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The partial molar entropies of aqueous chloro complexes of Cd(II)
.I. Chem. Thermodynamics 1910, 2, 193-796
The partial molar entropies aqueous chloro complexes RONALD
H. PROVOST
Department of Chemistry, St. Michael’s Winooski Park, Vermont 05404, U.S.A. CLAUS
of of Cd(ll)t
College,
A. WULFF:
Department Burlington,
of’ Chemistry, The University of Vermont, Vermont 05401, U.S.A.
(Received 13 April
1970)
The enthalpies of reaction of a Cd0 + Cd(OH)2 mixture with aqueous HCl + HC104 solutions of variable composition but constant ionic strength, Z = 1 mol kg-‘, are presented. The results are interpreted to derive enthalpy increments for the simultaneous reactions leading to the three reported chloro complexes of Cd(I1). Several methods of extrapolating the results to the conventional standard state are discussed. The results may be characterized by the following partial molar entropies: CdCl+ (aq), 8.,; CdCl,(aq), 23; and CdCl; (aq), 48 cal mol-’ K-l.
1. Introduction The literature contains many reports concerning equilibria in aqueous solutions containing cadmium and chloride ions. (ly2) The important species in solutions of moderate chloride concentration appear to be those described by the equations: Cd2+(aq) + Cl-(aq) = CdCl’(aq), (1) Cd2+(aq) + 2Cl-(aq) = CdCl,(aq), (2) Cd2+(aq)+ 3Cl-(aq) = CdCl;(aq). (3) There is relatively little accord on values for the thermochemical quantities describing these reactions other than for a value of pK, = (2.0 + 0.1) and the observation that AH, is small in magnitude. The existing values for AH and AS have been derived from the temperature coefficients of extrapolated equilibrium data and contain the usual uncertainties associated with such methods. Of the various reports of equilibrium data that have been published, that of Vanderzee and Dawsonc3) appears to be one of the most reliable, with results covering a range of ionic strength and temperature. This report contains results for the enthalpies of solution of a Cd0 + Cd(OH), system in aqueous mixtures of HCl and HClO,. This solvent system was chosen on the basis of a reportc4’ that HClO, does not form complexes with aqueous Cd(I1). t Taken, in part, from a Ph.D. Thesis presented by R.H.P. to The University of Vermont, 1968. $ Correspondence addressee.
794
R. I-1. PROVOST
AND
C. A. WULFF
2. Experimental Methods for preparing samples of Cd0 and Cd(OH), that are suitable for solution thermochemistry have been detailed in a previous paper.(5) A portion of the Cd(OH), was dehydrated to produce a mixture of CdO, Cd(OH),, and y-Cd(OH),. Although this sample is not well characterized, it has the advantage of rapid solubility in 1 mol kg-l acid mixtures. The enthalpies of reaction of this mixture with HCl + HC104 solutions of constant ionic strength (Z = 1 mol kg-‘) were determined at (25.0 + 0.1) “C in a solution catorimeter described elsewhere. (6) The experimental results are presented in tabIe I where cal = 4.184 J. TABLE
aa,, mmol
AH kg-l
kcal mol-1
1. Enthalpies
.~ m(HC1) mol kg-’
m(HClOJ mol kg-’
3.63 3.79 3.74
-16.77 - 16.68 -16.66
0.0
1.0
3.61 3.64 3.57
-16.65 -16.62 -16.63
0.4
0.6
of reaction
(Z = 1 mol kg-‘)
mtotdC4 mmol kg-’
AH kcal mol-1
m(HCI) ___ mol kg-l
m(HCIOJ -__ mol kg-l
3.80 3.70
-16.63 -16.66
0.6
0.4
3.52 3.87 3.74
-16.42 -16.43 - 16.42
0.8
0.2
3.61 3.80
-16.08 -16.19
1.0
0.0
Results were interpreted in terms of the relations AH = AHo-~1AH,+u,AH,-cc,AH3, (4) where a, represents the fraction of cadmium in a complex with n chlorides and AH,, refers to the enthaply increment (at Z = 1 mol kg-‘) for the formation of that complex. Values of a,, were computed from the appropriate equilibrium quotients reported by Vanderzee and Dawson. (3) Over the range of HCl molalities covered in the present study, the x,, values lay between the limits: CI~,0.202 to 0.42,; ~1~,0.45, to 0.5&,; and CI~,0.06, to 0.24,. The results were fitted to the assumed equation by several graphical and analytical methods to obtain estimates of the uniqueness of fit (i.e. the uncertainties to be assigned to the “best” values). The only restriction adopted was that AH, be small in magnitude, less than + 1 kcal mol-‘. A “best” fit was obtained with AH, = (0.1 k 0.5) kcal mol-‘, AH2 = (0.7 &- 0.5) kcal mol-‘, and AH3 (3.6 & 1.O) kcal mol- ‘. The uncertainties assigned to these AH values are such that the data can be reproduced with a correlation coefficient of 0.95, or better, by substituting into equation (4) the extreme values of AH. Extrapolation of the AH values for Z = 1 mol kg- ’ to the usual standard state conditions can be accomplished in several ways-none of which is entirely satisfactory. In two recent studies(‘*‘) involving the dissolution of a metal oxide in strong acid, the results could be fitted (in terms of formal ionic charges, Z) to the equation: AH = AH” +0.28A(c Z’)(m,/mol kg - I)“( 1 +mM/mA),
CHLORO
COMPLEXES
OF Cd(U)
795
for acid molalities mA up to 1 mol kg- ’ and metal ion molalities mM comparable to those used in this study. Assuming that the same relation is valid here, we calculate AH; = (1.2 + 0.5) kcal mol-‘, mole, AH,” = (1.0 rt 0.5) kcal mol-‘, and AH; = (5.3 * 1.0) kcal mol-‘. Another extrapolation can be obtained using the molality dependence adopted by Vanderzee and Dawson (3) in the treatment of their results. If we accept their we calculate AH; = (0.5 f 0.5), AH; = values for (AZZ”-AH(Z = 1 mol kg-‘)}, -(0.2 + 0.5), and AH: = (4.1 + 1.0) kcal mol-‘. A third method of extrapolation can be used based on average values of relative apparent molal enthalpies for compounds of a given charge type. For example, the following sequence of reactions is used to derive AH;: AH = (0.6 10.2) kcal mol-l CdCl,(aq) = CdCI,(Z= 1 mol kg-‘); CdCI,(Z= 1 mol kg-‘) = CdCl+Cl-(I= 1 mol kg-‘); AH = (0.1 t 0.5) kcal mol-’ CdCI+Cl-(I= 1 mol kg-‘) AH = (0.0 + 0.2) kcal mole1 = CdCl+(aq) + Cl-(aq); _-.- -.- ~~-_ .^ ~~~~-. AH; = (0.7 & 0.5) kcal mol” Cd’+(aq) f Cl-(aq) = CdCl+(aq); The AH values (0.6 _+0.2) and (0.0 -t 0.2) kcal mol- ’ are mean values for the alkaline earth and alkali halides taken from NBS Circular 500.@’ In a similar manner, values of AH; = - (0. I + 0.5) and AH: = (4.2 & 1.O) kcal mol-’ can be obtained. From these results we average: AH; = (0.8 + 0.5), AH; = (0.2 &- l.O), and These choices are somewhat arbitrary, but the AH; = (4.5 f 1.0) kcal mol-‘. uncertainties assigned to the AH values are large enough so that the additional uncertainty created in extrapolation is not serious. For the calculation of S; for the complex species we choose the extrapolated equilibrium constants of Vanderzee and Dawson c3) for consistency rather than the slightly different values that may be obtained from recent tabulated data.“’ For the formation of CdCl+(aq) we have AG,” = -2.7, kcal mol-’ leading to AS: = 11.8 cal mol- ’ K-’ and to S; = (8.3 _+2) cal mol-’ K-l for CdCl+(aq). The latter value is consistent with partial molar entropies of - 17.0 cal mol- ’ K- 1,(5) and 13.5 cal mol-’ K-‘,‘9’ for Cd’+(aq) and Cl-(aq), respectively. For AG; we adopt -3.6, kcal mol-’ leading to AS,0 = 1.30 cal mol-’ K-’ and to ST = (23 rt 3) cal mol-’ K-’ for CdCl,(aq). In a similar manner we take AG: = -2.8s kcal mole1 and calculate AS: = 24.s and S,O= (48 + 3) cal mol- ’ K- ’ for CdCl;(aq). Uncertainties in the S,Ovalues correspond to those in the appropriate AH,” values. The value calculated for CdCl+(aq) differs by some 2 cal mole1 K-’ from that chosen by the authors of NBS Tech. Note 270-3. (‘I The source of this difference is in AGY for which Wagman et al. give -3.7 kcal mol-‘, corresponding to a dissociation constant of about 2 x 10e3 for the CdCl+(aq) complex. The Bureau’s choice is considerably smaller than experimental values(” 2, and its source is unidentified. The S,Ocalculated for CdCl,(aq) is 5 cal mol- ’ K-’ less than that tabulated in NBS Tech. Note 270-3.‘9) Of this, 3 cal mol - ’ K- ’ can be attributed to the different choice for AG; (-4.6 kcal mol-‘). Powell and Latimer”‘) have suggested an equation by which the partial molar entropy of an uncharged species may be calcu-
796
R. H.
PROVOST
AND
C. A. WULFF
lated. Data for the calculation of the Sint, in their notation, are not available, but substitution of the corresponding data for HgCl,” i) with a correction for the value of a principal vibrational frequency”” leads to S; = 26 cal mol-’ K-’ for CdCl,(aq). The S,O calculated for CdCl;(aq) agrees with that given in NBS 270-3.“’ The agreement is somewhat fortuitous since the Bureau’s choice for AG,” is about 1 kcal mol-’ more negative than ours. This difference is, however, within the experimental uncertainty we have assigned to our S;. In summary, we tabulate the following for the aqueous chloro complexes of Cd(H). These values are consistent with our thermochemistry and with the equilibrium data of Vanderzee and Dawson.‘3’ AH;
CdCl+(aq) CdCMaq)
CdCl;(aq)
kcal mol-’ -57.1 - 97.4 - 133.4
AG;
kcal mol- ’ - 52.6
- 85.0 -115.5
S;
cal mol- ’ K-i 8‘3
23 48
We thank Dr. Paul G. Abajian for his assistance with the experimental work. The financial support of the National Aeronautics and Space Administration through Sustaining Grant NGR-46-001-008 to the University of Vermont is gratefully acknowledged. REFERENCES 1. Sillen, L. G. ; Martell, A. E. Stub&y Constants of Metal Ions Complexes. The Chemical Society: London. 1964. 2. Sahu, G.; Prasad, B. J. Indian Chem. Sot. 1969,46, 233. 3. Vanderzee, C. E.; Dawson, H. J. J. Amer. Chem. Sot. 1953, 15, 5659. 4. Jena, P. K.; Prasad, B. J. Indian Chem. Sot. 1954, 31,480. 5. Provost, R. H.; Wulff, C. A. J. Chem. Thermodynamics 1970, 2,000. 6. Stephenson, C. C.; Abajian, P. G.; Provost, R. H.; Wulff, C. A. J. Chem. Eng. Data 1968, 13, 191.
7. Abajian, P. G.; Wulff, C. A. J. Chem. Eng. Data 1969, 14, 476. 8. Rossini, F. D.; Wagman, D. D.; Evans, W. H.; Levine, S. ; Jaffe, I. Selected Values of Chemical Thermodynamic Properties. US. National Bureau of Standards Circular 500. U.S. Govt. Printing Office: Washington, D.C. 1952. 9. Wagman, D. D. ; Evans, W. H. ; Parker, V. N. ; Halow, I.; Bailey, S. M. ; Schumm, R. H. U.S. Nat. Bur. Std. Tech. Note 2763. U.S. Govt. Printing Office: Washington, D.C. 1968. 10. Powell, R. E.; Latimer, W. M. J. Chem. Phys. 1951, 19, 1139. 11. Kelley. K. K.; King, E. G. Entropies of the Elements and Inorganic Compoands. U.S. Bureau of Mines Bull. 592. U.S. Govt. Printing Office: Washington, D.C. 1961. 12. Kohlrausch, K. W. F. Ramanspektren. Akademische Verlagsgesellschaft Becker and Erler: Leipzig. 1943.
The partial molar entropies aqueous chloro complexes RONALD
H. PROVOST
Department of Chemistry, St. Michael’s Winooski Park, Vermont 05404, U.S.A. CLAUS
of of Cd(ll)t
College,
A. WULFF:
Department Burlington,
of’ Chemistry, The University of Vermont, Vermont 05401, U.S.A.
(Received 13 April
1970)
The enthalpies of reaction of a Cd0 + Cd(OH)2 mixture with aqueous HCl + HC104 solutions of variable composition but constant ionic strength, Z = 1 mol kg-‘, are presented. The results are interpreted to derive enthalpy increments for the simultaneous reactions leading to the three reported chloro complexes of Cd(I1). Several methods of extrapolating the results to the conventional standard state are discussed. The results may be characterized by the following partial molar entropies: CdCl+ (aq), 8.,; CdCl,(aq), 23; and CdCl; (aq), 48 cal mol-’ K-l.
1. Introduction The literature contains many reports concerning equilibria in aqueous solutions containing cadmium and chloride ions. (ly2) The important species in solutions of moderate chloride concentration appear to be those described by the equations: Cd2+(aq) + Cl-(aq) = CdCl’(aq), (1) Cd2+(aq) + 2Cl-(aq) = CdCl,(aq), (2) Cd2+(aq)+ 3Cl-(aq) = CdCl;(aq). (3) There is relatively little accord on values for the thermochemical quantities describing these reactions other than for a value of pK, = (2.0 + 0.1) and the observation that AH, is small in magnitude. The existing values for AH and AS have been derived from the temperature coefficients of extrapolated equilibrium data and contain the usual uncertainties associated with such methods. Of the various reports of equilibrium data that have been published, that of Vanderzee and Dawsonc3) appears to be one of the most reliable, with results covering a range of ionic strength and temperature. This report contains results for the enthalpies of solution of a Cd0 + Cd(OH), system in aqueous mixtures of HCl and HClO,. This solvent system was chosen on the basis of a reportc4’ that HClO, does not form complexes with aqueous Cd(I1). t Taken, in part, from a Ph.D. Thesis presented by R.H.P. to The University of Vermont, 1968. $ Correspondence addressee.
794
R. I-1. PROVOST
AND
C. A. WULFF
2. Experimental Methods for preparing samples of Cd0 and Cd(OH), that are suitable for solution thermochemistry have been detailed in a previous paper.(5) A portion of the Cd(OH), was dehydrated to produce a mixture of CdO, Cd(OH),, and y-Cd(OH),. Although this sample is not well characterized, it has the advantage of rapid solubility in 1 mol kg-l acid mixtures. The enthalpies of reaction of this mixture with HCl + HC104 solutions of constant ionic strength (Z = 1 mol kg-‘) were determined at (25.0 + 0.1) “C in a solution catorimeter described elsewhere. (6) The experimental results are presented in tabIe I where cal = 4.184 J. TABLE
aa,, mmol
AH kg-l
kcal mol-1
1. Enthalpies
.~ m(HC1) mol kg-’
m(HClOJ mol kg-’
3.63 3.79 3.74
-16.77 - 16.68 -16.66
0.0
1.0
3.61 3.64 3.57
-16.65 -16.62 -16.63
0.4
0.6
of reaction
(Z = 1 mol kg-‘)
mtotdC4 mmol kg-’
AH kcal mol-1
m(HCI) ___ mol kg-l
m(HCIOJ -__ mol kg-l
3.80 3.70
-16.63 -16.66
0.6
0.4
3.52 3.87 3.74
-16.42 -16.43 - 16.42
0.8
0.2
3.61 3.80
-16.08 -16.19
1.0
0.0
Results were interpreted in terms of the relations AH = AHo-~1AH,+u,AH,-cc,AH3, (4) where a, represents the fraction of cadmium in a complex with n chlorides and AH,, refers to the enthaply increment (at Z = 1 mol kg-‘) for the formation of that complex. Values of a,, were computed from the appropriate equilibrium quotients reported by Vanderzee and Dawson. (3) Over the range of HCl molalities covered in the present study, the x,, values lay between the limits: CI~,0.202 to 0.42,; ~1~,0.45, to 0.5&,; and CI~,0.06, to 0.24,. The results were fitted to the assumed equation by several graphical and analytical methods to obtain estimates of the uniqueness of fit (i.e. the uncertainties to be assigned to the “best” values). The only restriction adopted was that AH, be small in magnitude, less than + 1 kcal mol-‘. A “best” fit was obtained with AH, = (0.1 k 0.5) kcal mol-‘, AH2 = (0.7 &- 0.5) kcal mol-‘, and AH3 (3.6 & 1.O) kcal mol- ‘. The uncertainties assigned to these AH values are such that the data can be reproduced with a correlation coefficient of 0.95, or better, by substituting into equation (4) the extreme values of AH. Extrapolation of the AH values for Z = 1 mol kg- ’ to the usual standard state conditions can be accomplished in several ways-none of which is entirely satisfactory. In two recent studies(‘*‘) involving the dissolution of a metal oxide in strong acid, the results could be fitted (in terms of formal ionic charges, Z) to the equation: AH = AH” +0.28A(c Z’)(m,/mol kg - I)“( 1 +mM/mA),
CHLORO
COMPLEXES
OF Cd(U)
795
for acid molalities mA up to 1 mol kg- ’ and metal ion molalities mM comparable to those used in this study. Assuming that the same relation is valid here, we calculate AH; = (1.2 + 0.5) kcal mol-‘, mole, AH,” = (1.0 rt 0.5) kcal mol-‘, and AH; = (5.3 * 1.0) kcal mol-‘. Another extrapolation can be obtained using the molality dependence adopted by Vanderzee and Dawson (3) in the treatment of their results. If we accept their we calculate AH; = (0.5 f 0.5), AH; = values for (AZZ”-AH(Z = 1 mol kg-‘)}, -(0.2 + 0.5), and AH: = (4.1 + 1.0) kcal mol-‘. A third method of extrapolation can be used based on average values of relative apparent molal enthalpies for compounds of a given charge type. For example, the following sequence of reactions is used to derive AH;: AH = (0.6 10.2) kcal mol-l CdCl,(aq) = CdCI,(Z= 1 mol kg-‘); CdCI,(Z= 1 mol kg-‘) = CdCl+Cl-(I= 1 mol kg-‘); AH = (0.1 t 0.5) kcal mol-’ CdCI+Cl-(I= 1 mol kg-‘) AH = (0.0 + 0.2) kcal mole1 = CdCl+(aq) + Cl-(aq); _-.- -.- ~~-_ .^ ~~~~-. AH; = (0.7 & 0.5) kcal mol” Cd’+(aq) f Cl-(aq) = CdCl+(aq); The AH values (0.6 _+0.2) and (0.0 -t 0.2) kcal mol- ’ are mean values for the alkaline earth and alkali halides taken from NBS Circular 500.@’ In a similar manner, values of AH; = - (0. I + 0.5) and AH: = (4.2 & 1.O) kcal mol-’ can be obtained. From these results we average: AH; = (0.8 + 0.5), AH; = (0.2 &- l.O), and These choices are somewhat arbitrary, but the AH; = (4.5 f 1.0) kcal mol-‘. uncertainties assigned to the AH values are large enough so that the additional uncertainty created in extrapolation is not serious. For the calculation of S; for the complex species we choose the extrapolated equilibrium constants of Vanderzee and Dawson c3) for consistency rather than the slightly different values that may be obtained from recent tabulated data.“’ For the formation of CdCl+(aq) we have AG,” = -2.7, kcal mol-’ leading to AS: = 11.8 cal mol- ’ K-’ and to S; = (8.3 _+2) cal mol-’ K-l for CdCl+(aq). The latter value is consistent with partial molar entropies of - 17.0 cal mol- ’ K- 1,(5) and 13.5 cal mol-’ K-‘,‘9’ for Cd’+(aq) and Cl-(aq), respectively. For AG; we adopt -3.6, kcal mol-’ leading to AS,0 = 1.30 cal mol-’ K-’ and to ST = (23 rt 3) cal mol-’ K-’ for CdCl,(aq). In a similar manner we take AG: = -2.8s kcal mole1 and calculate AS: = 24.s and S,O= (48 + 3) cal mol- ’ K- ’ for CdCl;(aq). Uncertainties in the S,Ovalues correspond to those in the appropriate AH,” values. The value calculated for CdCl+(aq) differs by some 2 cal mole1 K-’ from that chosen by the authors of NBS Tech. Note 270-3. (‘I The source of this difference is in AGY for which Wagman et al. give -3.7 kcal mol-‘, corresponding to a dissociation constant of about 2 x 10e3 for the CdCl+(aq) complex. The Bureau’s choice is considerably smaller than experimental values(” 2, and its source is unidentified. The S,Ocalculated for CdCl,(aq) is 5 cal mol- ’ K-’ less than that tabulated in NBS Tech. Note 270-3.‘9) Of this, 3 cal mol - ’ K- ’ can be attributed to the different choice for AG; (-4.6 kcal mol-‘). Powell and Latimer”‘) have suggested an equation by which the partial molar entropy of an uncharged species may be calcu-
796
R. H.
PROVOST
AND
C. A. WULFF
lated. Data for the calculation of the Sint, in their notation, are not available, but substitution of the corresponding data for HgCl,” i) with a correction for the value of a principal vibrational frequency”” leads to S; = 26 cal mol-’ K-’ for CdCl,(aq). The S,O calculated for CdCl;(aq) agrees with that given in NBS 270-3.“’ The agreement is somewhat fortuitous since the Bureau’s choice for AG,” is about 1 kcal mol-’ more negative than ours. This difference is, however, within the experimental uncertainty we have assigned to our S;. In summary, we tabulate the following for the aqueous chloro complexes of Cd(H). These values are consistent with our thermochemistry and with the equilibrium data of Vanderzee and Dawson.‘3’ AH;
CdCl+(aq) CdCMaq)
CdCl;(aq)
kcal mol-’ -57.1 - 97.4 - 133.4
AG;
kcal mol- ’ - 52.6
- 85.0 -115.5
S;
cal mol- ’ K-i 8‘3
23 48
We thank Dr. Paul G. Abajian for his assistance with the experimental work. The financial support of the National Aeronautics and Space Administration through Sustaining Grant NGR-46-001-008 to the University of Vermont is gratefully acknowledged. REFERENCES 1. Sillen, L. G. ; Martell, A. E. Stub&y Constants of Metal Ions Complexes. The Chemical Society: London. 1964. 2. Sahu, G.; Prasad, B. J. Indian Chem. Sot. 1969,46, 233. 3. Vanderzee, C. E.; Dawson, H. J. J. Amer. Chem. Sot. 1953, 15, 5659. 4. Jena, P. K.; Prasad, B. J. Indian Chem. Sot. 1954, 31,480. 5. Provost, R. H.; Wulff, C. A. J. Chem. Thermodynamics 1970, 2,000. 6. Stephenson, C. C.; Abajian, P. G.; Provost, R. H.; Wulff, C. A. J. Chem. Eng. Data 1968, 13, 191.
7. Abajian, P. G.; Wulff, C. A. J. Chem. Eng. Data 1969, 14, 476. 8. Rossini, F. D.; Wagman, D. D.; Evans, W. H.; Levine, S. ; Jaffe, I. Selected Values of Chemical Thermodynamic Properties. US. National Bureau of Standards Circular 500. U.S. Govt. Printing Office: Washington, D.C. 1952. 9. Wagman, D. D. ; Evans, W. H. ; Parker, V. N. ; Halow, I.; Bailey, S. M. ; Schumm, R. H. U.S. Nat. Bur. Std. Tech. Note 2763. U.S. Govt. Printing Office: Washington, D.C. 1968. 10. Powell, R. E.; Latimer, W. M. J. Chem. Phys. 1951, 19, 1139. 11. Kelley. K. K.; King, E. G. Entropies of the Elements and Inorganic Compoands. U.S. Bureau of Mines Bull. 592. U.S. Govt. Printing Office: Washington, D.C. 1961. 12. Kohlrausch, K. W. F. Ramanspektren. Akademische Verlagsgesellschaft Becker and Erler: Leipzig. 1943.