Talama. Vol. 27, pp. 95 to 100 0039-9140/80/0201-0095502.00/0 © Pergamon Press Ltd 1980. Printed in Great Britain

ON THE C O M P L E X - F O R M A T I O N BETWEEN Cd(II) AND EDTA

MOHAMMAD JAWAID* Department of Analytical Chemistry, The Royal Institute of Technology,

100 44 Stockholm, Sweden

(Received 28 May 1975. Acepted 28 August 1979)

Sumnmry--The complex-formation between cadmium and EDTA has been studied at 25 ° in 1.0M sodium nitrate medium, by measuring with a glass electrode the hydrogen-ion concentrations of a series of solutions containing varying amounts of cadmium and EDTA, and the free concentration of cadmium with a cadmium-amalgam electrode. The experimental data, which were analysed by using the ETITR version of the general error-minimizing computer program LETAGROP, may be explained satisfactorily by assuming the formation of the species CdU CdHL, CdH2L and Cd2L in the pH range 1.8-6.5. The equilibrium constants for the formation of these species are also reported.

The complex-formation between cadmium and EDTA has been studied by a number of workers using differ- ent methods, such as potentiometry, I-3 polarogra- phy, 4's liquid-liquid extraction 6 and electrophoresis. 7 Some of these methods and the values of the equilib- rium constants thus obtained have been reviewed critically by Anderegg. s A survey of the literature, however, reveals that no polynuclear C d - E D T A com- plexes have been reported so far, although from struc- tural considerations the formation of such species is not unexpected. Indeed, in the electrophoresis study of the complexation of cadmium and zinc with EDTA, 7 the experimental data seem to indicate the formation of a binuclear species when an excess of cadmium is present.

The present work was undertaken when we obtained some results of biochemical significance 9 in our experiments on the influence of different Cd- EDTA complexes on the toxicity and distribution of cadmium in mice. These results gave rise to a sus- picion that the equilibrium data so far reported in the literature might be incomplete, thus demanding a thorough investigation of the possibility of formation of a binuclear complex, especially at higher cadmium concentrations. Furthermore, in view of the fact that in chelation therapy EDTA is one of the few complex- ing agents that are administered to remove the heavy metals from biological tissues, 1° we believe that an equilibrium analysis of solutions, covering a wide range of the total concentrations of metal ion, EDTA and hydrogen ion in order to establish the presence of all probable species, and the equilibrium data on their formation, can provide useful information not only to analytical chemists but also to biologists and ecolo- gists.

E X P E R I M E N T A L

Reagents Cadmium nitrate was prepared by dissolving the pure

metal in nitric acid, and recrystallized. A solution prepared from the recrystallized salt was standardized with EDTA

* Present address: Department of Environmental Hygiene, Swedish Environmental Protection Board, 104 01 Stockholm, Sweden.

TAL. 27/2--n 95

at pH 10 (ammonia-ammonium nitrate buffer; Eriochrome Black T indicator). Solutions of the disodium or trisodium salt of EDTA were prepared from the free acid by appro- priate neutralization, and then standardized with lead nitrate solution at pH 5 (hexamine buffer; Methylthymol Blue indicator). Carbonate-free sodium hydroxide It was standardized potentiometrically by the Gran method as modified by Pehrsson et al. t2 Sodium nitrate (Merck p.a.) was recrystallized before use. Doubly distilled and freshly boiled water was used to prepare all the solutions.

Apparatus

The titrations were performed in a covered titration ves- sel of about 200 ml capacity, with five inlets for electrodes, burette, degassing tubes etc. In titrations where the amal- gam electrode was also used, the titration vessel was re- placed by a round-bottomed flask specially designed to hold the amalgam and with provision for insertion of the electrodes, burette and degassing tubes etc.

A micro combination glass and silver-silver chloride reference electrode was used. Cadmium amalgam was pre- pared by electrolysing a cadmium solution over polaro- graphic grade mercury (Merck p.a.), using the arrangement described by Aladjoff 13. The cadmium concentration in the amalgam was about 0.1% w/w. We chose to work with this concentration because the response has been found to be faster than that obtained with higher concentrations. To check the performance of the electrode during the experi- ment, the response of two similar electrodes was measured simultaneously. The two readings always agreed within 0.1 mY.

Titrant was added with a pneumatically-operated re- agent pipette (AGA, LidingiS, Sweden) that can be adjusted to deliver any volume between 0.1 and 5 ml with a high degree of reproducibility. The e.m.f, values were measured to 0.1 mV with a digital voltmeter.

The temperature of the titration vessel was kept at 25 + 0.05 ° by means of a paraffin oil-bath. All measure- ments were made in a room maintained at approximately 25 ~.

The solutions were protected from atmospheric carbon dioxide by maintaining a nitrogen atmosphere over them. The nitrogen was taken from a cylinder, passed through "Ascarite" and then saturated with water vapour by bub- bling it through 1.0M sodium nitrate.

Procedure

In the first series of titrations, with the glass electrode, the cell can be written as:

Reference Vo v ml of 1.0M Na(NO3, OH) Glass half-cell ml of 1.0M (Na, Cd, H)(NO3, L) electrode

9 6 I ~ J O H A M M A D J A W A I D

The hydrogen-ion concentration, i'H+], was calculated from the equation

E = E~g + q l o g [ H +] + Ej (la)

where E~)~ is the standard potential, including the reference electrode potential and the part of the junction potential that is independent of the acidity, and Q = In IO/nF = 59.157,/)7 mV at 25. El = y (jT,,~c),,,); see equation (2) for I, m and 77. The quantities E3 and j .+ in the Nernst relationship (la) were determined, as a rule, before and after each titration, as described by Pehrsson et al. t2 The Eo values before and after each titration were constant within 0.2 mV and in- was - 2 3 mV,

In the other series of titrations where the cadmium amal- gam electrode was also used. the measuring system can be represented as:

Reference! Solution h Cd(Hg) electrode

Reference! Solution [Glass electrode

where the solution had the composition 1.0M (Na, Cd. H) (NO~, LI or 1.0M (Na, Cd, Hi(NO3) depending on whether the titrant used was 1.0M Na(NO3, OH) or 1.0M Na(NO3, L).

Here. the hydrogen-ion concentration was calculated as before and the concentration of free cadmium, [Cd(ll)] was calculated according to the relationship

E = E~. + ½Q log [Cd(ll)] + E[ (lb)

C A L C U L A T I O N S A N D R E S U L T S

The experimental data from five different sets of e.m.f, t i t rat ions with glass electrode only, are plotted in Fig. 1 as Z = ( H - h ) / C c , as a function of log [H * ], where h = [H +] denotes the free concentrat ion of hydrogen ions and H is the total concentrat ion o1: protons added. Figure 2 shows the data from another set of t i trations using bo th the glass and the cad- mium-amalgam electrode, the plot being of F as a function of log [Cd(II)], where F is ( H - h)/Cc~, l o g (Ccd/[Cd(II)]) o r ( C c d - - [ C d ( I I ) ] ) / Q , and [Cd(II)] denotes the free concentrat ion of cadmium.

We assume that the following equilibrium reactions can take place in the solution in the course of titra- tion: la) protolysis of EDTA: (b) hydrolysis of cad- mium ions: (c) the reactions leading to the formation of various C d - E D T A species.

The protolysis of EDTA in 1.0M sodium nitrate medium at 2 5 was studied earlier, 74 and the protona- tion constants were evaluated by using the computer program LETAGROP. ~5 Biedermann and Ciavat ta 76 made a detailed study of the •hydrolysis of Cd(lI) in 3M sodium perchlorate in the pH range 5.0-7.5 at rather high concentrat ions (0.1-1.45M) of Cd(II). Since we worked with the pH range 1.8-6.5 and the Cd[ll) concentrat ions were much lower ( <0.08ML we considered it reasonable not to include any hydrolysed Cd(Ill species in analysing our data. This assumption was further justified when we made some HALTA- FALL 17 calculations, which did not indicate the pres- ence of any hydrolysed species under the experimental condit ions used. The following reactions are the most probable between Cd(lI), H ÷ and EDTA. Charges are omit ted for convenience.

=, ,.o --r

1",4

0.,5

i '

\ \'X

\

' \

5 ~ l "".-2

i \

• % ~ . X \ "X\ " \

\ X. x "~,

I I ~'1 ~ " I II 2 3 4. 5 6

- log r H ÷]

Fig. 1. Z = (H - h)/Cc.,, as a function of log [H+]. The curves shown represent the titration of solutions of initial composition as follows: I ( - - -} Cn = 6.23t x 10-aM. Cc'd = 2.717 x IO-~M, Ci = 3.115 x 10-~M, and Vo = 80ml;21 . . . . ) C , = 1.944 x 10-2M, Cod = 5.97,, x 10-3M, C) = 9.970 x 10-aM, and V o = 75 ml; 3( . . . . ) C. = 1.574 x 10-2M, Ccd = 7.624 x 10-aM, Ci = 7.871 x 10-3M, and Vo = 95 ml: 4 ( . . . . . ) CH = 3.98a x lO-2M, Ctd = 2.8% x 10-2M, CL = 1.994 x 10-2M, and V o = 75ml ;5 ( - -0 - . )CH = 4.98~ x lO-ZM, Cc,) = 3.621 x 10-2M C) = 2.492 x lO-ZM, and V0 = 80ml

against 0.0586M sodium hydroxide.

Cd + L ~ CdL

Cd + H + L ~ CdHL

Cd + 2H + L ~- CdH2L

C d + 3H + L ~ C d H 3 L

2Cd + L ~ Cd2L

where L denotes the fully depronated form of EDTA.

Chemical model

For the reagent components Cd, H and L we can represent the formation of different species by the general expression (Cd)t(H),.(L)., with the equilibrium constants fl~,,,., given by

fl, m. = [(Cd)7(H)=(L).] [ C d ] - ' [ H ] - ' E L ] - " (2)

None of the models in this work contains more~ than one mole of L per mole of complex. Consequently, this expression, in the following, will be simplified to

fit.. = [(CdJ~(H)m(L)] [ C d ] - ' [ H ] - r e [ L ] - 7 (2a)

The following mass-balance equations are valid

Ccd = [Cd] + Y, lfl,mECd]7[H]'[L] (3)

On the complex-formation between Cd(lI) and EDTA 97

15

Lt. LO

0.5

' i

////I /

2 / /

/ \ /1

\ . / \ •

\ / /

/ / / /

/ / / /

/ /

/ / / /

¢ / i I i I

2 3

- log [ C d ( I I ) ]

Fig. 2. F as a function of log [Cd(II)], where F = (H - h)/Cca, curve 1 ( - - - ) ; F = log (Cca/[Cd(II)]), curve 2 ( . . . . . ); F = (Ccj - [Cd(ll)])/Ct., curve 3 (-.-); [Cd(II)] is the free coricentrff, t~ri o--Vt3~//triff6ni_ TI% d-at-a plotted are from the titration of solution of initial com- position CH = 3.317 x 10-7M, Ccd = 7.239 x 10-2M, and Vo = 60 ml. The composition of the titrant was

Ca = 2.380 x 10-2M and CL = 3.190 X 10-2M.

C H ~- [H] + ~.mfl, m [Cd]+[H]m[L] (4)

C,. = [L] + Eft,,. [Cd] ' [H], . [L] (5)

where the quantities on the left-hand side of equations (3), (4) and (5) represent the total analytical concen- tration of cadmium, the total concentration of ionized or potentially ionizable hydrogen and the total con- centration of EDTA, respectively.

For potentiometric titrations the following relation- ship is applicable:

CH..,, = (CH*Vo -- Co.*V)/(Vo + v) (6)

where

CH*= the initial concentration of hydrogen ion (mole/1.)in the titration vessel;

C o n * = the concentration of sodium hydroxide (mole/L) in the titrant;

V0 = the initial volume (litres) of the solution i n the titration vessel;

v = the volume (litres) of titrant added.

Computer analysis of the data

For the given values of log [H], Ccd and CL, and a set of equilibrium constants fl,,~,, the computer pro- gram LETAGROP-ETITR ~s can calculate, for each titration point, the values of [Cd], Ca (CHo.,o) and ELI

from (3), (4) and (5), respectively. This is done by using the procedure BDTV, ' s which is also used to calcu- late CH (CH...,) from (6).

Supplied with the initial estimates of fl+,~, the pro- gram seeks the "best" values of the set of equilibrium constants, minimizing the error-square sum (typ 1, val !)

N p

U = ~ (CH .... -- C. .xp) 2 (7)

where Np is the number of experimental points avail- able.

To analyse the experimental data when the concen- tration of free cadmium, [Cd(II)], was also measured with the cadmium-amalgam electrode, another rou- tine (typ 3, val l) was used. In this case the program calculates the concentration of free cadmium [Cd(II)] not from equation (3), but from the given (V, E) data from the amalgam electrode and minimizes the same error-square sum, equation (7).

In practice the program is used to test various chemical models. The "best" model accepted is the one which gives the minimum error-square sum, Urea,, and which can explain the given data satisfactorily, within the limits of experimental error. Once the best model has been obtained, the program HALTA- FALL 1~ can be used to calculate the equilibrium con- centrations of different species.

Results

The protonation constants of EDTA that were used are given in Table 1. The sets of experimental data from the glass electrode only and from the glass and amalgam electrodes were analysed separately. Since the formation of the species CdL and CdHL is well established, and the present data show that the aver- age number of Cd(II) ions to each EDTA ion is greater than unity (Fig. 2) indicating the formation of polynuclear species at higher Cd(II) concentrations, we considered it reasonable to test the chemical models given in Table 2. The results of the calcula- tions, summarized in the table, show that model II, in which the formation of the species CdL, CdHL, CdH2L and Cd2L is assumed, gives the least error-

Table 1. The equilibrium constants log fl,,~ for the proto- lysis of EDTA in 1.0M (Na, H) (NO3, L) medium at 25 °, which minimize the error-square sum,

150

U = Y. (C. .... - c . . J 2 ; 1

the limits given correspond approximately ~+ to log L B _+ 3~(fl)]

Equilibrium reactions log [fl +_ 3a(fl)]

H + L ~ HL 9.99 _+_ 0.02 2H + L ~ H2L 16.05 _+ 0.02 3H + L ~ HaL 18.52 _+ 0.04 4H + L ~ H+L 20.42 _+ 0.06

U m i n = 11.6; a(H) = ( U m i n / N p ) 112 = 0.23.

98 MOHAMMAD JAWAID

Table 2. The equilibrium constants log film for the formation of species (Cd)t(H)m(L) in 1.0M (Na, H) (NO3, L) at 25 °, which minimize the error-square sum

Np U = 7 . ( C . ..... - C . o . , ) 2

1

N p = 120 N p = 6 0 Glass electrode only Glass + amalgam electrode

Model Equilibrium reactions log [fl _+ 3tr(fl)] U.,~,, a(H) log [fl -I- 3a(//)] U,,,, tr(H)

! Cd + L ~.~- CdL 15.52 + 0.05 2.37 0.142 15.17 -I- 0.17 8.69 0.394 Cd + H + L.~--- CdHL 18.05 -I- 0.05 17.67 -I- 0.14

Cd + 2H + L ~.~ CdH2L 19.63 +_ 0.08 18.96 max 19.24" !1 Cd + L ~ C d L 15.56 + 0.05 1.54 0.115 15.30 ___ 0.04 1.86 0.184

Cd + H + L ~-~ CdHL 18.11 + 0.05 17.87 -t- 0.02 Cd + 2H + L ~ - C d H 2 L 19.76 -I- 0.09 19.39 +__ 0.02

2Cd + L ~ C d 2 L 16.92 -I- 0.22 16.58 -I- 0.07 I1, Cd + L ~ CdL 15.47 -I- 0.01 1.57 0.114 15.30 _+ 0.14 1.86 0.184

Cd + H + L ~.~-CdHL 18.01 +__ 0.01 17.86 + 0.21 Cd + 2H + L ~ C d H 2 L 19.63 -I- 0.01 19.38 + 0.13

2Cd + L ~ C d 2 L 16.54 _ 0.01 16.54 _ 0.21

The limits given correspond approximately to log [~ + 3alfl)]. * When alfl).is >0.2fl. the maximum value ( = l o g [fl + 3a(fl)]) is given.

square sum in b o t h cases, a n d thus expla ins the ex- pe r imen ta l da t a satisfactorily. Therefore , it m a y be accepted as the " 'best" model .

F igure 3 shows the equ i l ib r ium d i s t r ibu t ion of var ious species as a func t ion of log [H +] at two dif- ferent c o n c e n t r a t i o n s of E D T A ; Fig. 4 shows the dis- t r ibu t ion as a func t ion of E D T A c o n c e n t r a t i o n at two different pH levels, pH 2 a n d pH 7.

These ca lcu la t ions are based on the equ i l ib r ium

c o n s t a n t s given in Tab le 2, model II (glass a n d amal - g a m electrodes)

DISCUSSION

T h e present work shows tha t a t h igher concen- t ra t ions , Cd( l l ) may also fo rm a b inuc lea r species,

/ "

2 I z

/ /

r

I I t /

/ • ~ 4 ; ' /

_w 5o I ',,

\ I , 2 ~ - 4 ~ ' f

2 3 4 5 6 7

- io 0 [H*]

Fig. 3. The equ i l ib r ium d is t r ibut ion o f var ious species as a funct ion of log [ H * ] . ( ) Cod = 0.05M. CL = 0.025M: ( . . . . . ) C(,,~ = 0.05M. C~ = 0.05M. (1) Cd( l l ) , (2) C d L (3) Cd2L, 14) C d H L and (5) CdH2L. The calculat ions are based on the equ i l ib r ium constants given in Tab le 2, model

1I.

c EDTA ( mole / I )

Fig. 4. The equilibrium distribution of various species as a function of the concentration of EDTA at pH = 2 ( ) and pH = 7 ( . . . . . ) (1) Cd(ll), (2) CdL, (3) Cd2L, (4) CdHL and (5) CdH2L. The calculations are based on the equilib-

rium constants given in Table 2, model II.

On the complex-formation between Cd(ll) and EDTA 99

E

.o

o

g

, . 0

8

P ~L

.o

0

o

o

o

~B

o o ~ + +

.=

o F

e , ¢-

~ z z ~ ~ ~ z z ' ~

. . . . .

o d d d d o d

i l l l l l l O

I + q l

I I I l L I I O

+ I l l

I I I L l

¢-q ¢-4 o . o .

I I I+1 ~ + 1 + 1

+ ~ - +l~.~ i~ . ° . i I +l+l+t

¢ -

.o

II

.o

II

.9

II

+

c a . .

N I II

o 4~

100 MOHAMMAD JAWAID

Cd2L with EDTA, and the mixed polyprotonated species, CdHL and CdH2L in acid solutions. A tripro- tonated species, CdHaL has also been reported, 2° which predominates in the pH range 1-2, but as the working pH in the present work was not sufficiently low, and no reliable values of K s and K6 for EDTA valid for the ionic medium used are available, we did not include this species in our calculations.

As regards the binuclear species, which to our knowledge has not previously been reported, it seems that no studies have been made where an excess of cadmium with respect to EDTA was used, probably to avoid the risk of formation of a solid phase at lower pH, or the precipitation of Cd(II) as hydroxide at higher pH.

The availability of powerful computer programs such as LETAGROP as supplements to the graphical methods (the common procedure for evaluating equi- librium constants in the earlier investigations) has made it possible to take into account most of the species that are likely to form in a solution of suitable composition. This is evident from the fact that both sets of data give comparable results.

The small difference between the two sets of results is not unusual, 2L22 and is probably due to small changes in the activity factors, arising from variations in the ionic medium. Such changes do not influence the selection of the final chemical model but they do influence the values of the equilibrium constants slightly. The difference can be minimized by making corrections for the junction potentials of various chemical species.

As a first approximation some calculations were made utilizing the technique that has been used in this institute. 23 These calculations show that the term j[Cd 2+] in equations (la) and (lb) has the largest effect because of the changing concentration of free cadmium in the course of titration. It may, however, be menti6ned that the maximum value of E~ is very small (0.2 and 0.7 mV for the glass electrode alone and glass and amalgam electrodes respectively) and the present experiments were not designed to obtain a good value for E~. Nevertheless, the results given in Table 2, model lla for the two sets of data seem to be in closer agreement after the correction is applied. We regard the data obtained by using the glass electrode in conjunction with the cadmium amalgam electrode as more reliable and the set of equilibrium constants suggested is that obtained by analysing these data.

Some of the results on the complex-formation between Cd(II) and EDTA reported by different workers are summarized in Table 3. Comparison of the values shows that the results obtained in the pre- sent work are in close agreement with those recom- mended by Anderegg a for the formation of CdL and CdHL, allowing for the different ionic medium and

temperature. His recommended values extrapolated to 1.0M ionic medium by use of the Giintelberg equa- tion are also given in the table. In these calculations the small difference between the activity factors of Na ÷ and K ÷, and the difference in temperature, were neglected.

EDTA is known to form a weak complex with sodium. This was taken into account in analysing the experimental data, both for evaluating the protona- tion constants of EDTA 14 and its complex formation with cadmium. A value, log K = 1.22, for the forma- tion of the Na-EDTA complex was used in all the calculations.

Acknowledoements--I am very grateful to Professor Folke Ingman for placiog all the facilities at my disposal and for

many fruitful discussions and comments on the manu- script. Thanks are also due to Professor Ingmar Grenthe, Mr. Ignasi Puigdom6nech and Dr. Olof Wahlberg for use- ful discussions and help with the computer program.

REFERENCES

1. G. Schwarzenbach and E. Freitag, Heir. Chim. Acta, 1951, 34, 1503.

2. G. Schwarzenbach, R. Gut and G. Anderegg, ibid., 1954, 37, 937.

3. R. W. Schmid and C. N. Reilley, J. Am. Chem. Soc., 1956, 78, 5513.

4. H. Ogino, Bull. Chem. Soc. Japan, 1965, 38, 771. 5. V. G. Sochevanov and G. A. Volkova, Russ. J. Inory.

Chem., 1969, 14, 61. 6. J. Star~, Anal. Chim. Acta, 1963, 28, 132. 7. B. Kozjak, Z. Marini~, Z. Konard, Musani-Marazovi~

and Z. Pu6ar, J. Chromatoo., 1977, 132, 323. 8. G. Anderegg, Critical Survey of Stability Constants oJ

EDTA Complexes, (preprint). 9. B. Engstr6m, H. Norin, M. Jawaid and F. Ingman,

Acta Pharm. Tox., In press. 10. M. M. Jones and T. H. Pratt, J. Chem. Educ., 1976, 53,

342. I 1. Some Laboratory Methods in Current Use at the Depart-

ment of Inorganic Chemistry, The Royal Institute of Technology, Stockholm, (available on request).

12. L. Pehrsson, F. lngman and A. Johansson, Talanta, 1976, 23, 769.

13. I. Aldajoff, Acta Chem. Scand, 1969, 23, 1825. 14. M. Jawaid, Talanta, 1978, 25, 215. 15. P. Brauner, L-G. Sill6n and R. Whiteker, Arkiv Kemi,

1969, 31,365. 16. G. Biedermann and L. Ciavatta, Acta Chem. Scand.,

1962, 16, 2221. 17. N. Ingri, W. Kakolowic'z, L-G. Sill6n and B. Warn-

quist, Talanta, 1967, 14, 1261. 18. R. Arnek, L-G. Sill6n and O. Wahlberg, Arkiv Kemi,

1969, 31,353. 19. T. J. Janjic', L. B. Pfendt and V. Popov, J. Inorg. Nucl.

Chem., 1979, 41, 63. 20. N. Oyama, H. Matsuda and H. Ohtaki, Bull. Chem.

Soc. Japan, 1977, 50, 406. 21. O. Wahlberg, Acta Chem. Scand., 1971, 25, 1045. 22. P. Ulmgren and O. Wahlberg, Trans. Royal Inst. Tech.

Stockholm, 1972, 274, 322. 23. ldem, Chemica Scripta, 1975, 8, 126.