March, 1933
HEATCAPACITY AND ENTROPY OF CALCIUM OXALATE
[CONTRIBUTION FROM TEE CHEWCAL
.LABORATORYOF
971
THE UNIVERSITY OF CALIFORNIA]
The Heat Capacity and Entropy of Calcium Oxalate from 19 to 300" Absolute. The Entropy and Free Energy of Oxalate Ion 13Y
WENDELL hT. LATIMER, PHILIP
w.
S C H U T Z AND
J. F. G. HICKS,JR.
The determination of the entropy of oxalate ion is an important step in the program for the evaluation of ionic entropies,' since we wish to use its value in obtaining the entropies of a number of positive ions, especially those of the rare earth group. Moreover, it is of interest theoretically, as there are but few simple divalent negative ions. The heat capacity of CaCzOa-HzOwas measured directly from 19.31 to 300°K. using the experimental method described by Latimer and Greensfelder.lc The heat of solution and free energy of solution were calculated from solubility data. The entropy of calcium ion was calculated from existing data. Material.-The calcium oxalate used was prepared by precipitation TABLE I HEATCAPACITY OF CaCaOcHpO Molecular weight, 146.09 T,OK. 19.31 23.16 26.12 27.21 28.99 30.10 33.72 37.76 40.55 44.95 49.22 52.41 52.96 55.64 59.87 63.31 65.75 68.81 72.13 76.53
Cp/mole in cal./deg.
T,OK.
&/mole in cal./deg.
T, OK.
Cp/mole in cal./deg.
0.602 1.048 1.628 1.813 2.153 2.334 3.006 3.819 4.191 5.045 5.886 6.495 6.616 7.123 7.938 8.658 9.163 9.723 10.471 11.300
81.72 87.06 91. e14 97.28 101.36 105.74 111.25 117.98 123.74 128.Ell 133.99 138.St5 144.15 149.34 154.90 160. €19 165.55 173.23 180.71 194.87
12.218 13.178 13.948 14.922 15.626 16.314 17.150 18.043 19.087 19.834 20.182 20.800 21.363 22.194 22.858 23.500 24.190 24,860 25.703 27.226
210.69 219.51 224.66 228.12 232.52 236.58 241.26 247.18 249.39 256.82 257.39 264.60 267.20 272.12 275.43 281.39 283.10 291.41 299.23 299.78
28.436 29.331 29.619 29.953 30.086 31.063 30.732 32.138 31.593 32.182 32.561 33.424 33.524 33.780 34.108 34.722 36.329 36.082 36.537 36.418
(1) For the general theory and previous determinations see (a) Latimer and Buffington, THIS JOURNAL, 48, 2297 (1926); (b) Latimer, ibid , 48, 2868 (1926); ( e ) Latimer and Greensfelder, ibid., 60, JOURNAL, 2202 (1928); (d) Latimer, J. Phys. Chem., 81, 1267 (1927); (e) Latimer and Kasper, THIS 61, 2293 (1929); (f) Greensfelder and Latimer, ibid., 60, 3286 (1928); (g) Latimer and Ahlberg, ibid., 61, 549 (1930); (h) Latimer and Ahlberg, Z. physik. Chem., Abt. A, 148, 464 (1930); (i) Latimer and 64, 1900 (1932). Ahlberg, THISJOWRNAL.
972
WENDELL M. LATIMER,PHILIPW. SCHUTZ AND J. F. G. HICKS,JR.
Vol. 55
from calcium chloride solution with ammonium oxalate. The chloride solution was kept a t about 70' and the precipitation took place over a period of three days. The reaction mixture was stirred constantly. The precipitated material was washed by decantation until the washings gave no test for chloride with silver nitrate. This washed material was dried at 105' and the dried product showed 100.007% CaCzO4.Hz0on the basis of oxide formed on ignition. Specific heat measurements were made on a sample weighing 73.50 g. Measurements.-The molal heat capacity values fall on a smooth curve up to 200°K. and deviate only slightly above that temperature. The experimental data are given in Table I and are shown graphically in Fig. 1. The temperature intervals employed in various regions were as follows: 19 to 30°K., about 3" per run; 30 to 200'K., about 5' per r u n ; above 200"K., from 5 to So per run,
Fig. 1.--Molal heat capacity of calcium oxalate,
Entropy of Calcium Oxalate.-The
entropy of calcium oxalate was
obtained by a graphical integration of the expression S
=
6'
C, d In T using
the curve shown in Fig. 1. The curve below 19.31"K. was extrapolated by means of the Debye T3 rule. A summary of the entropy calculations is given in Table 11. TABLE I1 ENTROPY OF CALCIUM OXALATE 0-19.31 OK. Extrapolation 19.31-298.1"K. Graphical
0.08 E. U. 37.20 E. U.
Entropy of calcium oxalate a t 298.1 OK.
37.28 E. U.
HEATCAPACITY AND ENTROPY OF CALCIUM OXALATE
March, 1933
973
Heat of Solution-The heat of solution of calcium oxalate was calculated from the solubility-temperature coefficient data of Kohlrausch2 by In The solubility product, K , was means of the relation AH = -R -
4 I/T ) '
evaluated from the molal solubility and the activity coeEcient, y , calculated from the Debye-Hiickel expression -log y = cz2
