HARRYP. HOPKINS, JR.,AND CLAUSA. WULFF
1980
There was some frequency lowering for increased mass effects. All internal rotations were assigned as low librational frequencies. The fit of k, given by these models as compared with the thermal isomerization datal6was good for trifluoromethylcyclopropane (within -50%) and fair for trifluoroethylcyclopropane (within a factor of 3). The frequency assignments are tabulated in Tables I1 and 111. Further computational details and results of calculations for various models may be found else~here.~' Computations. The I , ratio in eq. 1 reduces to the
product of the ratio of the principal moment of inertia ratio of the complex and molecule and the reaction path degeneracy. The moment of inertia ratio is -1.1, and the reaction path degeneracy is 10.
Acknowledgment. The evaluation of the vibrationalrotational energy eigenstate sums and density terms was done on an IBM 709 computer using a program written by Mr. G. Z. Whitten. (27) F. H. Dorer, Ph.D. Thesis, University of Washinpton, 1965.
The Solution Thermochemistry of Polyvalent Electrolytes. 111. Barium Hydroxide Octahydrate
by Harry P. Hopkins, Jr., and Claus A. Wulff' Department of Chemktry, Carnegk Institute of Technology, Pittsburgh, Pennsylvania (Received Decembm 28, 1964)
16815
The solution thermochemistry of Ba(OH)2.8Hz0has been investigated using a newly determined enthalpy of solution with data from the literature. The major problem besetting this system is the value of the ionization constant for Ba(0H)f. Evidence is presented favoring a value of K Z = 0.006 rather than the commonly accepted value of 0.23. For dissolution of the octahydrate, we compute AGO = 4.9 f 0.2 and AHo = 13.7 f 0.1 kcal./ mole, and for the standard partial molal entropy of Ba(OH)+, 14 cal./(mole OK.).
As part of a continuing investigation of the solution thermochemistry of polyvalent electrolytes, we have determined the enthalpy of solution of barium hydroxide octahydrate in water, i e . , AHlo for eq. 1. A previous Ba(OH)d3Hz0(c) = Ba+"aq)
+ 20H-(aq) + 8Hz00) (1)
paper in this series2supported the conclusion that calcium hydroxide is a "weak" base in its second ionization. Data in the literatureS-6 indicate similar behavior for barium hydroxide but show considerable discord with respect to the value for the second ionization constant. D a v i e ~ , ~and & Gimblett and Monk,ab The Journal of Physical Chemistry
using the data of Harned and Mason4p5report Kz = 0.23 for Ba(OH)+(aq) = Ba+2(aq)
+ OH-(aq)
(2) Kruger and T h i l ~however, ,~ report Kz = 0.006 a t 20". (1) To whom inquiries should be addressed. (2) H. P. Hopkins, Jr., and C. A. Wulff, J. Phys. Chem., 69, 6 (1965). (3) (a) C.W.Davies, J. Chsm. SOC.,349 (1939); (b) G. R. Gimblett and C. 33. Monk, Trans. Faraday SOC.,50, 965 (1954). (4) H. S. Harned and C. M. Mason,, J . Am. C h m . SOC.,54, 1439 (1932). (6) H. S.Harned and C. M. Mason, ibid., 54,3112 (1932). (6) G. Kruger and E. Thilo, 2. anorg. allgem. Chem., 308, 242 (1961).
&OLUTION
THERMOCHEMISTRY OF POLYVALENT ELECTROLYTES
(Temperature coefficients for such changes in state are sufficiently small that no error is introduced by taking the latter value to be 0.006 a t 25” also.) Both sets of data are based upon e.m.f. studies and could be in error because of carbon dioxide in the solutions. Harned and utilized the cells Hz-Ba(OH)r (m), BaClz(m’)-AgC1-Ag, and Hz-Ba(OH)z(m)-Ba,Hg-Ba(OH)z(m’)-Hz, whereas the results of Kruger and Thilo6 were based upon the cell Hz-Ba(OH)z(m)saturated calomel. Harned and Mason, themselves, point out the difficulties involved in the use of the barium amalgam, and the AgC1-Ag couple is less reliable in basic than in acidic media. Robinson and Stokes’ compute the Bjerrum distance of closest approach for the Ba(OH)+ and Ca(OH)+ species (using KZ = 0.23 for barium) and compare these with the sums of the crystallographic radii. For calcium the agreement is excellent, while the Bjerrum value for barium is almost twice the sum of the radii. Substitution of KZ = 0.006 into the Bjerrum relations’ gives a distance of closest approach (2.7 8.) quite close to the sum of the radii (2.9 A.). In view of the lack of an a priori choice between the two values for Kz,we have investigated the thermodynamics of eq. 1 and 2 in an attempt to resolve the discord. The standard Gibbs free energy of solution of the octahydrate, AGIO, is given by AGIO
=
-RT In mBa+nmoH-2YBs+*YOH-2aH108 (3)
The activity of water in the saturated solution (m = 0.274s) may be approximated by using the osmotic coefficient for CaCI2’-and is clme to unity in any case. The concentrations and activity coefficients are solutions to the following set of equations. log
~i
=
+
+
-0.505~i~1’/’/(1 1’”) 0.151
I
=
m(l
+2 4
(4)
1981
datum and the tabulated standard entropies’O as 29 f 3 cal./(mole OK.). The standard enthalpy of solution, A H I ” , is then either 11.8 1.0 or 13.5 f 1.0 kcal./mole-the two values again reflecting a choice of K z = 0.23 or Kz = 0.006, respectively. Literature data for this quantity are 14.5 (de Forcrandl2), 15.2 (ThomsenIa),16.2 (SUI4), and 19.8 (calculated from the temperature dependence of the solubilitys) kcal./mole. The work of de Forcrand and Thomsenjwas done in “dilute solution,’’ presumably a t about Bo,that of Sill in saturated solution, and that from the solubility relation is inherently dubious. From the preceding it is obvious that an accurate determination of the enthalpy of solution of the octahydrate is a necessary datum in the resolution of the thermodynamics of this system.
*
Experimental Fisher Certified Reagent grade barium hydroxide was used without further purification in all calorimetric determinations. Titration with standard HCl indicated a purity of 99.7 0.2%. Calorimetric measurements were carried out in a solution calorimeter, similar to one already described,15 in which a laboratory wound, nickel coil resistance thermometer was used as the temperature-sensing device. AI1 measurements were made into 950 ml. of freshly boiled distilled water. A gram formula mass of 315.50 was used to convert the observed heats to enthalpies of solution. I n the concentration range m = 0.002 to 0.007, the data were fitted, by least squares, to the straight line
*
AHobed
=
13.72
+ 7.13m’/z* 0.035 kcal./mole
(7)
where the uncertainty is the standard deviation.
Discussion
(5)
The concentration dependence of a H o b s d in eq. 7 is three times as steep as that of a typical completely (mBa+zmoH-/mBaoH+) (YB~+*YOH-/YB~OH+) (6) dissociated 2-1 e l e ~ t r o l y t e . ~From ~ ~ ~ ~this obsenraEquation 4 is an extended Debye-Hiickel relation of the type introduced by D a v i e ~where , ~ the constant 0.15 (7) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworths Scientific Publications, London, 1959,p. 410. has been chosen to reproduce the measured activity (8) E. Terres and K. Bruchner, 2. EZektTochnn., 26, 1 (1920). coefficients of BaClz and BaBr2. The parameter a (9) C. W. Davies, J. Chem. Soc., 2093 (1938). is the degree of second ionization defined by a = (10) K. K.Kelley and E. G. King, “Contributions to the Data on mB8+z/(mBa+z 4- mBaOH+). These equations have been Theoretical Metallury, XIV. Entropies of the Elements and Inorganic Compounds, U. S. Government Printing Office, Washingsolved by an iterative process to give AGIO = 3.2 ton, D. C.,1961. or 4.9 kcal./mole, reflecting the choice of K z = 0.23 or (11) W. M. L a t h e r , “Oxidation Potentials,” Prentice Hall, Inc., K z = 0.006, respectively. New York, N. Y.,1952,p. 359. The entropy of the octahydrate has not been de(12) R. de Forcrand, Compt. rend., 130, 834 (1900). (13) J. Thomsen, “Thermochemische Untersuchungen,” Johann termined calorimetrically but may be estimated from Ambrosius Barth Verlag, Leipzig, 1883. the data for B:tO, CaO, and Ca(OH)210and from Lati(14) H. F. Sill, J. Am. Chem. Soc., 38, 2632 (1916). mer’s rulesll :is 102 cal./(mole OK.). The entropy (15) C . Wu, M. M. Birky, andL. G. Hepler, J. Phys. Chem., 67,1202 increment for t:q. 1, A & O , may be estimated from this (1963).
K2
=
Volume 69,Number 6 June 1966
HARRY P. HOPKINS, JR.,AND CLAWA. WULFF
1982
tion we can conclude that our measurements encompass the heat effects of a secondary process as well as those of solution. The observed enthalpy of solution can be expressed in the form
AH&,&- 4~ = AH,'
- (1 -
C Y ) m 2 '
(8)
where $L is the concentration-dependent, relative, apparent heat content of the solution (estimated from the known quantities for completely dissociated 2-1 electrolyte^^^), AHl' and AHz' are the standard enthalpy increments for eq. 1 and 2, respectively, and CY is as defined before. Table I contains representative values for a and +L, a t various concentrations for both values of K2. Equation 8 was fitted, by least squares, to the straight lines
AHobsd- (PL
=
13.81 f (1 - (r)9.6
(K2
= 0.23)
(9%)
AHobsd -
4L =
13.61
+ (1 - ( Y ) l . l
(K2 = 0.006) (9b)
Table I : Enthalpies of Solution and Dilution" m
a
0.002 0.007
0.988 0.967
0.23 14.041 14.319
0.095 0.171
0.002 0.004 0.006 0.007
Kz = 0.006 0.70 14.041 0.58 14.169 0.52 14.226 0.49 14.319
0.090 0.120 0.130 0.150
AHobad
Kz
a
=
9L
Units: kca;l./mole.
The value of AHz', -9.6 kcal./mole, from the assumption that K z = 0.23 is very uncertain in view of the small variation of LY over the concentration range studied. A better estimate of this quantity can be obtained from the value of A H o b s d in saturated solution14 and estimates of 41,from those for BaC12and BaBr2.1* These data lead to AH2' = -8.3 kcal./mole. We are now in a position to compute the standard entropy increment for eq. 2, bsz", and the standard partial molal entropy, s", for Ba(OH)+(aq). For K z = 0.23, AG2" = -1364 log 0.23 = 0.9 kcal./mole, and for K2 = 0.006, AGz" = 3.0 kcal./mole. The corresponding VaheS of M z " are then (-8.3 - 0.9)/0.298 = -31 and (- 1.1 - 3.0)/0,298 = - 14 cal./(mole OK.). Comparison with the corresponding entropy increment
The Journal of Physical Chemistry
for Ca(0H) +, - 12 cal./(mole indicates that the latter value is to be preferred for Ba(0H) +. From the tabulated standard entropies'O we compute So = 14 cal./(mole OK.) for Ba(0H) +. Gimblett and Monk3b have estimated AHzO from the temperature dependence of K z as -1.75 kcal./ mole. In view of the data leading to that value, it is difficult to justify their implied precision since a reasonable estimate of the uncertainty is 0.8 kcal./mole. Even so, this datum can be considered to accord with our derived value (eq. 9b) of - 1.1 kcal./mole, based, however, on KZ = 0.006. Such a coincidence might indicate an unnoticed systematic error in the e.m.f. work leading to KZ = 0.23. Our derived value for AH1' can be compared with the estimates made previously from the free energies and entropy of solution. Such a comparison indicates the schema utilizing KZ = 0.006 to be preferable. However, the uncertainties in the computed values of AHl" are large, owing to the estimated entropy of the octahydrate. We can now make a choice between the two literature values for Kz. If the smaller value, 0.006, is assumed then (a) calculated and observed values of AH1' agree and (b) the values of $IL and A&" (which are not independent in our derivation) are consistent with those of similar systems. If, on the other hand, we adopt KZ = 0.23, the accord between calculated and observed values of A H 1 " is poorer, and the concentration dependence of #L and/or ASz" must be assumed to be substantially different from those for similar substances. We conclude that Kz = 0.006 is to be preferred and on that basis calculate the following values for the thermodynamic state function increments for the solution of Ba(OH)2.8H*O(c): AGIO = 4.9 f 0.2 kcal./ mole; AH1" = 13.7 f 0.1 kcal./mole; AX1" = 29 cal./(mole OK.).
Acknowledgment. The authors are grateful to Professor Loren G . Hepler for his discussion of the problem and for the use of his laboratory facilities. The assistance of Dr. Gary Bertrand in compiling the data is gratefully acknowledged, as is the partial financial support of the National Science Foundation. (16) C. W. Davies, Endeavour, 4, 114 (1945). (17) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Gorp., New York, N. Y., 1958.
(18) F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine, and I. Jaffe, "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. S. Government Printing O5ce, Washington, D. c., 1952.
