April 20, 1954
INTERACTION OF ETHYLENEDIAMINETETRAACETATE AND ALKALINE EARTH IONS
2 153
[CONTRIBUTION OF DEPARTMENT OF CHEMISTRY OF CLARK UNIVERSITY 1
Thermodynamic Quantities Associated with the Interaction between Ethylenediaminetetraacetate and Alkaline Earth Ions B Y FRANCIS F. CARINIAND ARTHURE. MARTELL RECEIVED NOVEMBER10, 1953 Thermodynamic equilibrium constants are reported for reactions between M +2(aq)and V-4(aq), where M + 2 is a n alkaline earth ion, and V-4 is the tetranegative anion of ethylenediaminetetraacetic acid. The calculations were carried out with , II,V "-4(m4), AgC1-Ag a t various temperatures e.1n.f. data obtained from cells of the type Pt-Hz, K+(ml), M + 2 ( m ~ )Cl-(wzs), and ionic strengths. For each temperature the data were extrapolated t o infinite dilution with the aid of the Debye-Huckel activity coefficient relationship, and the thermodynamic chelate formation constant was evaluated. The thermodynamic quantities Ar?", AH" and A S " are calculated and discussed in the light of present theories of metal chelate formation in aqueous solution.
The reasons for abnormally high affinity of ethylenediaminetetraacetate and iminotriacetate anions for the alkaline earth ions have never been clarified in the light of the strongly-basic properties of these metal ions. Indeed, before the discovery of these cornplexing agents, the alkali and alkaline earth ions were considered to be examples of cations which did not form coordination compounds. Perhaps the most reasonable suggestion advanced to explain the high stability of chelates of this type is that of Calvin and Bailes.' According to this theory, the entropy increase associated with the formation of chelate rings is considered to make a major contribution to the stability as measured by the equilibrium formation constant. This idea was more recently carried a step further and extended to the calcium ethylenediaminetetraacetate chelate.2 The purpose of this investigation is the determination of the experimental values of AF', AHo and A S o associated with chelate formation between the ethylenediaminetetraacetate ion and magnesium, calcium, strontium and barium ions. Information of this nature would be helpful in correlating the entropy effect with the formation of metal chelates of abnormally high stability. With few exceptions, previous work on the stability of metal chelates has not resulted in the determination of thermodynamic constants, since most investigations were made in a supporting electrolyte having a concentration much higher than that of the chelate compound. The only thermodynamic chelate stability constants known to the authors of the present paper are that of Kety3 for lead" and citrate ions, of Calvin and Zebroski4for thenoyltrifluoroacetone and thoriumIv ions, and of Carini and MartelP for ethylenediaminetetraacetate and calcium ions. In the present paper the latter work is extended to other alkaline earth ions, and to measurements over a series of temperatures for the calculation of heats and entropies of chelate formation.
Experimental The experimental method employed in this research has not been applied previously to the determination of metal chelate stability constants. In principle, i t consists of the (1) M. Calvin and R. Bailes, THISJOURNAL, 68, 949 (1946). (2) A. E. Martell and M. Calvin, "Chemistry of the Metal Chelate Compounds," Prentice-Hall, Inc., New York. N. Y..1952. p. 151. (3) 5 Kety, J . Biol. Chem., 142, 181 (1942). (4) I3 L Zehroski, Thesis, University of California, 1947. ( 5 ) F Carini and A E Martell. THISJOURNAL, 74, 5745 (1952).
measurement of hydrogen ion activities in solutions containing a n alkaline earth metal ion, ethylenediaminetetraacetic acid, and inert electrolyte, at equilibrium. This was accomplished by measurement of the e.1n.f. of the cell
Pt-Hz, EC+(mi), M+'(?rtz), Cl-(mj), € L V " - 4 ( ~ 4 )AgCI-Ag , (1)
where M + 2represents an alkaline earth metal ion, V-4 is the ethylenediaminetetraacetate anion, and n may be varied from 0 to 2. The e.m.f. data thus obtained were extrapolated to infinite dilution, allowing the calculation of the standard free energy change, AF', for the reaction M+l(aq)
+ V-4(aq)--+
MV-2(aq)
Apparatus and Materials.-A Leeds and n'orthrup type R potentiometer was used v ith a cell similar to t h a t described in a previous publication.s The platinum electrodes wcre prepared according t o the directions given by Weissberger.6 The silver-silver chloride electrodes were prepared by the method of Shedlovsky and MacInnes.' The ethylenediaminetetraacetic acid, obtained through the courtesy of the Bersworth Chemical Company, Framingham, Massachusetts, was further purified by two successive recrystallizations from water. Carbon dioxidefree potassium hydroxide, prepared from silver oxide and potassium chloride by the method of Schwarzenbach and Biedermann,* was standardized against potassium acid phthalate as recommended by Kolthoff and S a ~ ~ d e l lThe .~ alkaline earth chloride solutions were standardized by the Yolhard niethod.'O All solutions made up i n the course of this investigation were either prepared on or corrected to a molal basis. Procedure and Experimental Data.-The e.m.f. of cell I was first measured for definite values of mi, m2, l l z ~ and md at 25'. The cell was then cooled to approximately 0" and the initial reading was taken. The temperature was then raised by 5" increments, and e.m.f. readings were taken after equilibrium was established. I n most cases, 5-10 hours was suficierit to obtain reproducible readings, which were then found to remain constant for as long as 3 or 4 days. At 25" a check was made for reproducibility of the initial reading. The solutions employed in cell I were made up so as to give a constant ratio of (mM+Z)(mAnT"-') :mMr-z: mcl-, as is required for the extrapolation method described below (equation 13). In the more dilutr solutions there was a tendency for this ratio to be changed by greater dissociation of the metal chelate. Under these conditions the ratios were maintained by appropriate addition of potassium hydroxide. These ratios were kept constant for each temperature investigated. (6) A. Weissherger, "Physical Methods of Organic Chemistry," Second Edition, Vol. 11, Interscience Publishers, Inc., New York, N . Y., 1949, p. 1722. (7) T. Shedlovsky and D. A. MacInnes, THIS JOURNAL, 68, 1970 (1936). (8) G. Schwarzenbach and W. Biedermann, Helw. Chim. Acta. S1, 331 (1948). (9) I. M. Kolthoff and E. B . Sandell, "Textbook of Quantitative Inorganic Analysis," Revised Edition, The Macmillan Co., New York, N . Y., 1948, p. 553. (IO) W. Scott, "Standard Methods of Chemical Analysis," Fifth Edition, Vol. I, D. Van Nostrand Co., Inc., New York, N . Y.,1930, p. 271.
FRANCIS F. CARINIAND ARTHURE. MARTELL
2154
Vol. 76
TABLEI I,
“C.
Metal
0
h k Ca Sr Ba
5
E.m.f. (mv.) of cell I 11111
653.18 539.91 628.95 621.25 657.29 542.06 635.48 624.78 661.67
hlg
Ca Sr BCL h k
10
c‘l
544.65 ij10.77 Ij28,41
Sr B‘l hlg Cd Sr
15
6 6 j . 67 546.92 645.66 631.93
Bd 20
669.11
hfg Ca Sr Ba M g
25
549.30 650.74 635.67 673.06 X5l. 26 654.43 639.05 677.20 553.30 658 . 37 642.37
Cd Sr Ba Mg
30
c‘1 Sr Hd
Llct al Acid >Ictal Acid hletal Acid Metal Acid a
>I g
643.15 530.32 624.02 610.69 647.13 532.28 G30.41 614.19
638.16 524.62 616.00 606.84 642.17 526.50 622.30 til0, 21 (i46. 16 528. 60 ii27 ,29 titX.58
651.28 ,534. ti5 ( K j 5 . 55 617. 74
fi54.97 .53A , 86
649, 81)
,-):30,74 632. 16 616.73 653.00 532.78 636.83 620.20 656.62 534. 46 640.7; 623.26 660.36 536.2 1
640.45 621.19 658,30 538.95 645.27 624.39 662.00 540. 79 649.34 627. 63 665. 83 5X2.65 6-52,9ti wn. 77
fi43.1X
62G. in
P P
P P
P65
634.10 521.81 613.56 602.77 637.97
630.03 518,45 610. i4
515 36 606. 08
600.01 033.82
523.41
520.26
619. 7rj ti06, 02
616.95
517.22 612.15
GO3 .37 637.68
ti41,89 .72.i, 77 ti24, T,:i 609. :j 1 ti45.51
522.51 ti2 1, x4 (iO6. 5fj
519.26 617.29
t i l 1 .20
527,s:j 629.42 612.50 648.64 529.76 633.93 til5.90
524.51
626,27
521.25 tj21.59
609.75
614.28 526.62 630.90 613.22 647.75 527.96 634. 79 G15,92 651.28 329.78 ( 5 3 8 ,46
652,18
53 1 , 4 5 638.16 619.00 655.85 3 2 . 97 612.01 621.92
523.01 626 07
524 64 630 06
526 17
ti33.65
li18.80
AIolnl coiirctitratioti X 1113 t i ,Si4 Il).890 14.i)Ol 17.119 21 ( l f i ( ) , 8572 1.:i534 1 ,7084 2,0626 2.5132 J;L816 21.643 28.66 38.14 32,89 :: ,249 2,1957 4.214 4.481 5.006 T ,283 9.153 13,246 17.021 14.978 1.1451 1.8306 2,061 2.629 2,320 22.32 13.342 27.29 33.02 37.49 3.355 4,102 5.649 2.005 4.963 etc., , differ for each e.m.f. measurement, and may be found as points in Fig. 1. ,
c ‘1 Sr Ba
The values of
U P
1120
PI, pz,
~
3
Sample e.m.f. data for cell I obtained a t 0, 5 , 10, 15, 20, 25 and 30” for each of the four alkaline earth ions a t various ionic strengths are given in Table I. Because of space lirnitations only one value is given for each set of conditions, and all duplications and minor variations are omitted.
e.m.f. of cell I is given by the
Calculations.-The equation E = E”
- XT 111 uR+1?2CI-YCl-
(1)
43 90 5 ill 20 39
3,141
third and fourth acid dissociation equilibria of the amino acid HzV-2
Hf
HV-3
+ HV-a + V-4
H+
The corresponding thermodynamic acid dissociation constants are defined by
where y represents activity coefficient alld the other terms have their usual meaning. The stability of the metal chelate is defined in terms of the chemical equilibrium
+ V-4
MC2
liearratigenient of equations ( Z ) , ( 3 ) , and (4) gives
hIV-2
where M+2 represents an alkaline earth ion and VP4 represents the tetravalent anion of ethylenediaminetetraacetic acid. The corresponding stability constant expression is =
=
Yal-4
(2)
At the pH employed in the experimental solutions for cell I, i t is necessary to take into account the
‘ E 2 g T
+ log
17zc,-
(5)
aMv-z
Combination of equations 1 and 5 relationship
( L \ I T j aM+2
(ax+z X aH,vy k3k~K)”’ = -‘/a
log
in the
April 20, 1954
INTERACTION OF ETHYLENEDIAMINETETRAACETATE AND ALKALINEEARTH IONS 2 155
Rearrangement of 6 with the substitution of msys for as and of @,H for ( E - E0)F/2.3 RT log m a -, according to standard practice, results in the relationship
+
PwH
-
'/2(pk3
+
Pk4)
+ '/Jog mMC' x
mHzT2
=
mhfv-2
The activity coefficient term was defined as a function of ionics trength in terms. of an arbitrary parameter, a*, the "distance of closest approach" obtained from the Debye-Hiickel relationship
ASo =
TABLE I1 EVALUATION OF ACTIVITYCOEFFICIENTS Metal ion
t , OC.
Mg+2
0 5 10 15 20 25 30 0 6 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30
ea-' 2
where A , Z and B have their usual significance. The quantity @ was evaluated by the method described by Hamer and Acree.l' Since the properties of each ionic species present in the mixture are additive functions of those of the individual ions present, i t follows that ZPmi = Z(l/n)Pinpi. If the ionic strength contribution of each ion is some fraction of the total ionic strength (ie., pi = constant X p where p , q and r are constants for a specified ratio of salts) and since pi = nmi and p = Z p i , it follows that
Sr +2
Ba +2
The relationship derived from equation 8 to fit the requirements for the extrapolation of the quantities of equation 7 to infinite dilution is
AHo - AFO
a*
6.0 6.0 6.0 6. 1 0.1 6.2 0.2 10.3 10.4 10.4 10.3 10.6 10.7 10.8 10.5 10.6 10.7 10.8 10 9 11.0 11.o 6.0 6.1 6 2 ti.4 8 5 6.6 6.7
B
log r
0.7 .7 .6 .0 .5 .5 .6 1.0 1.o
2.759 2.804 2,856 2.914 2.953 3,008 3.026 1.025 1.087 1.156 1.235 1 ,309 1,380 1.446 1.716
0.9 .9 .9 .9
.9 0.8 .8 c
. I
.7 .7 .6 .5 0.6 .6 .6 .A .tj
.A .ti
1,840
1.932 2.023 2.116 2.189 2,248 0.811 ,840 .879 ,934 ,983 1,029 1.069
The values of p obtained by means of equa15 Log lie tion 9 and the values arbitrarily selected for LogKcd h the constant a* so as to give a straight-line lo extrapolation of equation 7 with minimum slope were substituted into equation 10 to r. give values of log y., equal to the quantity ,lo5 -1 / z log ( Y M + ~X Y H ~ V X- ~ ~ c 1 - I m v for -4 7 each temperature and each metal ion system. e The values of log mM+2( m H z V - q ' m M V - 2 )were llo calculated and listed in Table I1 as log r , 7 along with the values of a* and p, determined as described above. ".IO. All the terms in the resulting relationship for equation 7 with the exception of K were placed on the left side of the equation and extrapolated as a function of ionic strength L o g K u to infinite dilution. Thus, the thermodynamic constant K was evaluated for each temperature investigated. The graphical extrapolations to infinite dilution are given in Fig. 1. The values of pk3 and pkr used in equation 7 were reported in an earlier publication. l 2 The standard thermodynamic auantities AFO, A H o and A S o were calculated 6y means Fig. 1.-Extrapolation of potentiometric data to infinite dilution of the usual relationships (see equation 7). AFO = -2.303 RT log K (11) The equilibrium constants and thermodynamic AHQ = _-___ 2.303 RTiT2 (log kz - log ki) constants calculated by means of equations 7, 11, (12) Tz - T I 12 and 13 are given in Table 111. (11) W. Hamer and S. Acree, J. Research iVall. Bur. Standards, S6, 381 (1945). (12) F. F. Carin1 and A. E. Martell. THISJ O U R N A L , 75,4810 (1~53).
Discussion From the equilibrium formation constants listed
3156 Since the value of A l l o determined in this investigation is quite small compared to heats of hydration, it seeiiis that the heats of forination of lug 6 the metal chelate bonds are of approximately the !! i!" 8 11.14 'J 02 s.01 same magnitude as the ion-dipole bonds of the J 11.12 9.24 8 O(i 7.9
