Nov. 20, 1932
5iG
ETHYLENEDIAMINOTETRAACETE-CALCIUM IONEQUILIBRIUM [CONTRIBUTION FROM
THE CHEMICAL
LABORATORIES O F CLARK UNIVERSITY]
The Effect of Potassium Chloride on the Equilibrium between Ethylenediaminetetraacetate and Calcium Ions1 BY FRANCIS F. CARINIAND A. E. MARTELL RECEIVED OCTOBER 2 5 , 1951 The various ionization constants of ethylenediaminetetraacetic acid, and the stability constant of the calciuin-cthylenediaminetetraacetate anion are reported a t various potassium chloride concentrations. The data are extrapolated graphically to infinite dilution t o give the corresponding thermodynamic constants.
Introduction Schwarzenbach and Ackermann2 have determined the apparent ionization constants of ethylenediaminetetraacetic acid and the chelate stability constant of the calcium ion with its tetranegative anion, a t 20°, in 0.100 M KCl. The present investigation was undertaken to determine the effect of neutral salt (KC1) concentration on the dissociation and complex formation equilibria. I n view of the high degree of interaction of simple dipolar ions with various basic metal ions, a large effect would be expected for dissociation of the various species of ethylenediaminetetraacetic acid. Further, since the stability of the complex is usually expressed in terms of the tetranegative anion of the complexing agent, the equilibrium constant involving the metal ion should show a large salt effect. Potassium chloride was chosen as the neutral salt since the potassium ion has been shown by Schwarzenbach2 not to interact with the ethylenediaminetetraacetate anion, and since the chloride ion makes it possible to employ a silver-silver chloride reference electrode. Ethylenediaminetetraacetic acid (I) contains two dipolar groups and would be expected to interact more strongly with neutral salts than do simple HOOCCHr
dipolar ions such as glycine. The next higher ionic species which is well-defined in solution is the divalent anion (11) which contains two carboxylate ions in addition to the two dipolar ions. The monovalent anion (not shown) probably also exists as an intermediate in solution. The trinegative anion is illustrated with a hydrogen bridge of the type suggested by Schwarzenbach2to account for the abnormally large difference between the third and fourth dissociation constants. Although there are theoretical reasons for doubting the stability of a bridge of this type, it is certain that additional interaction of some kind must take place. Possibly the carboxylate ions are also involved in the hydrogen bridging, and the hydrogen ion is complexed to some extent in the same manner as are the more basic metal ions. The tetranegative anion (IV) is usually used as the reference ion for expressing the stability constant of the metal complex. The structure now generally accepted for the calcium complex, in which the calcium ion is hexacoordinate, is illustrated by formula V. The use of molecular models indicates that this structure may be achieved approximately with little strain in the organic molecule.
CHvCOOH
,’ L -0OCdII2
[
\A/
/
,”’ ‘ 2
I1
CHzCOOI11
-0OCCHz )KCHICHZN
-00CCHz
/ \
CHzCOO-
117 (1) Ahstract’ed from a thesis submitted by Francis F. Carini t o t h e Faculty of Clark University, in partial fulfillment of t h e requirements for t h e degree of Master of Arts, June, 1951. (2) G . Schwarzenbach ond H. Ackermann, Helv. c h i m . r l ~ l u ,31, 1783 (1847).
V, Calcium chelate of ethylenediaminetetraacetate ion
Experimental Apparatus.-The titration vessel consisted of a 250-ml. flask fitted with seven necks t o accommodate a mercuryseal stirrer, acid and base microburets, and platinum, silversilver chloride, saturated calomel, and glass electrodes. A %inch shielded glass electrode (Beckman No. 11YO-75) and a saturated calomel clcctrode (Rcckman N o . 1170) were
used with a Beckman model G pH meter. The hydrogen electrodes were platinized by the method outlined in Weissberger, a and the method described by Shedlovsky and MacInnes' was employed in preparing the silver-silver chloride clectrodes. The e.1n.f. of the hydrogen silver-silver chloride cell was determined with the help of a Leeds and Sorthrup type K potentiometer. The temperature wits maintained a t 25.03 f 0.0lo. Materials.-The analytical-reagent grade ethylenedixininetetraacetic acid, kindly donated by the Bersworth Chemical Company, was twice stirred with hot water for IO hours arid decanted. The rcmainiiig solid was twice recrystallized from hot water. Carbonate-free K O H was prepared according to the tnethod outlined by Schwarzenbach.5 4 stock solution of the disodium salt of ethylenecliaminetetraacetic acid was itiatle by weighing out approxiinatcly 0.0100 mole of acid, addiiig slightly more than 0.020U mole of K O H , and diluting to oiie liter. Measurements.-The calibratioii of thc I3eckiriau glass electrode-calomel electrode systern was carried out at 0 . 0 1 , 0. I atid I . i ) .\I KCl coiicci~tratioiis by coinparing the p € I rciiiding with the pH calculated froiii the nicasiircd c . i i i . f . of the cell 1'1, 113f), I 1 -in), Cl-,:,',, AgCl -- Ag I'hc rcuiings of thc two cells were takeii siniultaneously and under the same conditions that wcre employed for the potentiometric titrations ( i . r . with the complexing agent present). 111 the calibration runs a t least two hydrogeii electrodes and at least two silver-silver chloride electrodes were employed. Equilibrium was obtained for the hydrogen electrodes within a few minutes 011 i i buffered solution, but 20 to 30 minutes werc required in lion-buffered regions of the titratioii curvc. The />I3 of the solution \vas c:ilcuI'ited from the equation ~
lined above, but readings were taken 011 the pH meter only. The solutions employed for the determination of the calcium complex constants were made up and titrated in the same manner, except that sufficient CaC1. solution was added to make its molarity approsimately equal to that of thc cotriplexing agent. Calculations.--The conditions employed in the titration and the method ctnployed ill calcula&g the various equilibrium constants differ from previously published reports and s o are IJriefly described here. The syinbsIs and terms arc dcfilletf as c', = total colicelitration of complexiiig ageiit specics i i i solutioii i',,, = t o t d coiiceiitratioii ol metal ion species present ( = III(JI;II. couceiitratioii of species indicated ri = irioles of lxtsc added per n ~ o l cof complexing agent prcwit [.I4\', H:{\'--l, Hs\' -2, H\'--3, \1--4 represent fortlls of etl~ylciietliarnitietet~~acetic acid and its tlissociatioii proclucts Ca\' ? r e j ~ r c w i i t sthe c:ilciuni coiiil~lcx Othcr tcriiib huve their uaual iiicaiiing. l'he acid equilibria ;irid the correspoiiditig iipparcnt ionizatioii constants may
be rcpresentcd by
+
I1,L'I-H' H:j\.
11
lI1\'. ? Z I i
lI\
J
hi" = ( W ' ) ( H s \ ' ~ l),'(I&\.) ( I ) '
Hj\'
+ " hic = ( ~ ~ . ~ ) ( H ~ ~ - ' ) ~ ((2H) ~ \ ' - ' ) ' + I I \ ' . k$ = (El ' ) ( ~ ~ \ . - a ) , ~ ( l - I ~ ~ ' -(z3~ ) + k,' = ( H - ' ) [ \ . - 4 ) / ( H \ . - 3 ) ( 4 ) €iZ\
J
\'-I
~vhereK,,? is the cquilibriuni constarit a t a definite concentration of KCI. In the abieiice of calcium ions, thc following relationship holds ('% = ( l i d \ ' )+ ( I 1 \ . - 1 ) (HL\. 2) ( H L ' . 3) (\. 1) ( 5 , 1;roin elcctroneutrality rec~uireineritsit is sect1 that u C ' ~ ( I 1 ''j = ( O H - ) (H2\..-') 42(H2\'-2 , 3(H\'---') 4 ( H Y d l ( r j )
+
+
\\
+
hcrc
fi,,11 = incasured potciitial = potential of Ag-AgCI clcctrode, -U.2224 volt E, tiicaii ionic activity coeflicient of KCI, obtaiiicd fro111 t h e Ivork of I-Iariiccl arid Cookti ~ i i ( : ~=- niolality of c*hloridcioii T*
=
Other sytril~o~s have thcir u s u d trieu~iiiig
+
+
+
+
'lhc lirst t \ v o ioiiizatioii coustuits inay be coinbitled to give kt'k;" = ( H -)'(H?\'--'J/'(ff4\.) = k i z c (7) I t niay IJCA secii from the shnpc of the titratioii curve of the amino acid (curve A , Fig, 1) that i t i the region betwecn (I = ( 1 ; ~ n d(i = 2 , (l-f\'--iI) iind ( \ - - 4 ) may be neglected. At the i)oiiit O I I the titratioii curve where ti = 1, CIC+ = (H?\'-..2).Liming th:it thc ratio k l ! k ? has the statistical , the a h v e cquatioiis iiiay be c o i ~ ~ b i i ~toc dgive thc rclxtioiiships 1 : i ( ' [ { , v - 4fC8 - 1 3cII*)cI1,v ( c b - C" 1 2 = 0 ( 8 , ,J :jL'il.\ - L' - - l ( c ' e 1 ;jCI1')CH.\- - L' (c8 -k L']l j : = 0 (9)
+
+
'fhr vctlues of L ' P I , ~- 2 a11d Ckr4v c;ilculated from equations ( 8 ) anti ( 9 ) are used in equation ( 7 ) for the deteriniiiation of k,.'. The individual constants klc arid ks' were not calculated since they are subject to much larger errors than is k t 2 O , The statistical ratio of 8 / 3 was the c o r n l ~ i ~ ~constant ctl choseii for k t r / k z r since i t gave the best ;igrecinetit for values of k12' calculated from tliffereiit titratioiis. The third dissociation constunt, k a r , is \'cry siilip~ycalcu0 I 2 3 4 latrtl from the PH of curve -1,Fig. 1, at n = 2.cj. .It this 11 poirit ( H \ ' - a j = (H2\*-?)u1d 1;ig. l.--Titr;itioii ( ~ . i ) o l*\I etliyleiictfia~riiiictetraacctic k;' = ( l ~ ~ ~ J ( I ~ \ = ~ (I-I~'., ~ , i ~ / 110) ( l ~ ~ \ ~ ~ ~ ~ acid in 0.1 .II KCI \?it11 aiitl Jvithout 0.001 .IT Ca c 2 : - --, 'fhe fourth ionization coilstant \vas tictcrlniriecl from the E D T A ; - - - -- -, EIlT.4 i- Ca -z; (1 = niolcs of KO13 per b b r at (1 = -4. Since hydrolysis of the tctraiicg'itive atiioii tiiole of EI)1'A. k c u r s , CW\- = Co~i,a t (1 = 4.0 the PH is considerably a b ? v e the neutral point, and the ionization of water may br Titration of the amino acid a t other salt coriceiitrations neglected. Also, at this high pH the concentrations of was carried out in a manner analogous to the procedure outIT,\', K,\;-', and H n V + may be dropped from equation ( 5 ) . As a result the expression for k4rreduces to k , ' = ( ~ ~ + ) ( \ ' - ' ) ~ ( I I \ . - , {= ) I I I + j ( C , - C,,1,1,'C,,1,(11)
ETHYLENEDIAMINOTETRAACETATE CALCIUM I O N EQUILIBRIUM
Nov. 20, 1952
The equilibria for complex formation may be expressed by the relationships Ca +z V-4 CaV-2 KC,"= (CaV-')/( Ca +')( V - 4 ) (12) The possibility of intcrniediate complexes of the CaHV-' type is neglected since it has been shown by Schwarzenbach2 that in the case of cthylenediaminetetraacetic acid this is a relatively unstable intermediate. Also, the conditions of the present investigation did not allow calculation of the concentration of this substance since the bivalent metal ion concentration was not maintained constant. I t was not feasible to do this (by using a large excess of calcium ions) since it was necessary to make up solutions of known and relatively low ionic strength. In the presence of calcium ions, equations (6) and (6) must be modified to include the metal complex species. In the regioh between a = 3.5 and a = 3.8, it is possible to effect a sitnplificdtion by neglccting H4V and HsV-l, the concentrations of which arc very low. Thus (5) becomes Cs = (HzV-') (HV-3) (1'-4) (CaV-') (13) Also, equation (6) is convcrtcd to ( a - 2)C. (H') = (OH-) f ( H V 3 ) 2 ( V 4 ) 2 ( C a V 4 ) (14) Combination of ( 3 ) , (4), (13) and (14) yields ( U - 3)C, (H') - (OH-) = 1 -
+
TABLE I aa
+
+
+
+
+
1 1 1 1 1 2.5 2.5 2.5 2.5 2.5 2.5 4.0 4.0 4.0 4.0 4.0
+
+
+
Equation (15) is solved simultaneously by the use of two different "a" values. For the purpose of calculating the equilibrium constant, the experimental data were plotted on a large scale graph, the ml. of HC1 or KOH added being first converted to a moles of base added per mole of complexing agent present, with the pure acid as the reference point, a t which a = 0. Smooth curves were drawn through the points of corrected p H v s . a, and values from the graph were taken to solve the equations for apparent dissociation constants and apparent chelate formation constants. Curves A and B of Fig. 1 are typical of the plots obtained for titration of the acid in the absence of and in the presence of calcium ions.
Discussion of Results The results, together with some of the quantities from which they were calculated, are listed in Table I. The product of the first two ionization constants, klzc, was found to be the least reliable of the equilibrium constants; but, as already noted, it is more satisfactory in this respect than either of the first two constants taken separately. The third ionization constant, k$, is the most reliable, since it is calculated from the hydrogen ion activity, which is directly determined. Since the positions of the inflection points are obtained from the graph, the estimation of kaC is not subject to errors in standardization of the solutions and to the presence of small amounts of impurities. The fourth ionization constant, k4C, depends on the value assumed for the ionization constant of water, K,, which is not readily found either experimentally or theoretically. The value of 1.008 X lo-" reported by Harned and Owen for 25O, was used in this paper. Since Schwarzenbach used 1.14 X as the value of K,, his value of k4" differs somewhat from that calculated in the present investigation. Calculation of the formation constant, KcaC,depends on the value of K , chosen. The small difference (0.13 X 10-14) in the ion-product constants of water given above results in a difference of 0.2 log KcaCunit in the calculated chelate stability constant.
5747
1O'mUDTA
5.03 4.70 5.63 5.11 6.17 5.86 4.95 5.49 5.84 5.86 5.04 5.26 4.32 5.01 5.66 4.64
PH 2.84 2.78 2.72 2.75 2.71
rnKCl
0.0536 .02575 .543 ,496 .975 0.00987 .0528 .0879 .3000 .546 .781 0,00887 .0464
6.35 6.29 6.24 6.14 6.22 6.28 10.80 10.65 10.72 10.61 10.39
,0x00
.49G ,720
WaCI%lO3
3.5 4.46 0.0176 4.61 3.5 4.48 .0473 4.66 3.5 4.49 .OS56 4.66 3.5 5.49 .523 4.81 3.5 4.46 .744 4.94 Only sample data are given here. Constants tually determined from a spread of "a" values.
4.63 4.66 4.67 4.71 4.63 were ac-
The apparent ionization and stability constants listed in Table I are plotted as a function of the square root of the ionic strength in Figs. 2 and 3. The considerable variation in the equilibrium constants with ionic strength which is observed may be interpreted in the following manner: Since the measured p H may be considered equivalent to the reciprocal of the hydrogen ion activity, the apparent ionization constants may be formulated as kna =
(16)
au+CA-/CBA
where a and c represent activity and molar concentration, respectively, and HA represents the species which ionizes. The thermodynamic equilibrium constant may therefore be written as
or pkna = p k
+ log r!C
(17)
YHA
The values of the thermodynamic equilibrium constants were determined by extrapolating the curves in Figs. 2 and 3 to infinite dilution. The results listed in Table I1 are accurate to the nearest tenth of a unit except in the case of pK3 for which the values are somewhat better. From these values it is possible to determine the ratio of the activity coefficients of the ions in the reactions involved. TABLE I1 THERMODYNAMIC DISSOCIATION CONSTANTS, CALCIUM CHELATE STABILITY CONSTANT, AND CORRESPONDING FREE ENERGY CHANGES PKlZ
PKI
fiK4
Equilibrium constants 5 . 8 6.47 1 0 . 1 Free energy changes, kcal. mole-' 7 . 9 8 . 8 2 13.8
log KCa
11.1
-15.2
The fourth ionization constant involves the ratio y v - ~ / y = v - ~ . The negative slope of Fig. 2
FRANCIS F.C l n ~ r i v rA N D A. E. MARTELL -- -
-.
__
_ _ _ I .
--.- .
-
1
, .
I 0
I
0.2
-
I
I
0.4
0.0
0.8
1.0
Pig. 2.-\'ariation of the dissociatioii constatits of ethyieticdiatninctetraacetic acid with ionic strcrigth: K I S = product of the first and second dissociation constants ; K Sand K 4 represent the third arid fourth dissociatioil conztants, respectively.
11.2 10.8
2 -
10.0 0.i;
92
I
i
11
U.2
0.4
I).(;
(1.8
1.o
VI;.
Fig. 3.--Variatioii of stability constant of the calciumethylenediamiiietetrancetate ailion with ionic strength.
indicates that this ratio decreases with increasing ionic strength. Therefore the reasonable conclusion may be drawn that the activity coefficient of the more highly charged ion is decreased to a greater extent. The p K , f values listed in Table I
Vol. 74
are not exact since , ' A a t infinite dilution was used in the calculation by equation 13. However, since the activity of water is not available for dilute salt solutions. it was not nossible to further refine the calculations. Figure 2 indicates that klzC and kdLalso vary in the same manner at low ionic strength. Kirkwoods has shown that extensive interaction takes place between dipolar ions and simple ions. On this basis a considerable decrease in activity coefficient of H4V with increasing ionic strength would be predicted. However, further increasing the number of charged groups in the amino acid should result in even greater interaction. It is to be qxpected, therefore, that the values of k l f and kdc decrease with increasing ionic strength. However, the bituation here seems to be somewhat more complicated in view of the fact that the constants increase again a t high ionic strength. This effect 14 suggestive of the use of higher terms in the Kirkwood And Debye-Huckel relationships, although these idealized equations would not be expected to .ipply to the present system. The cheldte stability constant, KcaC,is an even more striking example of the effect of ionic strength. This involves the ratio T L a - z T \ r - * / T C a V - - . One would expect a much greater change in KcaCwith ionic strength than has been noted for the acid dissociation constants, since the numerator contains a bivalent and tetravalent ion, while the denominator contains only a bivalent ion. The fact that the negative slope of Fig. 3 is much larger than those of Fig. 2 is in agreement with this concept. Comparison of the results of this investigation with published work on the salt effect of glycine and other simple amino acids indicates that the variation with ionic strength of the equilibrium constants involving ethylenediaminetetraacetic acid is much greater than that observed for ordinary dipolar ions. This is probably due to ( I ) the larger number of charges and polar groups in ethylenedianiinetetraacetic acid and ( 2 ) extensive deviation of the structure of this amino acid from the approximately spherical structural models used for the simple dipolar ions. Acknowledgment.-The authors are indebted to the U. S. Navy Office of Naval Research for the support of this investigation under contract Nonr5 96 ( 00) . \\C)RCE 5 f F R
.'i. hIA5bACHLbLllb
