430 3 783 times 10minus1 564 times 1014 022
HBr 18 2 109 times 100 186 times 1016 007HCl 20 7 105 times 100 153 times 101 094HClO
425 10 106 times 100 286 times 1014 213
HNO3
20 7 142 times 100 603 times 1014 238KBr 20 5 236 times 10minus1 602 times 1014 021KC2H3O2
30 3 114 times 100 927 times 10minus2 040KCNS 25 12 936 times 10minus1 471 times 100 034KCl 20 10 107 times 10minus1 196 times 1016 033K2CrO4
30 15 249 times 10minus1 114 times 1018 035K3Fe(CN)
625 16 191 times 10minus6 191 times 10minus6 067
KI 25 12 191 times 10minus6 191 times 10minus6 317KNO
325 6 166 times 10minus1 273 times 1015 038
KOH 20 4 307 times 10minus1 846 times 1015 035K2SO4
25 12 191 times 10minus6 191 times 10minus6 072LiBr 30 4 640 times 10minus1 999 times 10minus2 034LiCl 25 7 470 times 10minus1 131 times 101 061LiI 18 2 654 times 10minus1 131 times 100 299 times 10minus6
LiOH 20 4 128 times 10minus1 596 times 1014 040Li2SO4
18 2 436 times 10minus1 357 times 10minus2 015MgCl
220 12 728 times 10minus1 250 times 10minus1 113
MgSO4
10 12 831 times 10minus1 543 times 10minus3 075MnCl
218 6 644 times 10minus1 720 times 10minus3 023
NH4Cl 25 6 290 times 10minus1 568 times 1014 010
NH4NO3
20 9 520 times 10minus1 642 times 10minus2 032(NH4)2SO4
30 4 577 times 10minus1 608 times 100 048NaBr 20 4 485 times 10minus1 177 times 10minus2 021NaCHO
230 12 371 times 10minus1 186 times 1016 029
NaC2H3O2
30 12 112 times 100 204 times 1016 104NaC3H5O2
30 12 191 times 100 127 times 1018 026NaC4H7O2
30 12 328 times 100 194 times 1016 077NaCl 20 9 222 times 10minus1 205 times 1016 066NaClO
315 2 138 times 100 431 times 10minus1 003
NaClO4
25 3 861 times 10minus1 216 times 1016 017Na2CrO4
30 4 423 times 10minus1 159 times 10minus2 027NaI 25 8 615 times 10minus1 907 times 1014 016NaNO
320 4 259 times 10minus1 116 times 1015 021
NaOH 18 6 347 times 10minus1 246 times 10minus3 046Na2SO4
30 3 150 times 10minus1 563 times 1017 022Na2S2O3
40 4 448 times 10minus1 900 times 10minus3 021
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Journal of Thermodynamics 5
60
62
64
66
68
70
72
74
76
78
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 2 250UO2SO4 molality
Figure 8 Prediction of surface tension of UO2SO4-water binary
system using the competitive adsorption model Experimental dataare taken from [10] (⧫ 119879 = 29315 K ◼ 119879 = 31815 K 998771 119879 = 33315 Kand e 119879 = 34815 K)
70
72
74
76
78
80
82
84
86
88
90
Surfa
ce te
nsio
n (m
Nm
)
5 10 15 20 250NH4NO3 molality
E-NRTL modelExp data (T = 30
∘C)Exp data (T = 25
∘C)Exp data (T = 18
∘C)
Figure 9 Prediction of surface tension of NH4NO3-KNO
3-water
ternary system using the competitive adsorption model with non-competitive approach (KNO
3molality = 052) Experimental data
are taken from [10] (⧫ 119879 = 29115 K ◼ 119879 = 29815 K and 998771 119879 =30315 K)
by correlating the experimental values of surface tension ofbinary electrolyte solution in single temperature For othertemperatures and ternary systems competitive adsorptionmodel could predict the surface tension of aqueous solutionThe agreement between experimental and calculated values
73
74
75
76
77
78
79
80
Surfa
ce te
nsio
n (m
Nm
)
05 1 15 20KCl molality
Figure 10 Prediction of surface tension of KBr-KCl-water ternarysystem using the competitive adsorption model at 29115 K (KBrmolalityKCl molality = 1) Experimental data are taken from [10]
74
76
78
80
82
Surfa
ce te
nsio
n (m
Nm
)
1 2 3 4 5 60NH4Cl + (NH4)2SO4 molality
Figure 11 Prediction of surface tension of NH4Cl-(NH
4)2SO4-
water ternary system using the competitive adsorption model at29115 K (NH
4Cl molality(NH
4)2SO4molality = 15) Experimental
data are taken from [10]
of the competitive adsorption model could introduce thisnew model as effective one
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
6 Journal of Thermodynamics
Table 1 The optimized values for adjustable parameters (119870lowast 119870) of competitive adsorption model Experimental data are from [10]
System 119879 (∘C) 119873119901
119870lowast
119870 AADAgNO
320 4 699 times 10minus2 616 times 1014 023
Al2(SO4)3
30 12 895 times 10minus1 393 times 1022 046BaCl2
30 5 0 453 times 104 061CaCl2
30 11 660 times 10minus1 427 times 104 081CdCl2
20 5 734 times 10minus1 219 times 101 008CdSO
420 2 747 times 10minus1 362 times 10minus2 915 times 10minus7
CoCl2
20 2 620 times 10minus1 751 times 10minus5 105 times 10minus4
CsCl 25 15 130 times 10minus1 165 times 1016 043CsI 25 11 191 times 10minus6 191 times 10minus6 045CuSO
430 3 783 times 10minus1 564 times 1014 022
HBr 18 2 109 times 100 186 times 1016 007HCl 20 7 105 times 100 153 times 101 094HClO
425 10 106 times 100 286 times 1014 213
HNO3
20 7 142 times 100 603 times 1014 238KBr 20 5 236 times 10minus1 602 times 1014 021KC2H3O2
30 3 114 times 100 927 times 10minus2 040KCNS 25 12 936 times 10minus1 471 times 100 034KCl 20 10 107 times 10minus1 196 times 1016 033K2CrO4
30 15 249 times 10minus1 114 times 1018 035K3Fe(CN)
625 16 191 times 10minus6 191 times 10minus6 067
KI 25 12 191 times 10minus6 191 times 10minus6 317KNO
325 6 166 times 10minus1 273 times 1015 038
KOH 20 4 307 times 10minus1 846 times 1015 035K2SO4
25 12 191 times 10minus6 191 times 10minus6 072LiBr 30 4 640 times 10minus1 999 times 10minus2 034LiCl 25 7 470 times 10minus1 131 times 101 061LiI 18 2 654 times 10minus1 131 times 100 299 times 10minus6
LiOH 20 4 128 times 10minus1 596 times 1014 040Li2SO4
18 2 436 times 10minus1 357 times 10minus2 015MgCl
220 12 728 times 10minus1 250 times 10minus1 113
MgSO4
10 12 831 times 10minus1 543 times 10minus3 075MnCl
218 6 644 times 10minus1 720 times 10minus3 023
NH4Cl 25 6 290 times 10minus1 568 times 1014 010
NH4NO3
20 9 520 times 10minus1 642 times 10minus2 032(NH4)2SO4
30 4 577 times 10minus1 608 times 100 048NaBr 20 4 485 times 10minus1 177 times 10minus2 021NaCHO
230 12 371 times 10minus1 186 times 1016 029
NaC2H3O2
30 12 112 times 100 204 times 1016 104NaC3H5O2
30 12 191 times 100 127 times 1018 026NaC4H7O2
30 12 328 times 100 194 times 1016 077NaCl 20 9 222 times 10minus1 205 times 1016 066NaClO
315 2 138 times 100 431 times 10minus1 003
NaClO4
25 3 861 times 10minus1 216 times 1016 017Na2CrO4
30 4 423 times 10minus1 159 times 10minus2 027NaI 25 8 615 times 10minus1 907 times 1014 016NaNO
320 4 259 times 10minus1 116 times 1015 021
NaOH 18 6 347 times 10minus1 246 times 10minus3 046Na2SO4
30 3 150 times 10minus1 563 times 1017 022Na2S2O3
40 4 448 times 10minus1 900 times 10minus3 021
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
6 Journal of Thermodynamics
Table 1 The optimized values for adjustable parameters (119870lowast 119870) of competitive adsorption model Experimental data are from [10]
System 119879 (∘C) 119873119901
119870lowast
119870 AADAgNO
320 4 699 times 10minus2 616 times 1014 023
Al2(SO4)3
30 12 895 times 10minus1 393 times 1022 046BaCl2
30 5 0 453 times 104 061CaCl2
30 11 660 times 10minus1 427 times 104 081CdCl2
20 5 734 times 10minus1 219 times 101 008CdSO
420 2 747 times 10minus1 362 times 10minus2 915 times 10minus7
CoCl2
20 2 620 times 10minus1 751 times 10minus5 105 times 10minus4
CsCl 25 15 130 times 10minus1 165 times 1016 043CsI 25 11 191 times 10minus6 191 times 10minus6 045CuSO
430 3 783 times 10minus1 564 times 1014 022
HBr 18 2 109 times 100 186 times 1016 007HCl 20 7 105 times 100 153 times 101 094HClO
425 10 106 times 100 286 times 1014 213
HNO3
20 7 142 times 100 603 times 1014 238KBr 20 5 236 times 10minus1 602 times 1014 021KC2H3O2
30 3 114 times 100 927 times 10minus2 040KCNS 25 12 936 times 10minus1 471 times 100 034KCl 20 10 107 times 10minus1 196 times 1016 033K2CrO4
30 15 249 times 10minus1 114 times 1018 035K3Fe(CN)
625 16 191 times 10minus6 191 times 10minus6 067
KI 25 12 191 times 10minus6 191 times 10minus6 317KNO
325 6 166 times 10minus1 273 times 1015 038
KOH 20 4 307 times 10minus1 846 times 1015 035K2SO4
25 12 191 times 10minus6 191 times 10minus6 072LiBr 30 4 640 times 10minus1 999 times 10minus2 034LiCl 25 7 470 times 10minus1 131 times 101 061LiI 18 2 654 times 10minus1 131 times 100 299 times 10minus6
LiOH 20 4 128 times 10minus1 596 times 1014 040Li2SO4
18 2 436 times 10minus1 357 times 10minus2 015MgCl
220 12 728 times 10minus1 250 times 10minus1 113
MgSO4
10 12 831 times 10minus1 543 times 10minus3 075MnCl
218 6 644 times 10minus1 720 times 10minus3 023
NH4Cl 25 6 290 times 10minus1 568 times 1014 010
NH4NO3
20 9 520 times 10minus1 642 times 10minus2 032(NH4)2SO4
30 4 577 times 10minus1 608 times 100 048NaBr 20 4 485 times 10minus1 177 times 10minus2 021NaCHO
230 12 371 times 10minus1 186 times 1016 029
NaC2H3O2
30 12 112 times 100 204 times 1016 104NaC3H5O2
30 12 191 times 100 127 times 1018 026NaC4H7O2
30 12 328 times 100 194 times 1016 077NaCl 20 9 222 times 10minus1 205 times 1016 066NaClO
315 2 138 times 100 431 times 10minus1 003
NaClO4
25 3 861 times 10minus1 216 times 1016 017Na2CrO4
30 4 423 times 10minus1 159 times 10minus2 027NaI 25 8 615 times 10minus1 907 times 1014 016NaNO
320 4 259 times 10minus1 116 times 1015 021
NaOH 18 6 347 times 10minus1 246 times 10minus3 046Na2SO4
30 3 150 times 10minus1 563 times 1017 022Na2S2O3
40 4 448 times 10minus1 900 times 10minus3 021
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Journal of Thermodynamics 7
Table 1 Continued
System 119879 (∘C) 119873119901
119870lowast
119870 AADNiSO
415 2 714 times 10minus1 860 times 10minus2 175 times 10minus7
Pb(NO3)2
20 3 191 times 10minus6 191 times 10minus6 377RbCl 25 11 194 times 10minus1 965 times 1015 036SrCl2
20 9 595 times 10minus1 441 times 10minus3 049Sr(NO
3)2
18 8 339 times 10minus1 814 times 1014 050UO2SO4
30 12 870 times 10minus1 123 times 101 032Zn(NO
3)2
40 5 767 times 10minus1 127 times 10minus1 037Overall 404 055
Table 2The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorption model for binarysystems Experimental data are from [10]
System 119879 (∘C) Molality 119873119901
AADAgNO
3100 103ndash1316 10 381
BaCl2
10ndash80 001ndash596 51 110CaCl2
10ndash100 01ndash737 122 138CsCl 20ndash30 006ndash888 28 052CuSO
410ndash80 033ndash111 21 212
HCl 25ndash90 03ndash3 18 382HClO
415ndash50 051ndash2592 23 256
HNO3
30ndash80 155ndash4686 66 371KBr 10ndash90 044ndash56 40 115KC2H3O2
0ndash80 05ndash2378 36 482KCl 25ndash80 071ndash516 56 103K3Fe(CN)
61235ndash208 029ndash062 4 076
KI 20ndash60 001ndash012 55 445KNO
318ndash100 01ndash263 27 128
KOH 30ndash95 477ndash1328 22 439LiBr 10ndash90 128ndash1727 48 152LiCl 10ndash90 119ndash1573 79 197MgCl
210ndash70 055ndash35 23 290
NH4Cl 19ndash60 102ndash721 39 101
NH4NO3
40ndash95 061ndash2943 29 121(NH4)2SO4
18ndash95 07ndash561 33 207NaBr 10ndash90 00007ndash648 58 314NaC2H3O2
0ndash25 050 6 094NaC4H7O2
0ndash50 050 10 163NaCl 10ndash200 071ndash942 81 173NaI 20ndash50 033ndash881 32 089NaNO
318ndash100 102ndash1177 42 159
NaOH 20ndash70 049ndash625 26 130Na2SO4
10ndash1934 02ndash124 62 287RbCl 20ndash30 011ndash693 22 059SrCl2
10ndash25 048ndash192 7 124UO2SO4
20ndash75 018ndash234 48 081Zn(NO
3)2
21 262 1 110Overall 1215 198
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
8 Journal of Thermodynamics
Table 3The absolute average deviation percent (AAD) in prediction of surface tension using the competitive adsorptionmodel for ternarysystems Experimental data are from [10]
Ternary system 1198981
1198982
119879 (∘C) 119873119901
AADBaCl2-HCl 045ndash113 010 25 3 047
CaCl2-HCl 037ndash148 010 25 4 192
LiCl-HCl 055ndash488 010 25 5 223SrCl2-HCl 048ndash192 010 25 4 113
KBr-KCl 035ndash208 034ndash189 18 10 065KBr-NaBr 044ndash357 051ndash42 101ndash908 45 259KNO
3-NH4NO3
052ndash243 012ndash1954 18ndash30 143 693KNO
3-Pb(NO
3)2
0-1 0-1 20 33 266KNO
3-Sr(NO
3)2
023ndash13 019ndash117 18 10 092NH4Cl-(NH
4)2SO4
051ndash286 033ndash204 18 10 063NH4NO3-Pb(NO
3)2
033 0ndash0333 35 6 207NaNO
3-Sr(NO
3)2
071ndash348 025ndash117 18 9 124NaClO
4-HCl 05ndash134 010 25 3 070
KNO3-NH4Cl 023ndash13 049ndash286 18 10 106
NH4Cl-Sr(NO
3)2
051ndash286 019ndash117 18 10 091(NH4)2SO4-NaNO
3033ndash204 056ndash347 18 9 103
Average 314 170
References
[1] Z Li Y Li and J Lu ldquoSurface tension model for concentratedelectrolyte aqueous solutions by the pitzer equationrdquo Industrialamp Engineering Chemistry Research vol 38 no 3 pp 1133ndash11391999
[2] K Ariyama ldquoA theory of surface tension of aqueous solutionsof inorganic acidsrdquo Bulletin of the Chemical Society of Japan vol12 no 3 pp 109ndash113 1937
[3] P B Lorenz ldquoThe specific adsorption isotherms of thiocyanateand hydrogen ions at the free surface of aqueous solutionsrdquoJournal of Physical and Colloid Chemistry vol 54 no 5 pp 685ndash690 1950
[4] T F Young and S R Grinstead ldquoThe surface tensions of aque-ous sulfuric acid solutionsrdquo Annals of the New York Academy ofSciences vol 51 pp 765ndash780 1949
[5] V G Gleim and I K Shelomov ldquoCalculation of surfacetension of aqueous salt systemsrdquoThe Russian Journal of AppliedChemistry vol 30 pp 29ndash35 1957
[6] S Oka ldquoAdsorption and surface tension of strong electrolytesrdquoProceedings of the Physico-Mathematical Society of Japan vol 14pp 649ndash664 1932
[7] A LHorvathAqueous Electrolyte Solutions Physical PropertiesEstimation and Correlation Methods Halsted Press ChichesterUK 1985
[8] L Onsager andN N T Samaras ldquoThe surface tension of debye-huckel electrolytesrdquoThe Journal of Chemical Physics vol 2 no8 pp 528ndash536 1934
[9] E Schmutzer ldquoIons at liquidair and liquidliquid interfacesrdquoZeitschrift fur Physikalische Chemie vol 204 pp 131ndash156 1955
[10] A A Abramzon and R D Gaukhberg ldquoSurface tension of saltsolutionsrdquo Russian Journal of Applied Chemistry vol 66 no 6ndash9 pp 1428ndash2156 1993 (Russian)
[11] Y Yu G Gao and Y Li ldquoSurface tension for aqueous electrolytesolutions by themodifiedmean spherical approximationrdquo FluidPhase Equilibria vol 173 no 1 pp 23ndash28 2000
[12] Z Li and B C Lu ldquoSurface tension of aqueous electrolyte solu-tions at high concentrationsmdashrepresentation and predictionrdquoChemical Engineering Science vol 56 no 8 pp 2879ndash28882001
[13] M Sadeghi V Taghikhani and C Ghotbi ldquoApplication ofthe MSA-based models in correlating the surface tension forsingle and mixed electrolyte solutionsrdquo Journal of ChemicalThermodynamics vol 41 no 11 pp 1264ndash1271 2009
[14] L L LeeMolecularThermodynamics of Nonideal Fluids Butter-worth Publishers 1988
[15] C Ghotbi and J H Vera ldquoExtension to mixtures of two robusthard-sphere equations of state satisfying the ordered close-packed limitrdquo The Canadian Journal of Chemical Engineeringvol 79 no 4 pp 678ndash686 2001
[16] G AMansoori N F Carnahan K E Starling and TW LelandJr ldquoEquilibrium thermodynamic properties of the mixture ofhard spheresrdquo The Journal of Chemical Physics vol 54 no 4pp 1523ndash1526 1971
[17] C-C Chen and L B Evans ldquoLocal composition model forthe excess gibbs energy of aqueous electrolyte systemsrdquo AIChEJournal vol 32 no 3 pp 444ndash454 1986
[18] F B Sprow and J M Prausnitz ldquoSurface thermodynamics ofliquidmixturesrdquoTheCanadian Journal of Chemical Engineeringvol 45 no 1 pp 25ndash28 1967
[19] A W Adamson and A P Gast Physical Chemistry of SurfacesWiley Interscience New York NY USA 3rd edition 1997
[20] I Langmuir ldquoThe adsorption of gases on plane surfaces ofglassmica and platinumrdquoThe Journal of the AmericanChemicalSociety vol 40 no 9 pp 1361ndash1403 1918
[21] C Desnoyer OMasbernat and C Gourdon ldquoPredictivemodelfor the calculation of interfacial tension in nonideal electrolyticsystemsrdquo Journal of Colloid and Interface Science vol 191 no 1pp 22ndash29 1997
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Top Related