6
HARRYP. HOPKINS, JR., ,4ND CLAUSA. WULFF
The Solution Thermochemistry of Polyvalent Electrolytes.
I.
Calcium Hydroxide
by Harry P. Hopkins, Jr., and Claus A. Wulff Department of Chemistry, Carnegie Institute of Technology, Pittsburgh, Pennsylvania’ (Received September 5 , 1964)
Values for the thermodynamic functions characterizing the solution of calcium hydroxide have been obtained by utilizing data from the literature and newly determined values for the enthalpy of solution both in water and in dilute hydrochloric acid. It has been shown that previous evaluations of these quantities are in error, partially because of nonconsideration of the “weak” second ionization step. For the change in state, Ca(OH)z(s) = Ca+2(aq) 20H-(aq), the following values have been determined for increments in the thermodynamic state functions a t 25” : A G O = 7100 cal./mole, AH” = -4290 cal./mole, and A S o = -38.2 cal./(mole OK.). The standard entropy of the aqueous Ca(OH)+ ion has been estimated as -4.4 cal./(mole OK.).
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An analysis of the solution thermochemistry of calcium hydroxide, ie., values for the thermodynamic functions characterizing the change in state Ca(OH)z(s)
=
+ 20H-(aq)
Ca+2(aq)
(1)
is dependent upon the assumptions made concerning the second ionization step Ca(OH)+(aq)
=
Caf2(aq)
+ OH-(aq)
(2)
Values for the standard Gibbs free energy, AGIO, the standard enthalpy, AHIo, and the standard entropy, A s l o , increments for eq. 1 have been reported by Latimer, Schutz, and Hicks’ and by Greenberg and Copeland.2 Their values, at 25O, have been summarized in Table I.
Table I : Literature Values for the Thermodynamics of Solution of Ca(OH)*(s)
Reference 1 Reference 2
AGIO, cal./mole
AH]’, cal./mole
A S I ” , cal./(mole OK.)
6810
- 3290 - 3385
-34.0 -34.7
6960
,4lthough the accord shown by these data is excellent, the values cannot be accepted until the effects of several The Journal of Physical Chemistry
sources of errors are considered. The data used by Latimer, et al., include a standard entropy for Ca(OH)2(s) of 18.24 cal./(mole O K . ) , which has since been superseded by a value of 19.93 cal./(mole Their enthalpy of solution is derived from the determinations of Thonisen4 and Berthelot5 with estimated corrections for dilution and temperature changes. Latimer, et uZ.,I do not consider the effect of a possibly “weak” second ionization, and Thomsen and Berthelot’s work was performed during the period when the existence of ions in solution was still questioned. Greenberg and Copeland,2 while cognizant of the “weak” second ionization step, made no use of it in their data reduction. Their value for the entropy increment, derived from the temperature dependence of the solubility, is markedly different from the value that can be computed from tabulations of standard entropy values. A number of studies have been made to determine (1) W. M. Latimer, P. W. Schutz, and J. F. G. Hicks, Jr., J . Am. Chem. SOC.,55, 971 (1933). (2) S. A. Greenberg and L. E. Copeland, J . Phys. Chem., 64, 1057 (1960). (3) W. E. Hatton, D. L. Hildenbrand, G. C. Sinke, and D. R. Stull, J . Am. Chem. SOC.,81, 5028 (1959). (4) J. Thomsen, “Thermochemische Untersuchungen,” Vol. 111, Johann Ambrosius Barth Verlag, Leipaig, 1883. (5) M .Berthelot. Ann. chim. phys., 4, 531 (1875).
SOLUTIOK THERMOCHEMISTRY OF POLYVALENT ELECTROLYTES
the value of the ionization constant, KP,for eq. 2.6-'2 The results range between K2 = 0.04 and 0.07. Bates, et 01.,12in the niost exhaustive study, conclude that no unambiguous value can be derived for KP. They present three equations for that quantity as a function of the ionic strength, each reflecting a different concentration dependence for an activity coefficient ratio. Their intermediate relationship has been adopted herein and appears as eq. 5 below. The standard free energy increment for eq. 1 can be computed from
aGl0 = -RT
111 mcs+2moH-2yCa+zYOH-2(3)
where the m and y values are, respectively, the molal concentrations and molal activity coefficients in the saturated solution. The solubility of Ca(OH)z(s) is given as 0.0203 m.I3 The activity coefficients and concentrations in eq. 3 are solutions to the following set of equations. 1 = '/2[4mca-2
-log K2
+
=
moH-
1.221
+
~ C ~ ( O H ) + ]
+ 2.8021
[%a*mOH-/~ka(OH)-1 [ Y C a + f Y O H - / Y C a ( O H ) + I -log
y =
(5) =
K? (6)
+ 1"')] - 0.31
[0.505~*1"'/(1
(4)
(7)
Equation 7 is an extended Debye-Huckel relation at 25' for the activity coefficient of an ion with charge z in a solution of ionic strength 1. The solutions to these equations are mcat2 = 0.0145, moH- = 0.0345, yca+2 = 0.507, y o H - = 0.838, and AGlo = 7100 tal./ mole. The standard entropy of the aqueous hydroxide ion is -2.5 cal./(mole OK.),' l 4 that of the aqueous calcium ion is -13.2 cal./(mole and that of Ca(OH)&) is 19.93 cal./(mole leading to AS,' = -38.2 cal./(mole OK.). The enthalpy of solution can now be computed as AHl' = 7100 298.15(-38.2) = -4290 cal. 'mole. This value differs by almost 1 kcal./mole from those given in Table I. To resolve this discrepancy a direct determination of the enthalpy of solution of Ca(OH),(s) was undertaken.
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Experimental Fisher certified reagent calcium hydroxide was used without further purification although efforts were made to minimize its exposure to moist air during weighing and loading. Satisfactory rates of dissolution were obtained for samples ranging between 0.25 and 1.45 g. All samples were dissolved into 950 ml. of freshly boiled, distilled water. The solution calorimeter, which has been described previously,16has as its tem-
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perature-sensing element a laboratory-wound resistance thermometer. The Mueller bridge circuitry and adjuvant electrical standards have also been described. Sixteen experimental determinations of the heat of solution in water, a t 25.0 i 0.1", between m = 0.004 and 0.020 were fitted, by the method of least squares, to the straight line, AHobsd = -4535 7160m"' f 30 cal./mole, where the uncertainty is the r.m.s. deviation. A second series of measurements were perfornied in which calcium hydroxide samples, ranging from 0.18 to 1.05 g., were dissolved into 950 ml. of 0.04 N hydrochloric acid. The observed heat effects approached the upper limit of the calorimeter's useful range, and are, therefore, less reliable. I n addition, rates of dissolution were slower-as long as 6 min. being required for attainment of equilibrium. Ten determinations (corrected for dilution of the unreacted acid) at 25.0 f 0.3' were fitted by least squares to the straight line, AHaold = -31.09 8.76m1/' f 0.18 kcal./niole. Three additional data points, more than 300 cal./mole different from the straight line value, were observed but were not included in the least-squares analysis.
+
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Data Analysis The observed concentration dependence of the heats of solution in water has almost twice the slope reported for other electrolytes of the type lIX2.17 The additional heat effect must be caused by the "weak" second ionization, the extent of which is a function of concentration. The observed heats of solution can be represented by
AHobsd
-
AHctil
=
AHlO
-
(1 - CY)AH*' (8)
where AHdil is the concentration-dependent heat of dilution, AHlO and AH,' are the standard enthalpy (6) C. W. Davies, Endeavour, 4, 114 (1945).
(7) R. P. Bell and J. E. Prue, J . Chem. SOC.,362 (1949). M .Wiand, ibid., 1979 (1950). (9) C. W. Davies and B. E. Hoyle, ibid., 233 (1951). (10) R. P. Bell and J. H . B. George, Tians. Faraday Soc., 49, 619 (8) R. P. Bell and G.
(1953). (11) F. G. R. Gimblett and C. M .Monk, ibid.,50, 965 (1954). (12) R. G. Bates, V. E. Bower, R. G. Canham, and J. E . Prue, ibid., 55, 2062 (1959). (13) R. G. Bates, V. E. Bower, and E . R . Smith, J . Res. S a t l . Bur. Std., 56, 305 (1956). (14) W. M. Latimer, K. S. Pitzer, and W. V. Smith, J . Am. Chem.
SOC.,60, 1829 (1938). (15) C . C. Stephenson, personal communication. (16) C. Wu, hf. M. Birky, and L. G . Hepler, J . Phys. Chem., 67, 1202 (1963). (17) H . S.Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corp., New 'I-ork, N. Y., 1958.
Volume 60, .Vumber 1
January 1965
HARRYP. HOPKINS,JR.,AND CLAUSA. WULFF
8
Increments for eq. 1 and 2, respectively, and CY = [mea+* ma(oH)+] is the degree of second ionization. The quantity CY can be determined, as was indicated previously for the saturated solution, and is given in Table I1 for selected concentrations. Also listed in Table I1 are A H o b s d and AHdil-the latter estimated from data for alkaline earth halide@ which are strong electrolytes in both steps.6
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Table I1 : Heats of Solution and Dilution m
AHobed, Cd./mOk
AHdil, Cd./mOh
a
0.0064 0.0100 0.0144 0,0203
- 3962 -3819 - 3681 -3515
165 200 230 270
0.878 0,828 0,775 0.713
The values of AHl' and AH2', as determined from a least-squares analysis of eq. 8, are -4360 f 50 cal./ mole and -2.0 f 0.4 kcal./mole, respectively. It should be remarked, at this point, that assumption of the alternate equations for log K1 proposed by Bates, et uZ.,12 leads to estimates of AH1' within 50 cal./mole of the value derived above. If twice the enthalpy of ionization of water, 13.36 kcal./mole'* is subtracted from the limiting heat of solution of Ca(OH)z(s) in dilute HCl, a value of 4.37 f 0.20 kcal./mole is obtained for AH1'.
Discussion The accord of the two experimentally determined values of the enthalpy of solution of calcium hydroxide (4.36 and 4.37 kcal./mole) with the value calculated (4.29kcal./mole) from ionic entropies and the solubility substantiates the existence of a "weak" second ioni-
The .Journal of Phyaical Chemiatry
zation step. That these values are almost 1 kcal./mole different from that derived from a temperature derivative of a solubility relation indicates the care that must be exercised in the latter method. By combining literature data and our experimental determinations, the values for the thermodynamic functions characteristic of the solution of calcium hydroxide are AGlo = 7100 cal./mole, AH1° = -4290 cal./mole, and A x l o = -38.2 cal./(mole OK.). The data for solution in HCl are in fair accord with previous determinations of this enthalpy of solution : 30.85,1e3O.7ll2O30.85,21and 31.23.22 The values of K z at infinite dilution [0.06 from eq. 51 and of AHz' lead to an entropy increment for eq. 2 of -12.3 cal./(mole O K . ) . That value is in good accord with estimates of -10.4lo and -11.311 from the temperature derivative of K 2 . The standard entropy of the aqueous Ca(0H) + ion can be calculated as -4.4 cal./(mole OK.) from the previous datum and the standard entropies of the aqueous calcium and hydroxide ions.
Acknowledgment. The authors are grateful to Professor Loren G. Hepler for the use of his laboratory facilities and to Professor Clark C. Stephenson, of the Massachusetts Institute of Technology, for suggestion of the problem. The partial financial support of the National Science Foundation is also gratefully acknowledged. (18) K.9. Pitaer, J. Am. Chem. SOC.,59, 2365 (1937). (19) T. Thorvaldson and W. G. Brown, ibid., 52, 80 (1930). (20) W. A. Roth and P. Chall, 2.Elektrochem., 34, 185 (1928). (21) H.E. Sohweite and E. Hey, 2. anorg. allgem. Chem., 217, 396 (1934). (22) K. Taylor and L. 9. Wells, J. Rea. Natl. Bur. Std., 21, 133 (1938).
