Ind. Eng. Chem. Fundam. 1981, 20, 89-94

Diffusivities of Gases in Aqueous Electrolyte Solutions

Kiyomi Akita

Department of Chemical Engineering, Tokushima University, Tokushima, 770, Japan

Diffusivities of oxygen in aqueous electrolyte solutions were measured, using 18 species of cations, 13 species of anions, and combinations thereof. Electrolyte concentrations were varied to near saturation and temperatures were set at 10, 20, and 40 OC. The results were correlated on the basis of the Eyring theory of rate processes. The free energy of activation of oxygen in a solution is assumed to consist of the sum of contributions due to various chemical species in the solution. The variations of the free energy with temperature for different diffusing solutes are discussed. With the results of this work, prediction of the diffusivities of gases in aqueous electrolyte solutions is possible, if gas diffusivities in pure water and the densities of the solutions are available.

Introduction Diffusivities of gases dissolved in aqueous electrolyte

solutions are necessary for the chemical engineer in the design and the analysis of gas absorption equipment using electrolyte solutions.

Podolsky (1958) proposed a perturbation model and applied it to diffusion processes in electrolyte solutions. He assumed that in such solutions the free energy of ac- tivation for one mole of diffusing particles in pure water, AGw*, was perturbed by the amount Gi, when a water molecule adjoining a diffusing particle was replaced by a single ith ion. In a solution in which the mole fraction of the ith ion is x i , AGw* is perturbed on the average by the amount Ginxi due to the ith ion alone so that the total contribution by all the ions is ZGinxi, where n is the number of solvent molecules surrounding a diffusing particle. Therefore, the free energy of activation for one mole of diffusing particles in the solution is given by

(1)

According to Podolsky, 6i is proportional to the viscosity B coefficient of Jones and Dole (1929).

Ratcliff and Holdcroft (1963) determined diffusivities of carbon dioxide in various liquids at 25 "C by measuring absorption rates of the gas into liquids flowing over spheres. Six species of electrolyte involving Na+, Mg2+, C1-, NO<, and Sodz- were employed in their work. They proposed two different methods for the prediction of diffusivities. One is based on the Podolsky perturbation model, the other on a power relationship between diffu- sivity and fluidity.

McCall and Douglas (1965) measured self-diffusivities of water in aqueous electrolyte solutions by the method of nuclear magnetic resonance. As many as 29 species of electrolyte were employed in their work. A concentration dependence parameter for the self-diffusivity of water, AD = (Dw - D1)/Dw, was calculated, where Dw and D , are the diffusivities in pure water and in 1 M solution, respectively. The value of AD for an electrolyte solution was assumed to be the sum of ionic values, A+ for the cation and A for the anion in the solution. Values of A+ and A for various ions were evaluated and tabulated.

Gubbins et al. (1966) used a diaphragm cell to measure diffusivities of hydrogen and of methane in aqueous so- lution of potassium chloride, magnesium chloride, and magnesium sulfate at 25,45, and 65 "C. They calculated perturbation terms based on the Podolsky model for each ionic species. These terms were found to be independent of species of solute gas.

AG* = AGw* + nZGixi

Hung and Dinius (1972) also used a diaphragm cell to measure diffusivities of oxygen a t 25 "C in six sorts of aqueous solutions of sodium salts including three organic ones. The results were correlated by DIDw = 1 - k(Ce)1/2, and the coefficient k was found to be related with the viscosity B coefficient of Jones and Dole (1929). Theory

According to the Eyring theory (Glasstone et al., 1941) of rate processes, the diffusivity of a solute is given by

where D is the diffusivity, AG* is the free energy of ac- tivation of a diffusing particle, X is the length of a step for a diffusing particle to move from one equilibrium site to another, T is absolute temperature, and K, h, and R are the Boltzmann, Planck, and gas constants, respectively. If X can be assumed equal to the size of a solvent molecule, it can be found by

(3)

where V is the molar volume of the solvent and No is the Avogadro number. Equation 3 is assumed to hold for electrolyte solutions as well as for pure solventa. The molar volume V of a solution is given by

1 V = c+ + c- + cw (4)

where C+, C-, and Cw are the molar concentrations of cation, anion, and water, respectively. The molar con- centration of water Cw can be calculated by

p - M+C+ - M-C- 0.01802 (5)

where M+ and M- are the formula weights of the cation and the anion, respectively, and p is the density of the solution. The relationship between the molar concentra- tion Ci and the mole fraction x i is

x i = vci (6) Naturally, the following relationship should hold

(7) The free energy of activation of a mole of diffusing

particles in the solution, AG*, can be expressed by a linear function of xi's as follows

AG* = CYX+ + Px- + YXW (8)

cw =

c x i = x+ + x- + xw = 1

0196-431 3/81/1020-0089$01 .OO/O 0 1981 American Chemical Society

90 Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981

@ @ O Q O

r 1 5 c m

liquid sample reservaii

lagoon

sample well

gold cathode

0 - r , n g

Teflon membrane

silver anode

epoxy resin

- 0 - i- 1 @ O-ring fa hold membrane @, ---o _,I

0 0

1 sensor cap

I -T -_--- @ cable leading to detecfor i-

o Figure 1. Oxygen diffusion cell,

where a , 0, and y are partial molar quantities and should be functions of x + , x - , and xw. Combination of eq 7 and 8 through elimination of xu' gives the following expression for 1G*

AG* = Aax+ + Apx- + 7 (9)

where ACY 5 CY - y and AD /3 - y. This is an expression similar to eq 1 derived previously by Podolsky (1958).

Substitution of eq 3 and 9 into eq 2 gives

The law of conservation of electric charge gives the fol- lowing relationship between x + and x -

x + u+ = x- u- = 2 (11)

where u+ and u- are the ionic valencies of the cation and of the anion of an electrolyte, respectively, and z (always positive) is a new variable defined by eq 11. By the change of variables from x + and x - into z with the use of eq 11, eq 10 is transformed into the following final equation

Experimental Procedure and Analysis of Data Diffusivities of oxygen were measured with the use of

the polarographic oxygen diffusion cell devised by Keller and Friedlander (1966). The diffusion cell used in the measurements is shown in Figure 1. A Beckman polaro- graphic oxygen electrode, Type 39065, was cemented with epoxy resin to a stainless steel liquid sample reservoir. A Toshiba-Beckman dissolved-oxygen analyzer, Type 777, was used as a detector. A sample solution of about 0.06 mL was placed with use of a syringe into the sample well, 4 mm in diameter and 5 mm in depth, and the liquid surface was kept as flat as possible. The well bottom was a Teflon membrane which covered the oxygen electrode. To prevent the liquid sample from evaporating, a small amount of the same sample was dropped to a filter paper which was placed at the bottom of the lagoon, 1 mm in depth, around the well. Air, as an oxygen source, was brought into contact with a solution at its free surface. The diffusion cell was kept in a glass capsule submerged in a constant temperature bath and was left for more than 3 h until a steady state had been reached. Most of the measurements were made at 20 "C and for some electrolyte solutions, 10 "C and/or 40 "C were used as well. Tem-

Figure 2. Oxygen concentration profile in a diffusion cell.

peratures were controlled within k0.5 "C. An example of oxygen concentration profiles is shown

in Figure 2. Oxygen with a partial pressure of p diffuses through a gas film to reach the as liquid interface. The

be p , because the gas-phase resistance is considered to be sufficiently small. The oxygen concentration in the liquid at the interface is CL1. From the interface, oxygen diffuses through a liquid layer of a thickness X L to the liquid- membrane interface, where the concentration of oxygen is CL2 in the liquid and Cs2 in the membrane. Then, ox- ygen diffuses farther through the solid phase of a Teflon membrane of thickness Xs to the cathode surface, where the oxygen concentration c3 is substantially zero because of the rapid rate of reduction on the surface. Since the cross-sectional areas for oxygen transfer in the liquid and in the membrane vary along the diffusion path because of the geometry of the diffusion cell, their effective values AL and As for the liquid and for the membrane must be de- termined from calibration experiments.

The diffusivities of oxygen in the liquid and in the membrane are denoted by D and by Ds, respectively. Under the steady states, the rate of oxygen transfer N is given by

oxygen partial pressure there p d - may be still assumed to

N = ( XL E ) A L ( C L 1 - CL2) = ( 2 ) A s C s 2 (13)

The concentrations of oxygen can be transformed to partial pressures as follows

p = HLcL'; pL2 = HLcL2; ps2 = HsCS2 (14)

where HL is the Henry's law constant for the gas and liquid system and Hs is the constant for the gas and membrane system.

A t the liquid-membrane interface, the partial pressure pL2 is identical with ps2. Combining eq 13 and 14 through eliminations of CL1, CL2, Cs2, and ps2, the following equa- tion is derived

This equation has two unknown terms in the denominator, i.e. (XL/AL) and ( H s / D s ) ( X s / A s ) . Two preliminary ex- periments with the air-membrane and with the water- membrane systems were carried out independently for the

Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 91

0 lithium chlorlde 0 potassium chloride 0 sodium chloride 0 cesium chloride

A magnesium chloride

A calcium Chloride A barium chloride 0 manganese chloride

nickel chloride

elimination of these two terms. With the air-membrane system, eq 15 becomes

(16) P

( H s / D s ) ( X s / A s ) NA =

With the water-membrane system

(17)

where the subscripts A and W denote air and water, re- spectively. Since the oxygen transfer rate N is proportional to the reading of the scale I attached to the detector, N , NA, and Nw in the above equations can be conveniently replaced by I , I*, and Iw, respectively. If eq 15, 16, and 17 are combined through the elimination of (XL/AL) and (Hs/Ds)(Xs/As), and Ns are replaced by I's, the following relation is obtained

P W s / D s ) ( X s / A s ) + ( H w / D w ) ( X L / A L )

Nw =

The reading I A was usually adjusted to 21 corresponding to the partial pressure of oxygen in air.

Solubility of oxygen in liquid or the Henry's law constant HL was measured as follows. Oxygen was bubbled through a liquid sample of about 200 mL under atmospheric pressure for about 1 h in a constant-temperature bath, and the oxygen concentration in the saturated liquid sample was analyzed by the chemical method of Winkler (Treadwell and Hall, 1935). If a liquid sample contained either an oxidizing or a reducing reagent, or had dark color, the amount of oxygen in the sample was determined as follows. A liquid sample of about 200 mL, saturated with oxygen, was introduced quickly into a 250-mL flask and was sealed. The liquid was stirred and was brought into contact with air in the flask for more than 3 h to reach an equilibrium. With the equilibrium partial pressure of oxygen and volumes of the gas and the liquid in the flask, the solubility of oxygen was calculated from an oxygen balance.

In order to justify these methods, diffusivity and solu- bility of oxygen in aqueous glycol solutions were measured in the same manner as stated above and results were compared with the similar data of Hayduk and Malik (1971) on carbon dioxide gas in aqueous glycol solutions. The diffusivity ratios DIDw obtained here were found to be in close agreement with those of Hayduk and Malik.

From the results, the percentage errors of the diffusivity measurements in this work were considered to be within &lo%. Densities of liquids were measured with a 10-mL Ostwald-type pycnometer and viscosities with a Canon- Fenske-type viscometer.

Electrolyte solutions were prepared from reagent grade chemicals and distilled water. The pH values of the so- lutions were not adjusted to any definite level because the amount of hydrogen ion, hydroxyl ion, or other chemical species produced by the hydrolysis of electrolyte was considered to be negligible.

A supplementary table of experimental results listing diffusivities of oxygen, viscosities, and densities of the solutions is available. (See the paragraph at the end of the paper regarding this supplementary material.) Results and Discussion

a. Correlation of Diffusivity with Viscosity. In Figure 3 the diffusivity ratios DIDw for solutions of various chlorides are plotted against the viscosity ratios ~ / p w . DW is the oxygen diffusivity in water and pw is the viscosity of water. Using these ratios, the following relationship has

A 4

Figure 3. Logarithmic plot of DIDw vs. F/pw for chloride solutions.

5 t 1

0.8 i8 0 0.02 0.04 0.06 0.08

2

0.6

Figure 4. Semilogarithmic plot of diffusivity of oxygen in sodium chloride solutions at 20 O C against z .

been proposed by various authors to correlate diffusivity data.

From Figure 3, it seems difficult to assign a definite value for the exponent n in the equation. Ratcliff and Holdcroft (1963) tried to evaluate n from their data and recom- mended a single average value, 0.637, although their data showed that n varied from 0.4 to unity. A check of the data of McCall and Douglas (1965) on chloride solutions also revealed that n varied from 0.6 to unity. These suggest that some properties such as molar volumes of solvent and solute as well as viscosity should be taken into consider- ation in a better correlation. Instead of trying to make a correlation with the use of viscosity and molar volumes, a quite different method based on eq 10 is proposed here.

b. Determination of 7 for Water. In Figure 4 diffu- sivities in sodium chloride solutions are plotted against z. Since Aa, A@, and y in eq 12 are partial molar quantities, they are expected to vary with the electrolyte concentration or z. However, the figure shows that a linear relationship exists between the logarithm of diffusivity and z. This means through eq 12 that definite numerical values can be assigned to Act, A@, and y, irrespective of the value of z. Therefore, y can be evaluated from the diffusivity in pure water. Then, eq 12 becomes

From the diffusivity data presented by Akgerman and Gainer (1972), values of y were evaluated in the present work to be 13.7 kJ mol-' for oxygen, 14.3 kJ mol-' for carbon dioxide, and 13.2 kJ mol-l for methane. These values remain substantially constant in the temperature range from 10 to 60 "C. When water is a diffusing solute, y was determined as 13.5 kJ mol-' from the data by McCall and Douglas (1965).

92 Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981

Table I. Values of Act and Ap for Ions in Aqueous Solution

~ I-.. L ~...~ ~ . . 30 c. r, "n L _

A 3 5 , ~ , 1 0 1

Figure 5. Temperature independence of relationship between log (D/Da)(V/l'w)~2'3 and z / R T .

4i- ~ ~. . . . - ~ ..- ~-~ ' r~~ -~ -;

i i I 3 corbw 3io*lJe , 25°C , Rorcilff 8 Holdcroft

' water , 23°C , M c C i l l €3 Dour j 'os 2 . j 0 nefqune 25 'C , 'Gubblrs e! 0'

, E - _ - _ _ _ L L I

15 20 3 0 40 50 60 70

( z / ? T l X O6 , J mol

Figure 6. Independence of (D/Du)(V,' V,) on diffusing solutes.

c. Temperature Independence of Aa and AB. Di- vision of eq 12 by 20 leads to

Values of the left-hand side in eq 21 for sodium chloride solutions are plotted against z /RT on semilogarithmic coordinates in Figure 5. Although the measurements were carried out a t 10,20, and 40 "C, the results are correlated by a single straight line. This means that Aa/u+ + AP/u- in eq 21 does not vary with temperature. Since (Y and 6 as well as y are the partial molar free energies of activation and y remains constant in the temperature range of 10 to 60 "C, as stated in the preceding section, it may be ex- pected that both a and /3 and accordingly Aa and AP are independent of temperature.

d. Independence of Aa and AB on Diffusing Solute. Figure 6 shows the data on magnesium chloride solutions by other investigators as well as those obtained in the present work plotted in the same manner as in Figure 5. The data of various investigators differ in temperature and species of diffusing solute. The data of McCall and Douglas (1965) give the self-diffusivity of water a t 23 "C . The data of Ratcliff and Holdcroft (1963) are for carbon dioxide a t 25 "C and those by Gubbins et al. (1966) are for methane at 25 "C. All the data could be correlated by a single straight line. This shows that Aa/u+ + AP/u- does not vary with the species of diffusing solute.

This conclusion can also be obtained from considerations of various equations which correlate diffusivities in no- nelectrolyte solutions. In the diffusivity ratio DIDw cal- culated from the equations of Stokes and Einstein (Reid et al., 19771, of Wilke and Chang (1955), of Reddy and Doraiswamy (19671, and of Sridhar and Potter (1977), no properties of diffusing solute are involved. The ratio calculated from the equations of Scheibel (1954) and of Lusis and Ratcliff (1968) appears to be affected by the molar volume of diffusing solute. However, the effect is found to b~ negligibly small, hecause the difference be-

radii, Acu, radii, AP, cations nm Jmol - I anions nm Jmol- ' H' Li +

Na' K' cs +

MgZ +

Ca zt Sr2+ BaZ Cr3+ Mnzt COZ' Niz+ c u z + Zn2+ Cd2 +

A l 3 +

Pb2+ NH-+

. . . 0.068 0.100 0.133 0.168 0.068 0.099 0.116 0.134 0.058 0.080 0.071 0.067

0.070 0.097 0.050 0.121 0.144

. . .

100

7- 50

? 7 1

'11

u o

a

L 0

8

- 50

10 200 7 120

10 000 -4 190 -6 570 31 000 1 6 800 16 800 1 2 0 0 0 49 000 27 000 1 6 700 30 600 27 000 26 300 29 100 65 900 23 700

628

F- 0.133 c1- 0.182 Br- 0.198 I' 0.220 OH - 0.140 NO3- 0.189 CNS- . . .

C10,- 0.23 6 CO, '- 0.185 SO, 2- 0.230 CrO, '- 0.240 PO, 3 - 0.238

c10,- 0.200

-8 120 -1 050 -4 000 -7 870 3 810

0 -5 440 -7 950 -4 230 20 900 1 2 700

3 520 28 100

Pb" Cd2+ 'N i" AI^+ ' I

I 1 I 5 10 15

Y + / ( r + t rw) or p-/(r-+ rw) , nm-'

Figure 7. Relationship between Acr and u+/(r+ + rw) or between A@ and u./(r- + rwi.

tween the molar volumes of water and of the electrolyte solution is small.

e. Determination of A a a n d AP. From the slope of the straight line in Figure 5 or 6 , the value of Act/u+ + AP/u- can be determined. Since the term is a composite one, it should be separable into its components charac- teristic of each ionic species, Aa and A@. Unfortunately, however, the number of these composite terms obtained here is less by one than the number of components. In other words, we have a system of N - 1 linear equations in N unknowns. Thus, another relationship must be as- sumed to complete the system. Although the relationship between Aa and Ap may be assumed quite arbitrarily, it would be convenient, if it were chosen so as to get a single curve when Aa and Ab are plotted separately against some ionic property. As a first approximation, Aa for potassium ion was taken to be equal to Ab for chloride ion. When the values of Act and A@ for other ionic species thus de- termined were plotted against u+/(rw + r+) and u-/(rw + r-) , respectively, two separate curves were obtained for A a and AD. Here, r+, r-, and rw are radii of cation, anion, and water molecule, respectively.

In order to unite the two curves, Ab for nitrate ion was assumed to be zero. With this value, Act and AD for other ionic species were determined as given in Table I. In finding the value for hydrogen ion, however, the data of McCall and Douglas (1965) were used. The ionic radii in the table were taken from the book by Johnson (1968).

Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 93

by eq 22a and 22b (method 11). The value of y for oxygen used for the estimation was 13.7 kJ mol-'. the estimated and observed values at 20 O C for the solutions prepared here are listed in Table 11. Any superiority of one method over the other cannot be established. However, if Acti+ or A& values are found in Table I, preference should be given to method I over method 11. Conclusions

The results of the measurements of oxygen diffusivities in various aqueous electrolyte solutions were discussed on the basis of the Eyring theory of rate processes. The free energy of activation of oxygen in a solution, AG*, is as- sumed to consist of its component energies a, p, and y, characteristic of each chemical species in the solution. The values of Aa = a - y and Aj3 = /3 - y in eq 10 can be obtained either from Table I or by eq 22a and 22b. The temperature dependence of Aa, A@, and y can be neglected within the range of 10 to 60 "C. Furthermore, A a and A0 do not vary with species of diffusing solute. If the diffu- sivities in pure water and the densities of the solutions are known, the diffusivities of gases in aqueous electrolyte solutions can be predicted by eq 10 or 26. Acknowledgment

The author is grateful to Professor Fumitake Yoshida for helpful suggestions and criticisms. Assistance of Hi- deaki Inoue and Toshiyuki Hirai in the experimental work is appreciated. Nomenclature AL, As = effective cross-sectional areas for diffusion in liquid

C, = concentration of electrolyte, mol m-3 Ci = concentration of ith species, mol m-3 Ci+, Cj- = concentrations of ith cation and of jth anion, re-

spectively, mol m-3 CL*, CL2 = concentrations of oxygen in liquid phase at

boundary 1 and at boundary 2, respectively, mol m-3 Cs2 = concentration of oxygen in membrane at boundary 2,

mol m-3 Cw = concentration of water, mol m9 C+, C- = concentrations of cation and of anion, respectively,

mol m-3 D = diffusivity, m2 s-l D1 = diffusivity in 1 M electrolyte solution, m2 s-' Ds, Dw = diffusivities in membrane and in water, respectively,

m2 s-l HL, Hs, Hw = Henry's law constants for gas-liquid, for gas-

membrane, and for gas-water systems, respectively, Pa m3 mol-l

h = Planck's constant, 6.626 X I = reading of scale IA, Iw = readings of scale, when air and water, respectively,

k = constant in the equation of Hung and Dinius, m1.5 moP6 M+, M- = formula weights of cation and of anion, respectively,

Mi+, Mi- = formula weights of ith cation and of jth anion,

N = rate of oxygen transfer, mol s-', or number of equations

NA, N w = rates of oxygen transfer through air and through

No = Avogadro's number, 6.02 X loB mol-' n = number of solvent molecules surrounding a diffusing

p = partial pressure of oxygen in gas phase, Pa pcl =gartial pressure of oxygen at boundary 1, Pa pL2, p = partial pressures of oxygen defined by eq 14, Pa R = gas constant, 8.314 J K-' mol-' rw, r+, r- = radii of water molecule, of cation, and of anion,

and in membrane, respectively, m2

J s

are used as samples

kg mol-'

respectively, kg mol-'

consisting a set of simultaneous equations

water, respectively, mol s-l

solute molecule

respectively, m

Table 11 estimated values

by by method I method I1 obsd values,

solutions mz s-l mz s-l m2 s-I A 1.76 1.68 1.55 B 1.46 1.34 1.18 C 1.62 1.62 1.65 D 1.24 1.23 1.28

In Figure 7 A a and A@, given in Table I, are plotted against v+/(rw + r+) and v-/(rw + r-), respectively; v+/(rw + r+) is a quantity which is proportional to the amount of work for a water molecule to be brought from infinity to the surface of a cation. The statement holds also for the other quantity v-/(rw + r-). These quantities are re- lated to the hydration number of ion, and the larger the former, the larger the latter. The lines in the figure are represented by the equations

( 2 2 4 v+

A a = 5000 - 18000 io9(rw + r+)

V- Ap = 5000 - 18000 (22b)

109(rw + r-)

f. Prediction of Diffusivities in Aqueous Electro- lyte Solutions. Estimation of the diffusivities in aqueous solutions containing only one species of electrolyte would be possible, if eq 10 is used with the values of A a and A0 obtained either from Table I or from eq 22a and 22b. All the data of Ratcliff and Holdcroft (1963) were taken as illustrations and were compared with the values estimated by eq 10 and Table I. The percentage deviations of the estimated values from their data were within f13% except that +25% deviation was noticed for the 0.969 M mag- nesium sulfate solution.

This method can be extended to solutions containing more than two species of electrolyte. For such solutions, equations for V, Cw, and AG* must be somewhat modified. Equations 4, 5, and 9 are extended as follows

1 V = x i + + ccj- + c w (23)

where subscript i+ indicates the ith cation and subscript j - the j t h anion. Equation 10 can be written as

To test the method, the following four solutions of mixed nitrates were prepared at 20 OC: (A) 1 M cobaltous nitrate + 0.5 M strontium nitrate; (B) 2 M cobaltous nitrate + 1 M strontium nitrate; (C) 0.5 M cobaltous nitrate + 0.25 M strontium nitrate + 0.5 M calcium nitrate + 0.5 M magnesium nitrate; (D) 1 M cobaltous nitrate + 0.5 M strontium nitrate + 1 M calcium nitrate + 1 M magnesium nitrate. The molarities of solutions B and D are twice those of solutions A and C, respectively. The densities of the solutions were 1219.5 kg m-3 for A, 1434.4 kg m-3 for B, 1219.4 kg m-3 for C, and 1424.0 kg m-3 for D.

The values of Aai+ and A@,- were obtained in two dif- ferent ways: one from Table I (method I) and the other

94 Ind. Eng. Chem. Fundam. 1901, 20, 94-96

T = absolute temperature, K V = molar volume of solution given by eq 4, m3 mol-' Vw = molar volume of water, m3 mol-' XL, Xs = lengths of diffusion path in liquid and in membrane,

x , = mole fraction of ith species x,+, x,- = mole fractions of ith cation and of jth anion, re-

xw = mole fraction of water x + , x_ = mole fractions of cation and of anion, respectively z = variable defined by eq 11

Greek Let ters a, p, 7 = components of free energy of activation of diffusing

solute due to cation, to anion and to water, respectively, J mol-'

AG*, AGw* = free energies of activation of diffusing solute in electrolyte solution and in water, respectively, J mol-'

AD = concentration dependence parameter for diffusivity defined by AD = (Dw - D,)/Dw

A+, A- = components of AD due to cation and anion, respec- tively

La, A0 = values defined by La B - 1 , respectively, J mol-'

LaI+, &3,- = values of Acv for ith cation and for jth anion, respectively, J mol

6, = perturbation of free energy of activation of diffusing solute when a water molecule adjoining a diffusing solute are replaced by an ith ion, J mol-'

K = Boltzmann's constant, 1.381 X X = length of a step for a diffusing particle to move from one

equilibrium site to another, m

respectively, m

spectively

a - y and A13

J K

COMMUNICATIONS

g, gw = viscosities of solution and of water, respectively, Pa

LJ+, Y- = ionic valencies of cation and of anion, respectively p = density of solution, kg m-3 Li terature Cited Akgerman, A,; Gainer, J. L. J. Chem. Eng. Data 1972, 77, 372. Glasstone, S.; Laidler, K. J.; Eyring, H. "The Theory of Rate Processes",

McGraw-Hill: New York, 1941; Chapter 9, p 524. Gubbins, K. E.: Bhatia, K. K.; Walker, R . D., Jr. AIChE J. 1966, 12, 548. Hayduk, W.; Malik, V. K. J. Chem. Eng. Data 1971, 16, 143. Hung, G. W.: Dinius, R. H. J. Chem. Eng. Data, 1972, 17, 449. Johnson, D. A. "Some Thermodynamic Aspects of Inorganic Chemistry",

Jones, G.; Dole, M. J. Am. Chem. Soc. 1929, 51, 2950. Keller, K. H.; Friedlander, S. K. J. Gen. Physlol. 1966, 49, 663. Lusis, M. A.; Ratcliff, G. A. Can. J. Chem. Eng. 1968, 46, 385. McCall, D. W.; Douglas, D. C. J. Phy. Chem. 1965, 69, 2001. Podolsky, R. J. J. Am. Chem. SOC. 1958, 80, 4442. Ratcliff, G. A,; Holdcroft, J. G. Trans. Inst. Chem. Eng. 1963, 41, 315. Reddy, K . A.; Doraiswamy, L. K. Ind. Eng. Chem. Fundam. 1967, 6 , 77. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. "The Properties of Gases and

Schelbel, E. G. Ind. Eng. Chem. 1954, 46, 2007. Sridhar, T.; Potter, 0. E. AIChE J . 1977, 23, 590. Treadwell, F. P.; Hall, W. T, "Analytical Chemistry", Vol. 2, Part 3, Wiley:

Wilke, C. R., Chang, P. AICbE J. 1955, 7 , 264.

S

Cambridge University Press, England, 1968; Chapter 2, pp 37, 41.

Liquids", 3rd ed.; McGraw-Hill: New York, 1977; Chapter 11, p 567.

New York, 1935; p 704.

Received for review January 22, 1980 Resubmitted October 31, 1980

Accepted October 31, 1980

Supplementary Material Available: The experimental results on diffusivities of oxygen, viscosities, and densities of aqueous electrolyte solutions (11 pages). Ordering information is given on any current masthead page.

Hydrogenolysis of Organic Substances by Carbon Monoxide-Water Mixture. Examination of Hydrogenolysis of Diphenylmethane on the Various Catalysts

Hydrogenolysis of diphenylmethane with CO-H,O mixtures was examined on various catalysts in a batch-autoclave at 400 OC. Alumina-supported molybdenum oxide and tungsten oxide catalysts were found to exhibit the highest activities among the various catalysts examined for this reaction.

Introduction Considerable attention has been paid recently to hy-

drogenolysis of organic substances by carbon monoxide- water mixtures. Appell et al. (1968 and 1977), Fu and Illing (1976), and Appell and Pantages (1976) applied this pro- cess to lignite, bituminous coal, and carbohydrates, re- spectively. Appell et al. (1969) reported that sodium carbonate, iron sulfide, and mineral matter contained in lignite were effective as catalysts for the liquefaction of lignite. Jones et al. (1978) and Stenberg et al. (1978) have already studied, using sodium carbonate, sodium hydrox- ide, and iron sulfide, the reduction of various coal-related model compounds. However, their reaction temperatures were comparatively higher. The reactions of the model compounds, therefore, seemed to be similar to thermolysis; nevertheless, the reactions of some compounds, such as diphenylmethane, did not give sufficient conversions for the detailed discussion of the reaction mechanism. Fur- thermore, there have been no systematic studies on the

catalyst available for this hydrogenolysis process, and the function of the catalyst has not been clarified sufficiently. In the present work, hydrogenolysis of diphenylmethane is performed on the various catalysts with a view to finding the catalysts suitable for this hydrogenolysis process. Experimental Section

Batch-Autoclave Experiment. All the reactions were carried out in a 146-mL magnetically stirred stainless steel apparatus (SUS-316) at 400 "C for 60 min of nominal reaction time. For most runs, 1 2 mmol of diphenyl- methane, 250 mmol of water, and 2 g of catalyst were charged to the cold autoclave; 225 mmol of carbon mon- oxide was added and then the autoclave was heated; 65-70 min was needed to reach 400 "C. In some runs, 2 g of potassium carbonate or sodium carbonate was used in place of the catalyst. Otherwise, the experiments using nitrogen as an inert gas in place of carbon monoxide was also performed. After the reaction, the autoclave was cooled and then the gas volume was measured. Organic

0196-4313/81/1020-0094$01.00/0 0 1981 American Chemical Society