Some metal complexes of citric and tricarballylic acids

J. lnorg. Nuel. Chem., 1959, Vol. 12, pp. 122 to 128.

Pergamon Press Ltd.

Printed in Great Britain.

SOME METAL COMPLEXES O F CITRIC AND TRICARBALLYLIC ACIDS* N . C. LI, A . LINDENBAUM a n d J. M . W h i T E Argonne National Laboratory and Duquesne University Lemont, Illinois (Received 6 March 1959)

Abstract--The formation constants of several metal complexes of citrate and tricarballylate, and o f the "hydrogen complexes", i.e. complexes in which HA~- act as ligands, have been determined by a titrimetric method. For Mn(II), Cd(II), Zn(II) and Ni(II) complexes of citrate, the value o f K M x / K g r ~ x varies from 101"0 to 101'9, the ratio increasing with increasing value of KMx. The citrate complexes are more stable than the corresponding tricarballylate complex, as expected. The Co(II) and Mg complexes of citrate have reduction potentials which are too negative for direct polarographic method. In the p H region 1.9 to 2.5 the 1 : 1 uranyl-citrate complex has been shown to be a monomer with log K~A = 8"5.

As part of a continuing investigation of metal complexes of organic acids, tl) we report here the formation constants of several metal complexes of citrate and tricarballylate (AS-). By the use of the titrimetric method of SCHWARZENBACFIt2~(using metal ion concentration tenfold in excess over the ligand concentration), the formation constants of the "hydrogen complexes", i.e. complexes in which HA 2- act as ligands, are also obtained. M ~ r ~ s (aa) studied the cadmium complex of citrate by means of a conventional polarographic method, ~sb~while an e.m.f, method used by TREUMANNand FFRRIStse) has yielded an extrapolated value of 5-37 for log Kco ctt-. The Co(II) and Mg(II) complexes of citrate, however, have reduction potentials which are too negative and the reduction waves are irreversible. For the measurement of these metal complexes, an indirect polarographic method was developed. FF.LDMANand co-workers t4~ have studied the uranyl-citrate system and have found that when equimolar mixtures of uranyl nitrate and citric acid are raised to pH 3.5, there is present a 1 : 1 uranyl-citrate complex as a dimer (UO2Cit-)2. They also * Work done in part at Argonne National Laboratory under the auspices of the U.S. Atomic Energy Commission. The work ofN. C. LI and J. M. WHITEwas supported in part by the U.S. Atomic Energy Commission through Contract No. AT (39-1)-1922 with Duquesne University. Presented at the International Conference on Co-ordination Chemistry at London, England, April 11-16, 1959. (is) N. C. Lm, W. M. WESTFALL,A. LINDENBAUM,J. M. WHITE and J. SCHUBERT,,I. Amer. Chem Soc. 79, 5864 (1957); (b) j. SCHUBERT;E. LIND, W. M. WESTFALL,R. PF/.,EGERand N. C. LI, Ibid. 80, 4799 (1958). (2) G. SCHWARZENBACrl,Heir. chain. Acts, 33, 947 (1950); H. SErCt~,Der Einfluss yon Substituenten a u f dle Stabilitdt yon Chelatkomplexen. Brunner Bodner, Ztirich (1.956). (ga) L. MEIT~, J. Amer. Chem. Soc. 73, 3727 (1951); (b) I. M, KOLTHOFF and J. J. LINGANE,Polarography. Interscience, New York (1952); (e) W. B. TgEUMANNand L. M. FErtRIS.J. Amer. Chem. Soc. 80, 5050 (1958); (d) N. C. LI, J. M. WHITE and R. L. YOEST, Ibid. 78, 5218 (1956). (4a) I. FELDMAN and W. F. NEUMAN,J. Amer, Chem. Soc. 2312 (1951); (b) W. F, NEUMAN,J. R. HAVILL and I. FELDMAN, ]bid. 73, 3593 (1951); (e) I. FELDI~,N, J. R. HAV1LL and W. F. NEUMXN, Ibid. 76. 4726 (1954). 122

Some metal complexes of citric and tricarballylic acids

123

studied the uranyl-citrate system over a wide range of p H ; however, no quantitative value o f the formation constant of any of the complexes is given. HEITNER and BOBTELSKYtS~ state at p H < 7 the uranyl-eitrate complex is the monomer, UOsCit-, a n d gave the constant: log KraA = 3.16. This value seems too low, in view of the formation constant reported for uranyl-oxalate :te~ log KMA -----5.82. We have therefore redetermined the formation constant of the uranyl-citrate complex in the p H region where it is a monomer, and the result is reported here. EXPERIMENTAL Materials. All chemicals used were C.P. grade. The 0-1 M stock solution of uranyl ,nitrate conrained an equimolar amount of HCI, and was standardized by the gravimetric determination of uranium after ignition to UaOs. The solutions of citric acid and tricarbaUylic acid were checked by ~itration with standardized sodium hydroxide, and only fresh solutions were used. Procedure. pH determinations were made with a Beckman Model G pH meter and a Radiometer, ~ype PHM 3k, using a glass electrode with a saturated calomel electrode as the reference electrode. The instruments were standardized against standard buffer solutions at pH 4 and 7. Below pH 2.2 ~he instruments were calibrated with HCI-KC1 solutions. During all titrations a stream of presaturated, nitrogen gas was passed through the titration vessel. Polarographic measurements were made with a Sargent Model XXI or a Fisher Electropode polarograph in the manner previously described.t"qo) M E T H O D OF C A L C U L A T I O N (A) Dissociation constants o f lisA. The dissociation constants of the tricarboxylic acids, HaA, which are necessary for calculating the formation constants of metal ~omplexes with citrate or tricarballylate, are determined by the following equilibria present in aqueous solutions : HaA = H 2 A - + H+;

K1 = (H2A-)(H+)/(HaA)

(la)

H 2 A - = H A s- + H+;

K s = (HAS-)(H+)/(H2A -)

(lb)

H A S- = A 3- + H+;

Ka = (Aa-)(H+)/(HAg'-)

(lc)

Although citric acid has an O H group and acts as a tetrabasic acid, H4A, toward Cu(II) and Fe(III),CT~ we have found that for the metals reported in this paper, in the p H region below 9, citric acid acts as HaA. (See Fig. 1 for titration curves of Ni(II) and uranyl-citric acid mixtures.) Equations relating concentration o f the tricarboxylic acid, concentration of N a O H and p H to the dissociation constants can be derived in a manner similar to those for glutathione and oxidized glutathione reported by LI et al. es~ The equations are

pK1 =

p H + log~g - - 2 + l o g l l + -- g

pKs = p H + log g - - 1 2 ----g

K2(g ~ 1 ) - ] (H+)(g -- 2)J

(2a)

[ (n+)(3 - - g ) ] log,_l + K1 ~ - - - - ~ . J

(2b)

,_

[--

g pK3 ---- pH + log 1 -- g - - l o g [ 1

+

(H+)(_2- -

K s (1 - - gg) )J[

,~5)C. HEITNERand M. BOBTELSKY,Bull. Soc. Chim. Fr. 356 (1954). (6) L. J. HmDT,3'. Phys. Chem. 46, 624 (1942), 47~ R. C. W~NER and I. WgnER, J. Amer. Chem. Soc. 75, 5086 (1953). (s) N. C. Lt, O. GAWRON and 13. B,~cuAs, J. Amer. Chem. Soc. 76, 225 (1954).

(2c)

N . C . LI, A. LINDENBAUMand J. M. WHITE

124

where g = [ 3 T - (NaOH) - - (H +) + ( O H - ) ] / T and T = total molar concentration of citric acid in solution. 12

I

I

I

I

I

I

I

I

II ,0 9 8

pH 7 $ 5 4 3 S l

I

I

l

I

I

I

l

I

S

3

4 O

5

6

7

8

Fxo. 1.~pH titration of: curve 1, 0.01 M citric acid, 0.15 M NaCI; curve 2, 0.005 M citric acid, 0'05 M NifNOa)z; curve 3, 0-01 M citric acid, 0-01 M UOs(NOs)2, 0.01 M HCI, 0.11 M 1NaCI;curve 4, 0.02 M citric acid, 0.01 M UO2(NOs)a, 0.01 M HCI, 0.11 M NaCI. a = moles NaOH per mole citric acid plus HC1, when present. (B) Formation constants of metal complexes and "hydrogen complexes" (after SCnWARZENBACI~t2J). The chelating agents are taken to be the ions A s- and H A s- and the formation constants are defined by the equations M s+ + A s-

-----M A - ;

M s+ + H A s- = M H A ;

KMA = (MA-)/(MS+)(A s-)

(3a)

K~HA -----(MHA)/(MS+)(HA s-)

(3b)

I n the presence of tenfold excess metal ion over total acid concentration T, and in the p H region where (A s-) m a y be neglected, we have the following equations: T = (HA z-) q- (HsA-) d- (HaA) q- ( M H A ) d- ( M A - ) S = ( H A s-) + 2(HsA-) q- 3(HaA) q- ( M H A ) = 3T -- (NaOH) -- ( a +) q- ( O H - ) g = s/r

(4) (5a) (5b)

(6)

S may be defined as the total concentration of protons bound by A. Combination of equations (4), (5a) and, (6) gives g ( M A - ) q- (g - - 1)(MHA q- H A s-) + (g -- 2 ) ( H ~ - ) -t- (g -- 3)(HaA) = 0 (7) Since the metal ion is in tenfold excess, we may assume a constant concentration o f free metal ion [(M) constant] and introduce the following quotients, as developed by SCHWARZENBACHt2}

Some metal complexes of citric and tricarbaUylicacids

125

K1, = (MHA + HA2-)/(MA-)(H +)

(8a)

Kz, = (HzA-)/(H+)(MHA + HA g-)

(8b)

By combining equations (3a), (3b) and (1), it can be shown readily that K r and/(2, are really groups of constants: K r = [1 + KMHA(M)]/KaKMA(M)

(8c)

/(2, ---- [Kz(1 + KMaA(M)]-1

(8d)

Combination of equations (8a), (8b) with equations (1) and (7) gives g(1/Kx,) + (g -- 1)(H +) + (g -- 2)(a+)zKz , + (g -- 3)(H+)aKz/K1 = 0

(9) In equation (9), the unknowns are K r and K2, and may be evaluated by any suitable mathematical device. In the present investigation, we proceeded as follows: Let X = (H+)(1 -- g)/g;

Y=

1--g (H +) [(g -- 2) + (g -- 3)(H+)/Kd

(10)

For a given g in the regions g = 1.5 4- 0.2 and g = 0.5 + 0.2, the values of X and Y were calculated, giving one point each on the X and Y axes. A straight line is drawn through these two points. Straight fines are drawn in exactly the same way for the other values of g in the above regions. The X and Y values that correspond to the point of intersection of these straight fines yield the values of l/K1, and Kg.,, respectively. From equations (8c) and (8d), it is easy to derive the following relationships for the calculation of the formation constants KMA = [Kr K2, KzKa(M~+ )] -1

(1 la)

KMHA = [(K2"K2) -1 - - 1]/(M 2+)

(lib)

If the total concentration of the metal salt, Tra, is very much larger than the total concentration of the tricarboxylic acid, so that Tm may be substituted for (M s+) in equations (11), then the values of KI~A and KMH~, are easily obtained once the values of K1, and K2, are known. The uncertainties involved in locating 1(1" and Kz, graphically result in uncertainties in the values of the formation constants reported in this paper by about 0.15 log unit. (C) Formation constant ofuranyl-citrate complex. We have found that by titration in the pH region 1.9-2.5, a 1 : I uranyl-citrate complex is formed with A s- as the figand. The following equations are derived: (A a-) = h=

[3T - (NaOH) -- (H +) + (OH-)]

KIK2Ka K1K2(H+) + 2KI(H+) ~ + 3(H+) 3

T-

(A-S)[K1K2Ka + K1Kz(H+) + KI(H+) z + (H+)a]/K1KzK8

T,,,

(12a) (12b)

Inasmuch as the 1 : 1 uranyl-citrate complex has been postulated to be a dimer and a monomer by NEUMAN et al., (4) and by HEITNER and BOBTELSKY,tS) respectively, we propose the following equations T,n = (M z+) + (MA-) + 2(M2A2 2-)

(l 3)

126

N . C . LI, A. LINDEt~mAUMand J. M. Wma'E

t~ =

(MA-) + 2(M2A~ 2-)

(14)

T,~

KM~A~ = (M2As~-)/(MS+)2(Aa-) 2

(15)

Combination of equations (3a), (13), (14) and (15) gives h = KMA + KM,A2 × 2(1 -- ~)T,n(A)

(16)

(1 - , ~ ( A )

Equation (16) shows that if M A and MsAs complexes both exist in solution, a plot of t~/(1 -- t~)(A) vs. 2(1 -- ,~)Tm(A) should yield a straight line, the intercept of which is K~t.~ and the slope is K~A~. If the intercept of the linear plot is zero, only the (timer exists and the slope gives the value of K~A~. On the other hand, if the value of t~/(1 -- r~)(A) is constant, independent of variations in the value of 2(1 -- t~)Tm(A), then only the monomer exists and the value of t~/(1 -- t~)(A) is equal to KMA. (D) Indirect polarographic method for Co(II)- and Mg(II)-citrate complexes. In essence the half-wave potentials of solution (i) and solution (ii) are determined: Solution (i) consisting of 5.00 x 10-4 M Cd(NOs)2, 0"05 M sodium citrate; solution (ii) has the same composition as (i), except that it also contains 0.0495 M M(NO3)2 where M = Co(II) or Mg(II). The first polarographic waves in both solutions are due to the reduction of the cadmium ion, and therefore the dropping mercury electrode reactions in both are reversible. These half-wave potentials for solutions (i) and (ii) are related by the equation c8c~ (E½)(l) -- (Ei)(ti) ----- --0.030 log (A)0)/(A)( m (17) where (A) is the concentration of free citrate, and (A)(t) may be taken to be 0"0495 M. The value of (A)(a) is easily calculated from equation (17). The values of KOalA and KCdHA a r e taken from experiments described in Section (B), from which the concentrations of CdA and CdHA can be obtained. The total concentrations of citric acid and metal in solution are given by the equations T = (A 3-) + (CdA-) + (CdHA) + (MA-) + (MHA) + (HA s-) + (HsA-) + (HsA) (17a) Tm= (M s+) + (MA-) + (MHA) (1713) TABLE

Complex

1.--pH p.EStmTS OF SOME METAL COMPLEXES (25 °, Log KKA

Log KMA

Log Kurrx

Mn(II) CdflI) Zn(II) Ni~i)

3"67 3"98 4'85 5"11

2"08 2"28 2"96 3"19

1"59 1"70 1"89 1"92

Ni(II)

2"70 2"00

1 "56 0"91

1"14 1"09

KM~A

/.r = 0"15)

Log K ~ x (as reported in lit.)

Citrate*

Tricarballylatet

Mg(II) * Citric acid: pKx = t Tricarbailylic acid: :~ Value obtained by (91 J. S. WmERG, Arch.

2.94, pK2 = 4-34, pKa = 5"62. p a t = 3.50, pKg = 4.63, pK8 = 5.95. extrapolation to infinite dilution. Biochem. Biophys. 73, 337 (1958).

3.54(11; 4"2(8*1; 4.71(lb)

3.72(t) 5"36(8e~:

Some metal complexes of citric and tricarbaHylic acids

127

The ratio of KMHA/KMAis taken to be equal to the ratio KCdHA/KcoA,so that the concentration ratio (MHA)/(MA) is easily obtained. Since the concentrations of HA 9'-, H2A- and HaA are known in terms of (AS-), pH and dissociation constants of citric acid, the values of (MA-) and (MHA) in equation (17a) and (M 2+) in equation (17b), and hence KMA and KMHAcan be calculated. RESULTS

The acid dissociation constants of citric and tricarballylic acids and the formation constants of the metal complexes, determined in the manner described in Section (B) together with the values available in the literature, are summarized in Table 1. TABLE 2.~POLAROGP.AI,HIC RESULTSfOR Co(n)- AND Mg(n)-ClTRAam COMPLeXeS

(25°, (Ee)ti~= --O'658) In solution (ii): M(NOa)~ Co(]/) Mg(II)

--E½ 0.600 0"627

pH 5"57 6"86

(A -a) x 108 (MA) 0"58 0.0472 4"63 0.0445

(MHA) x 10a 1.1 0"~6 0"1 0-09

TAeLe 3.--Trn~TION oF URANYL NITRATE--uIIRIC ACID

MIXTURF~

IogKMA log KUHA 4"83 3"19 3"29 1.60 (25 °)

(a) 50 ml solution containing 0.0100 M UO2(NOa)a; 0.0100 M HCI; 0.0100 M citric acid; 0.110 M NaCI; plus v ml 0.2986 M N a O H

v(n'd)

pH

pA

0"00 1"00 2"00 3"00 4"00 4"50

1"86 1 "98 2"10 2"21 2"33 2"40

9"11 8"84 8-64 8"45 8"35

n

0"197 0"313 0"456 0"606 0"622

2Tin(1 -- ~) (A a-) x 1010

log (1 -- fi) (A a-)

0"12 0"19 0"24 0"26 0"31

8'50 8"50 8"57 8"63 8"56

(b) Same as above, except using 0.0200 M citric acid in the initial soln. 0"00 1"00 2"00 3"00 3 "50 4"00 5-00 6"00

1"81 1"91 2"01 2"11 2"16 2"21 2-32 2"48

8"97 8"75 8"47 8.35 8.24 7.98 7.60

0"235 0"356 0"473 0"544 0"613 0"757 0"890

0"16 0'22 0"34 0"38 0"41 0"46 0"49

8"46 8"49 8"43 8"43 8"43 8"47 8"50

(c) 50 ml soln. containing 0.0400 M UOa(NOa)~; 0"0400 M HC1; 0.0500 M citric acid; plus v ml 1.2970 M N a O H 0.00 3.00 3.85 5.00 5.80

1"37 1 "89 2"01 2"23 2"48

8"76 8"51 8 "05 7"52

0"392 0"557 0"771 0"923

0.80 1.02 1.49 1"67

8"57 8"61 8"58 8"60

128

N.C. L[, A. LINDENBAUMand J. M. WroTE

The results on the Co(II)- and Mg(II)-citrate complexes, using the indirect polarographic method described in Section (D), are summarized in Table 2. Table 3 lists the results obtained with the pH titration of uranyl-citric acid mixtures. The values of pA and r~ were calculated by means of equations (12a) and (12b), respectively. DISCUSSION From the data in Table 1 it is interesting to note for the citrate complexes that the value of KMA/K~HA varies from 101"8 to 101"9,and that the ratio increases as the MA complex becomes more stable. The higher stability of the citrate over the tricarballylate complexes is as expected, because of the presence of the OH group in citric acid. The formation constants of the Co(II) and Mg(II) complexes of citrate, obtained by an indirect polarographic method and listed in Table 2, are in fair agreement with values reported in the literature: ~l,t°~ log gco(II)-cltrate = 4"61; log gMg-eitrate = 3"25. Since the Co(II) and Mg complexes cannot be studied by means of the direct conventional polarographic method the demonstration of the validity of an indirect polarographic method for the measurement of such complexes may be of considerable usefulness. None of the formation constants of the "hydrogen complexes" listed in Tables 1 and 2 has been reported in the literature. Curves 3 and 4 of Fig. I give the titration of uranyl nitrate-citric acid systems for 1 : 1 and I : 2 mixtures, respectively. The first inflexion point in curve 3 is accounted for by assuming complete neutralization of the three carboxylic hydrogens in citric acid in the formation of UO~ Cit- chelate and the hydrochloric acid present in the uranyl nitrate stock solution. Comparison of curve 4 with curve 3 and with curve 1, which is the titration curve of citric acid by itself in the absence of uranyl nitrate, shows that the data of curve 4 correspond to the titration of curve 3 plus onefold excess citric acid. This indicates strongly that the uranyl ion does not form a 1"2 complex with citrate. From Table 3 it is seen that in the pH region 1.9-2.5, log ti/(l -- t~)(Aa-) remains essentially constant in spite of a fourteenfold variation in the values of 2Tin(1 -- ti) (A3-). Such constancy indicates, from equation (16), that only the monomer exists. The average value of log KMA is calculated to be 8-5. The titration data above pH 2.5 were not used in the calculation because of the well-known tendency of uranyl to undergo hydrolysis at higher pH. HEITNERand BOBTELSKY~5~report for uranyl citrate: log KMA = 3"16, whereas HEIDTttJ reports for uranyl-oxalate: log KMA = 5.82. It would seem that our value of log KuA for uranyl-citrate complex is more reasonable, inasmuch as the citrate anion is expected to exert a greater affinity for a divalent metal cation than the oxalate anion. It must be mentioned that in our calculations we have used the assumption ta~ that (H +) equals approximately to 10-pH. If for citric acid one uses an approximate activity coefficient of 0.8 for H + at /~ = 0-15, so that (H +) equals approximately 10-Pn t0.a and the dissociation constant equals approximately 10-pK/0.al, the values of log ~q/(1 -- ri)(A a-) in Table 3 still remain essentially constant. The average value of log K~A now becomes 8.6. Acknowledgement--The authors are indebted to Professor G. SCHWARZENBACHof the Eidg. Technischen Hochschule, Zilrich, Switzerland, for helpful discussions regarding uranyl-citrate complex. (10) A. B. HASTINGS, F. C. MCLEAN, L. EICHELBERGER, J. L. HALL and E. DACOSTA,J. BioL Chem. 107,

351 (1934).