On the complex formation between lead(II) and citrate ions in acid solution

J. inorg,nucl. Chem., 1973, Vol. 35, pp. 1269-1278. PergamonPress. Printedin Great Britain

ON THE COMPLEX FORMATION BETWEEN LEAD(II) AND CITRATE IONS IN ACID SOLUTION E. B O T T A R I and M. V 1 C E D O M 1 N I Istituto di Chimica Analitica, Universith di Roma, Roma, Italia

(Received 28 M a r c h 1972) A b s t r a c t - C o m p l e x formation between lead(ll) and citrate ions (L) has been investigated potentiometrically at 25°C and in 2 M Na(CIO4) by using a lead amalgam electrode and a glass electrode. The experimental data can be explained by assuming the following equilibria: Pb ~+ + L ~ PbL

log ill.0,1 = 4.08 _ 0 . 1 0

Pb 2+ + H ÷ + L ~ P b H L

logflL,~,~ = 8,15 ±0.05

P b ~ + + 2 H ÷ + L ~ PbH2L

logfll,2,1 = 10"85 ±0"10

Pb ~++ 2L ~ PbL2

log/31,0.2 = 6'06±0-20

Pb 2+ + 2H + + 2L ~,~ PbH2L2

log J3L2,2 = 14"95 ± 0" 15

Pb 2+ + 4H ÷ + 2L ~,~ PbH4L2

log fll,4,2 = 21.68±0'15

Symbols: L= B= b= A = a = H = h= Kn =

citrate ion = CsH5073total concentration of Pb 2+ free concentration of Pb 2+ total concentration of citrate ions free concentration of citrate ions total concentration of hydrogen ions free concentration of hydrogen ions formation constants of citric acid, defined as follows:

[HnL] Kn = h[Hn_lL]

where n = 1, 2, 3

/3q,p,r = stability constants of a species PbqH~Lr, defined as follows:

~q.p,~ =

[PbqH~Lr] bqh~a r

Charges are generally omitted.

INTRODUCTION

IN THE course of a study of the hydroxy organic acids as ligands of metallic cations in both acid and alkaline solution carried out in this laboratory, we have proposed to investigate the complex formation between lead(II) and citrate ions. Few data are reported in the literature, mainly related to the formation of a complex PbL. Dey and Mathur[1] from solubility measurements determine the value log •1,0,1 = 3.00 at 20°C, whereas Kety[2] by means of a potentiometric 1. A. K. Dey and K. C. Mathur, Proc. S y m p o s i u m on Chemistry o f Coordination C o m p o u n d s , p. 178 Pt I I I Agra, (1959). 2. S. S. K e t y , J . Biol. Chem. 142, 181 (1942).

1269

1270

E. BOTTARI and M. V 1 C E D O M I N I

measurements with a lead electrode report the value log/31,0,1 = 5.74 in 0.16 M NH4NOa and at 25°C. Several authors find evidence for the formation of mixed complexes with the hydrogen ion. Suzuki[3] determines at 25°C and 0.05 M ionic strength the value 7.8 × 10-a for the constant of the following equilibrium: Pb 2++ H3L ~ PbHL + 2H + Schubert [4] report the value 5.25 x 105 at 25°C for the constant of the equilibrium: pb2+÷ HL z- ~ PbHL. We have proposed to investigate by potentiometric measurements at 25°C and in 2 M Na(CIO4) the equilibria which take place in solution between lead(lI) and citrate ions in both acid and alkaline solution, in order to evaluate the nature of the complexes and to determine the relative stability constants. In the present work the results obtained in acid solution are reported. METHOD

OF INVESTIGATION

The measurements, in form of potentiometric titrations, were carried out at 25"00°C and in 2 M Na(CIO4) by measuring the electromotive force (e.m.f.) of the following cells:

~-) Pb(Hg)/Solution S/2 M NACIO4/1.99 M NaCIO4/AgC1, Ag (+)

(A)

0.01 M NaCl

(-) Ag,AgCI/1.99 M NaCIO4/2 M NaC104/Solution S/glass electrode (+)

(B)

0-01 M NaCI. All the solutions S were made 2 M in Na + by adding N a C I O 4 in order to keep the activity coefficients constant in spite of the variations of the concentration of the species which participate to the equilibria. Thus the solution S had the general composition: B M in Pb z+, H M in H+,A M inL, [Na +] = 2.00 M, [ C I O 4 - ] = (2 + 2B + H -- 3.4) M. In this way, by assuming the activity coefficients constant, concentrations can replace activities in all calculations. The titrations were performed as follows. To a known volume of 2 M NaCIO4, a solution of Pb(CIO4)2 and H C I O 4 w a s added stepwise until to have [H +] = H and [Pb ~+] = B. From the expressions of the e.m.f. (in mV units) of the cells (A) and (B): EA = EA ° - 29.58 log b -- Ej

(1)

E^ = EA° - 29"58 log b -- Ej

(2)

3. S. Suzuki, Sci. Reports Tohoku Univ. 5, 16 (1953). 4. J. Schubert, J. Phys. Chem. 56, 113 (1952).

Lead(l 1) and citrate ions in acid solution

1271

in this first part of each titration, where B = b and H = h because A = 0, the terms EA°, EB° and the liquid junction potential Ej were determined. In our experimental conditions we have found Ej = - 1 8 h mVM -1. Successively equal volumes of two solutions, one containing citrate ions, the other containing Pb(CIO4h and HCIO4 in concentration 2B and 2H respectively, were added gradually. In this wayA was increased, whereas B and H were kept constant during the titration. From the Equations (1) and (2) b and h could be determined for each experimental point, and the function: = log B

(3)

could be calculated for every - log h value. The titrations were carried on until stable E A values could not be obtained for several hours, as a consequence of the precipitation of lead citrate slightly soluble. EXPERIMENTAL Material and analysis Sodium perchlorate, perchloric acid, lead perchlorate and lead amalgam (ca. 1% in weight) were prepared and analysed as previously described[5l. Sodium citrate. A C. Erba RP product NaaCeHsO7.2HzO was used without further purification. The purity and the water content of this product were controlled as previously described [6]. Nitrogen, purified as previously described[6], was bubbled through the solution S to avoid oxidation of amalgam. Apparatus All the measurements were carried out in a thermostat at 25'00°C _+0.05, and the cell arrangement was similar to that described by Forsling et al.[7]. Ag,AgCI electrodes were prepared as described by Brown[8]. The e.m.f, of the cell (A) was measured by a SEB (Milano) compensator, and the e.m.f, of the cell (B) by a valve Radiometer PHM4 potentiometer. A Beckmann glass electrode No. 1190-80 previously calibrated against a hydrogen electrode was used.

RESULTS AND CALCULATIONS

Titrations at H = 0.025, 0.050, 0.100, 0.150, 0.193 M and B = 1.0, 2-0, 5.0 mM were performed. Solutions more concentrated in B could not be investigated on account of the precipitation of lead citrate at very low citrate concentration. The experimental data, in the form "0(-log h) are plotted in Fig. 1. It can be seen that for every H the experimental data obtained for different B fall on the same curve, whereas different curves are obtained for different H. Therefore rj is a function of H but not of B: this means that mixed complexes with hydrogen ion are present, but not polynuclear complexes, and thus the general formula of complexes is PbH~L~. In order to determine the nature of the complexes and to calculate the relative stability constants, the experimental data "0(- log h) were elaborated in the following way. By using the mass action law and the material balance, the following 5. 6. 7. 8.

E. Bottari and M. Vicedomini,J. inorg, nucL Chem. 34, 1897 (1972). E. Bottari and M. Vicedomini,J. inorg, nucl. Chem. In press. W. Forsling, S. Hietanen and L. G. Sill6n, A cta chem. scand. 6, 901 (1952). A. S. Brown,J.Am. Chem. Soc. 56, 646 (1934).

1272

E. BOTTARI and M. VICEDOMINI

'q B xIO3M 2.0 H=0.025 M o

1.0

H =0.050 M z~ 1.0 H = 0.100 M i

1.0 2.0 5.0

H =0.150 M v 2.0 1.0

[i 1,°

H = 0.193 M

I

2.0 5.0

"

}.r--

1.0

~

v

I

I

2.0

3.0

I

I

-log h

4.0

Fig. 1. ~ has a function o f - log h at different B and H values. The curves are drawn using the equilibrium constants proposed in this work. Equations can be written: B = b + ~ ~ fla,p,rbhPa r p

(4)

r

H : h + ~ , nKnhna--t-~ ~ pfll,19,rbhPa r I1

19

(5)

I"

where p I> 0 and r t> 1. In these expressions the hydrolytic species o f l e a d ( I I ) can be neglected for the selected experimental conditions according to Olin [9], and the values of K , : log

K1 =

5" 18, log KIK2 = 9"34, log K1K2K3 = 12"24

have been previously determined in the same experimental conditions As it results from Equations (4) and (5), it is necessary to know for evaluate the stability constants. Since in the H and B ranges B ~< 0-02 H , the last term of Equation (5) is negligible with respect values can be obtained from the expression: H -- h a = K l h + 2KIK2h 2 + 3KIK2K3h ~" 9. A. Olin, Acta Chem. Scand. 14, 126 (1960).

[6]. the a values investigated to H , and a

(6) ,.

Lead(l 1) and citrate ions in acid solution

1273

The a values so calculated, together with the experimental data, are collected in Table 1. In order to determine the p and r values and the stability constants it is necessary, as ~ is a function of both h and a, first to study ~3 as a function of a at h constant, and then as a function ofh. F r o m Equations (3) and (4) it can be written: (7) and (IOn - 1 ) a - ' = ~] ]~ fll,p,rhPa r - ' . p

(8)

r

F o r h constant, Equation (8) gives: (10 n - 1)a -1 = ~ y r a r-I

(9)

~,r = ~; ~,~,~h p .

(10)

where P

T h e ~h values corresponding to the selected values o f - log h have been obtained by graphical interpolation for every H , and the corresponding a values were calculated according to Equation (6). By plotting, for every selected h value, the function (10 '~- l ) a -~ vs. a, straight lines are obtained: then r can be 1 and 2. The intercepts, for a = 0, provide the values of y~ and the slopes the values of yz. T h e r e f o r e complexes with more than two citrate ions are not present. By plotting yl and Y2 values vs. h, straight lines are not obtained: then complexes with p > 1 are also present. Therefore, for the determination of the stability constants the curve fitting method [ 10] was employed. By supposing that p may assume the values 0, 1 and 2 for yl and 0, 2 and 4 for Y2, Equation (10) can be written respectively as follows:

logT1 = log/31,oa + log(1 + ~ h+/3Lz~ h 2) /2[1,0,1 ¢1,0,1 logy2 =

logfl, o 2+ log(l + 1~_.~ hZ + lfl_:.!.~,zh4) '" /31,o,~ ~1,o,~ "

(ll)

(12)

This hypothesis seems to be reasonable on the basis of both the structure of the citrate ion and the expected symmetry of the complexes, as it will be proved below. Equation (11) can be normalized with the function: y = log (1 + a u + u 2)

(13)

where u = h (flLz'a'~ 1/2 \B1,o,d

and

a = fl1,1,1(/31,0,~/3~,z,1)-,t2

(14)

T h e curves y (log u) calculated for different a were superimposed on the data 10. L. G. Sill6n,Acta chem. scan& 10, 186 (1956).

1274

E. B O T T A R I and M. V I C E D O M I N I Table 1. Experimental data H=0.025M IO-aM "0( - log h, - log a) : B = 1.0×

0.006(2.008,8.54) ; 0.007 (2.163, 8-02) ; 0.019(2.371,7.36) ; 0.062(2.628, 6.61) ; 0.134(2.863, 5.96) ; 0.221 (3.044, 5.49) ; 0.361 (3.254, 4.98) ; 0.523(3.438, 4.56) ; 0.705(3.607, 4.19). H=0.050M

B=

1.0×10 -aM

7 ( - log h, - log a) :

0.018(2.243,7-40);0-095(2.449, 6.80); 0.135(2-659, 6.20); 0.267(2.861,5.65);0.510(3.189, 4.85); 0.693(3.394, 4.35); 1.095(3.703,3.69). H =0.100M

B = 1"0× 10-aM series a 7(-- log h, - log a) : series b 7 ( - log h, - log a) :

0.001(1.123,10.94);0.065(2"023,7"72);1"043(3"411,4"01); 1"999(4'077,2"67). 0.086(2.126, 0.431 (2.839, 1.072 (3.440, 1'823(3"964,

7.42); 5.40); 3.95); 2.87);

0-220(2.505, 0.677(3.103, 1.327(3.629, 2.087(4.133,

6"32) ; 0.287(2.630, 5.97); 4.73); 0-874(3.281,4.31) ; 3-54); 1.560(3.789, 3"21); 2.57).

B = 2 . 0 × 10 - 3 M

series a 7(-- log h, - log a) : series b 7 ( - log h, - log a) :

B = 5"0x 10-a M 7 (-- log h, - log a)

:

0.059(i.984,7.84); 0'146(2'307,6"88) ;0.292(2.613,6.02); 0.478(2.866,5.33); 0'679(3"081,4"80) ;0.895(3.277,4.30). 0.004(1-348, 9.93); 0'023(1'680,8"79) ;0.059(1.952,7.94); 0.151(2.314,6.86); 0"354(2-697,5"78) ;0.597(2.990,5.12); 0.854(3.228,4.43). 0"013(1'353,9"92); 0"055 ( 1-931,8"00) ;0.138(2.270,6.99); 0"327(2"656, 5"90). H=0"i50M

B = 2 . 0 × 10 - 3 M

series a 7 (-- log h, -- log a) :

series b 7 ( - - I o g h , - - l o g a):

0.001 (I.081, 10-65) ; 0-023(1.575,8.91) ; 0.105(2.024, 7.66) 0.245(2.368, 6.53) ; 0.370(2.569, 5.96) ; 0.571 (2.810, 5.31) ; 0.848 (3.074, 4.63) ; 1.231 (3.380, 3.90) 0.001(!.313,9.77);0-021(1.563,8.95);0-069(1-892, 7.93); 0.132(2.124, 7-23); 0.229(2.352, 6.37); 0.341(2.542, 6.08); 0.420(2.645,5.75);0.510(2.760,5.44);0.603(2.856,5.18); 0.722(2.971,4.89);0.922(3.150,4.44);i-132(3-319,4-04); 1.285(3.456,3.73). H=0.193M

B=

l'0xl0 -aM

7 (-- log h, -- log a) :

0.088 (1"871,7.87) ; 0.274(2"329, 0.593 (2.750, 5"35) ; 0.799(2.949, 1"215 (3.287, 4.01) ; 1-431 (3'443, 1.888 (3'749, 3"01 ) ; 2-111 (3"894,

6"52) ; 0"457 (2"593, 4-83) ; 0.992(3.115, 3.65) ; 1-658 (3.600, 2.72) ; 2"335 (4"028,

5"78) ; 4"42) ; 3"31) ; 2"47).

Lead(l I) and citrate ions in acid solution

1275

Table 1. ( C o n t d . ) H = 0.193M B = 2 . 0 × 10 - a M

0.001 (0.864, 11.40); 0.002( 1-047, 10.57) ; 0.009( 1-326, 9-58) ; 0.052 (1.708, 8.37); o. 174(2.141,7.07); 0.421 (2.544, 5.91); 0.547 (2.703, 5.48) ; 0.678 (2-841,5.11); 0.815 (2.963, 4.80) ; 1.046(3.161,4-31) ; 1.470(3.480, 3.57) ; 1.832(3.715, 3.07).

"O(- log h, -- log a) :

B = 5"0 x 10 -a M

0.011 (1.308, 9-64); 0.059 (1.713, 8.35) ; 0.096 (1.876, 7.86) ; 0.180(2.126, 7.11) : 0-308(2.373, 6.40) ; 0.455(2.572, 5.84).

~1( - log h, -- log a) :

log yl (log h) and m o v e d along the t w o axis until the b e s t fit is obtained. I n the position o f the b e s t fit f o r a = 5, it is obtained: log 3'1 - Y = log/31,0,1

= 4 " 0 8 -4- 0 • 1 0

and f r o m E q u a t i o n s (14): log/31,2,1 = 2 log u - 2 log h + log/31,o,1 = 10-85 ___0-10 log/31,1,1 = log a + ½ log/31,0,1 + ½ log/31,2,1 = 8.15 + 0.05. E q u a t i o n (12) can be n o r m a l i z e d with the function: y = log (1 + a u

z+u

4)

(15)

where u = h

and

a =/31,2,2( °b11,4,2/J1,0,21 o ~-i/2 •

\/31,0,2/

(16)

By s u p e r i m p o s i n g the c u r v e s y (2 log u), calculated for different a, on the data log Yz (2 log h ) , in the position o f the best fit for a = 12.5 it is obtained: log T2 -- Y = log/31,0,2 = 6.06 _ 0-20 l o g / 3 1 ~ = 4 log u -- 4 log h + log/31,o,2 = 21.68 _ 0.15 log/31,z.2 = log ct + ½ log/31,4,2 + ½log/31,0,2 = 14.95 ___0.15. In Figs. 2 and 3 are r e p o r t e d the functions log yl and log y2 v s - log h and - 2 log h r e s p e c t i v e l y , with the relative n o r m a l i z e d c u r v e s in the position o f the best fit. T h e a g r e e m e n t b e t w e e n the n o r m a l i z e d c u r v e s and the data log y (log h) p r o v e s the c o r r e c t n e s s o f the a s s u m p t i o n m a d e for the p values. In o r d e r to confirm the a b o v e results, theoretical ~ ( - log h) c u r v e s h a v e b e e n calculated for each H by using the proposed/3q,p,r values. A s s h o w n in Fig. 1 theoretical c u r v e s and e x p e r i m e n t a l points v e r y well agree within the p r o p o s e d limits o f the/3~,p,r values uncertainty. T h e r e f o r e the f o r m a t i o n o f the c o m p l e x e s PbL, P b H L , PbH2L, PbH2L2 and PbH4Lz with the p r o p o s e d log/3q,p,~ values entirely explains the e x p e r i m e n t a l data.

1276

E. B O T T A R I and M. V I C E D O M I N I

/

O1 O

7.0

6.0

5.0

4.0~

I

I

I

4.0

3.0

2.0

-log

h

Fig. 2. Log T1 as a function o f - - log h. T h e curve represents the normalized curve in the position of the best fit.

CONCLUSIONS

T h e experimental data obtained in acid solution can be explained by assuming the following equilibria: Pb 2÷ + L ~ PbL

log fll,O.1 ----4"08 --0"10

pb2++ H + + L ~ P b H L

log fl1,1.1 = 8" 15 -- 0"05

Pb 2+ + 2 H + ~- PbHzL

log fll,2,1 = 10"85 --0"10

Pb 2+ + 2L ~ PbL2

log fll,0,2 = 6"06 "4-0"20

Pb z+ + 2H ÷ + 2L ~- PbH2L2

log/31,2,2 = 14"95 -----0" 15

Pb 2+ + 4 H ÷ + 2L ~ PbH4L2

log/31,4,2 = 21 "68 --+0"15.

T h e r e f o r e mixed complexes are mainly present, but not polynuclear complexes according to the data reported in the literature. H o w e v e r we find the existence o f complexes that are not reported in the literature, as PbH2L, PbL2, PbH2L2 and PbH4L2. By using the above/3q,p,r values, the distribution of the complexes as a function of --log h has been calculated for two different A values. Figure 4 shows the

Lead(l l) and citrate ions in acid solution

o.

1277

/

13.0

11.0

9.0

7.0 I

I

70

50

I

-21o9 h

3.0

Fig. 3. Log 1'2 as a function o f - 2 log h. The curve represents the normalized curve in the position of the best fit.

~. Pb

A = 0.025 M

100

Pb 50

PbHzL

0 1.0

2.0

3.0

4.0

- Io g

Fig. 4. Distribution of complexes as a function o f - l o g h at ,4 = 0.025 M.

1278

E. BOTTARI and M. V I C E D O M I N I

~Pb

A = 0.100 M

100

50

0

1.0

210

3.0

4.0

-log h

Fig. 5. Distribution of complexes as a function o f - log h at A = 0. 100 M.

distribution curves obtained for A = 0.025 M, and Fig. 5 for A = 0.100 M. From these plots it can be observed that the complex distribution is greatly affected by the total citrate concentration, as well as by the hydrogen ion concentration. For A = 0.025 M the complexes PbH2L and PbHL predominate in acidic range, whereas the complex PbL2 is quite negligible on account of the low A value. For A = 0.100 M therelative concentration of the complexes with two citrate ions considerably increases, and the complexes PbH4L2 and PbH2L2 are present in a more acidic range than for A = 0.025 M. Furthermore for A = 0.100 M the mixed complexes with hydrogen ion prevail on the others, and the complex PbL2 is now present in appreciable concentration for the higher ,4 value. It is interesting to compare the tartrate and citrate ions as ligands toward lead(II) in acid solution. In a previous work [5] it was shown that between lead(II) and tartrate ions in acid solution, at 25°C and in 1 M Na(CIO4), the complexes PbL, PbHL, PbL2 and PbHL2 are formed, with the following values of the stability constants: log fll,0,1 = 2.60 _+0.05, log/~l,x,1= 5.45 _ 0.05, log •1,0,2 = 3"95 -----0.20 and log flt,~,2 = 7-45 _ 0.15. From these data it results that the citrate behaves as a strOnger ligand than the tartrate toward lead(II) in acid solution. However it must be pointed out that, since citric acid is weaker than tartaric acid, complex formation between lead(II) and tartrate ions can take place in a more acidic range. Acknowledgement-This work was carried out with the aid of CNR, the National Research Council of Italy.