David E. Goldberg
Brooklyn College City University of New York Brooklyn, New York
Formation constants of a Metal-Anionic Ligand System in Dioxane-Water
In a recent paper ( 1 ) the determination of formation ronstants of metal-amine systems was described. The determination of formation constants of anionic ligand complexes is of comparable research interest and is also an application of solution equilibrium measurements to modern research problems. The problem of obtaining data is more complicated for anionic ligand complexes than for the amine complexes berause both the chelating agent and the metal chelate are often insoluble in water. The calculation method depends on having all the species in one phase so that measurements of the conrentration of a single species a t each point in a titration allow the calculation of the concentrations of all the species a t that point. I n order to achieve the desired solubilities, dioxanewater mixtures are often employed, as first described by Calvin and Wilson (2). Use of this mixed solvent, however, accentuates the problem of obtaining true thermodynamic data rather than merely quotients of molarities. The solution to the latter problem was first attempted by Van Uitert (3, 4). He solved the stoichiometric equations a t one point for each constant t o be determined in the calculation of transition metal io11-0-diketone systems. Later Block and McIntyre (6) solved the problem of true thermodynamic constants for aqueous solutions. They also added an algebraic calculation method, which allows the use of more of the data than does the method of Van Uitert. Their method does away with the necessity of using successive approximations (6). The procedure described here combines the methods of Van Vitert and of Block and McIntyre, with subsequent modifications also included. This prordure is more difficult than the amine procedure ( 1 ) from an experimental viewpoint because of the necessity of using purified dioxane and from a calculation viewpoint because of the greater importance and variabilit,? of the activity coefficients. The discussion is appropriate for a study of various systems; acetylacetone, benzoylacetoue, and dibenzoylmethane are satisfactory ligands. Dipositive transition metal ions or uranyl ion can be used. Copper or nickel ions are most appropriate, although some copper romplexes have too great a stability to be handled conveniently. The Experiment
The apparatus used for the potentiometric titration has been described previously ( 1 ) . A glass electrode designed for high pH should be used. The titrations are performed as previously described ( I ) , with the following differences:
A precisely known quantity of metal ion, about 1 X moles, and a precisely known quantity of chelatiug agent, about 4 X 10W3moles, 75 ml of purified (3, 7) dioxane and 25 ml of distilled water are placed in the titration flask. This solution is titrated with standardized tetramethylammonium hydroxide, also in 76 vol dioxane (8). The volume of base added and the pH meter reading a t each point are recorded. Measurement of the association constaut of the anionic ligand with the proton is performed using the same procedure except for the exclusion of the metal ion.
0
C. 1
0.2
03
m*
Figure 1 .
Plot of m*
versus log
(I/?+).
Calculations
Van Uitert (3) has shown that Activity Coe&ients. the glass electrode can be calibrated t o measure hydrogen ion activity in aqueous dioxane. His factor, Uno, converts the pH meter reading, B, into activity of hydrogen ion for a range of dioxane-water mixtures up to 75 vol 7, dioxane. U E o is dependent on mole fraction dioxane alone, and not on concentrations of thr electrolytes in the solutions. By graphical interpolation of the data of Harned and Owen (9) on the mean activity coefficients for dioxane-water solutions of HCI, Van Uitert has been able t o approximate the activity coeffirient a t any concentration of electrolyte a t any mole fraction dioxane. Instead of recording l / y i , he reports the quantity log URo log I/?* (10). A convenieut short cut for these calculations is to plot log l / y * versus na* for a particular mole fraction dioxane. Such a plot is shown in Figure 1. The mean molarity, nz*, is determined for combinations of bi-, univalent and ~ n i - univalent , salt solutions from thr equation ( 11 ) :
+
Volume
40, Number 7, July 1963
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341
Acid Association Constants. For the reaction in which the anionic ligand associates with one proton, the following constants may be defined:' H+
+ Ch- Ft HCh
(1)
using the approximations (3)
Assuming the activity coefficientof a neutral species to be unity, and those of unipositive and uninegative ions to he approximately equal to a mean activity coefficient, r + , then Ka = q ~ l r ~ '
and those listed after equatiou (3). Defining fi as the average number of ligands bound per metal ion, one obtains
(4)
Defining Gn as the average number of hydrogen ions bound per Ch-, one obtains
Suhstitution from equation (2) leads to
Note that equation (14) is defined in terms of concentrations, and q, and q2 are used as opposed to KI and Kz . The concentration of free chelating agent, [Ch-j, may be determined as follows:
But also
boundhydrogen
fin = bound hydrogen ion/total ligand bound - total hydmgen - hydmgen
reacted
(7)
Cach
The hydrogen ion concentration may be calculated by the equation (S,4)
+ log Uao - log -1
(8)
Y*
where B is the pH meter reading in the nonaqueous medium, log Uno the correction for the difference between the pH meter reading and the activity of hydrogen ion in the nonaqueoussolution, and log l/r* is the activity coefficient correction to concentrations in the solutio~. Suhstitution of the value for log [H+] from equation (8) into equation (7), along with the calculable values of C,, allows solution for fin. Solution of equation (6) for q, PA =
Z H / ( ~- En)[HfI
(9)
allows the calculation of this quantity. The thermodynamic constant can be obtained from a revision of equation (4). log Kn
=
log q~
1 + 2 log Y*
[HChl = Cnm - COX- IHtl qnIH*lICh-I
+ [OH-I (1.5)
Hence,
dissociated
- hydrogen - hydrogen = Cnoh - Corn - ( [ H t I - [ O H - I ) Cnch - Con - [H+I + [OH-I +in =
-log [H+] = B
=
=
(10)
The q, needed in equation (16) may be obtained from K Hwith the activity coefficient in the metal ion solution. I t will be different in general from the value of q, obtained directly from the association ronstant titration a t fi" = 0.5. The quantity li may be determined as follows:
All of the terms of the last equation are obtainable from stoichiometrv or from ouantities nreviouslv calrulated. Using theUvalueso f ' s from equation il9) with the corresponding values of [Ch-] from equation (16), one may solve for the molarity quotients q, and qr by the method of Block and McIntyre (5). (Sample calculations may be found in ref. ( I ) . ) Calculation of K, and Kt is most easily accomplished by the rearrangement of equation (12) to the form log K, = log q,
Metal Ion Formation Constants. For the reactions
1 + 2 log Y*
(20)
Sample Calculations
there are definable the following constants:
' The use of brsckeb [ I nail1 represent concentrations; parenthesis ( ) will represent activities. Cx will represent stoichinmetrio concentrations of X. 342
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Journal o f Chemicol Educclfion
Data for the sampIe calculations were taken from ref. (S), pp. 148, 158. The acid dissociation ronstant calculation is based on the titratiou of acetylacetone with tetramethylammonium hydroxide; the formation constant calculation is based on the Ni(C104)raeetylacetone system. Acid Dissociation Constant. The point chosen has meter reading B = 11.07 when 1.43 ml of 1.202 M
Formation Constants. V = 100 ml; 75 vol % dioxane 4.00 mmole aretylacetone; 0.9i5 mmole Ni(Cl0,)n Titrsnt - 1.302 M (CH,),NOH First Point 0.25 100.25 0.975 - 9.73 100.25
Second Point 1.00 101 .oo
x 10-8
4.00 = 3.99 X 100.25
=
9.65 X 10-2
10-a
(1.3WV.25) = 3.25 (100.25)3.25 2 Coe 1.59(Cu - C o d 1.68 X 1.04 0.59
COX(mmole/ml)
R (pH meter reading)
+
m i 2 (see footnote 2) log U"0 log I/-,+ (from Fig. 1) - Ion- .IHtl. = B log UaO - log l / Y * [H+l log q~ = log Kn
+
[Ch-I = CHCI,- Coa
!????
101 .oo
- 2 log l / r + 11.62 -
('" :,,r'H!y-')
At first point (half-way through first step of reaction)
+ HCh + MerN+OH- = MChC + H 2 0 + Me,N+ dipositive ion = Cu - Con mipositive inn = [Me.N+] + [MCht] = 2 [MeJi+l - ~ Y O H M'+
Hence m, = 1.5R(Ca
- Cox) + 2 COX
tetramethylammonium hydroxide was added to a solution containing 3.44 mmoles of acetylacetone yielding a total volume of Ij3.0 ml. Log Urno= 1.04 for 75 ~ 0 1 % dioxane (Tahle I). 3.44 ",mole5 cmh
=
=
3m
second step of the reaction) MCh+
+ HCh + Me,N+OH-
= MCha
+ H20 + M a N f
there is no dipositive ion. The unipositive ion concentration may be calculated a t the end of the first step as 2 CM. As seen by the equation, the second step neither contributes or uses up net ~ositiveions in the titration vessel, replacing MCh+ with M a N t . Thus t h e n * = 2 CKthroughout the remainder of the titration.
Table 1.
Data from Figure 1 of Reference 10
6.49 X 10-2 M
,,,,
,
1.43 ml X 1.202 Af = 53.0 rnl m, = CON = 3.24 X 10-I M log UHa = 1.04 for 75 "01 godioxme log l/u+ = 0.69 1.04 - 0.69 = 11.42 -log [H+] = 11.07 [H+] = 3.80 X 10-l2 log K , (75% diorane) = 18.7 approx. (ref. (b), p. 662) [OH-] neghgible Con =
A t the second point in the titration (half-way through the
,,_,
+
1 RH q~ = ( 1 - fix) [H+] 3.80 X log pH = 11.42
log KH = log qe
Calculation of ql and qx may be done by the method of Block and McIntyre, as demonstrated in (1). log K I = log ql log K? = log q,
=
2.63 X-10"
+ 2 lag -Y1 = 11.42 + 2(0.69) = 12.80
+ 2 log l / y +
+ 2 log l l y i
= =
9.09 7.07
+ Z(0.59)
=
+ 2(0.61) =
10.27 S.29
Acknowledgment
The author is indebted to Dr. W. Canard Fernelins for his help and encouragement. Volume 40, Number 7, July 1963
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343
Literature Cited (1) GOLDBERG, D. E., J. CHEM.EDUC.,39, 328 (1962). (2) CALVIN,M., AND WILSON,K. W., J. Am. Chem. Soc., 67, 'Inn7 ,-"*",. 114A5> -"""
(3) VAN UITERT,L. G., Doctoral Dissertation, Pennsylvania
State University, 1952. (4) . . VANUITERT.L. G.. A N D HAAS.C. G.. J. Am. Chem. Soc.. 75, 451 (1953).
(5) BI.OCK,B. P., A N D MCINTYRE, G. H., JR.,J . Am. Chem. Soe., 75. . .,MR7 .... (19531~ ....,. (6) BJERRUM,J., "Metal Ammine Formation in Aqueous \
344
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Solution," P. Haase (7) WEISGBERGER, A.,
$
AND
Son, Copenhagen, 1941. PROSKAUER. E. 8 , "Organic Sol-
vents," Oxford, 1935, p. 139. (8) Kmo, H., Master's Thesis, Pennsylvania State University, 1959.
(8) HARNED, H. S., AND OWEN,B. B., "Tlle Physical Chemistry of Electrolytic Solutiuns," Reinhold, l e n . Yark, 1958,
pp. 717-8. (10) VANUITERT,L. G., AND FERNELITS. W. C., J. Am. rh'hem. Soe.. 76. 5887 (1954). (11) HARNED, H. S.,AND OWEN,B. B., o p . ?it., p. 10.
