STANDARD PARTIAL MOLALHEATCAPACITIES OF CsI
Dec. 20, 1964
A plot of the left-hand side of eq. 25 against 1,'T will give much more accurate values of A H l * (or A F l * a t any temperature) than will assuming the ACp* term to be zero. C. Retrograde Kinetics.-Kinetic reactions can reasonably be divided into two classes: those having positive values of ACp*, with the others having negative values a t 25' (or any other convenient reference temperature). The latter class are particularly interesting. At a temperature such that
-AH'*
=
1:
ACp* (tz -
tl)
(26)
AH2* becomes zero. For temperatures above this inversion point, AH2*will become negative, and the ratedetermining step will proceed more slowly as the tem-
[CONTRIBUTION FROM
THE
540 1
perature is increased further. This retrograde temperature region depends upon a very literal interpretation of the statistical thermodynamic rate equation ( 2 3 ) . Whether the conditions and assumptions involved in the derivation of eq. 23 can accommodate negative activation energies is a mute question. However, there are a number of reactions where this interesting point can be tested between 25 and 100°, particularly for those having already small activation energies a t room temperature. (Unless A S * is also rather negative, some reactions will proceed too rapidly to measure over the whole temperature range of interest.) It is perhaps reasonable to inquire whether examples of kinetic systems having negative activation energies a t room temperature (for the rate-determining step') have been mistakenly interpreted as being due to some more complex reason than is actually required.
DEPARTMENT O F CHEMISTRY, P U R D U E UNIVERSITY, LAFAYETTE, IXDIAXA]
The Thermodynamic Properties of High Temperature Aqueous Solutions. VII. The Standard Partial Molal Heat Capacities of Cesium Iodide from 0 to looo1 BY R . E.MITCHELLzs3 AND J. u '.COBBLE RECEIVED MAY 15, 1964 T h e "integral heat method" developed in these laboratories has been used to obtain the standard partial molal heat capacities for the key electrolyte cesium iodide in the temperature range 0 t o 100" At 25" a value of -36.6 cal. mole-' deg.-l for E:" was obtained. The heat capacities for this electrolyte show unusual behavior in t h a t no maximum in G2" was observed over this temperature range. If such a maximum does exist, it is at 100' or higher temperatures.
Introduction The "integral heat method" of determining partial molal heat capacities at infinite dilution has been described in previous communications from this laborat ~ r y . ~This , ~ method has been used to determine values of for NaC1, BaC12, NaRe04, HRe04, and HCl from 0-100O with an average accuracy of better than 0.5 cal. mole-' deg.-l. Further, - the measurements upon which the evaluation of C P , O depends involve concentration ranges of 0.001-0.01 m , where methods for extrapolation of heats of solution are reliable. In the present research, the integral heats of solution of pure cesium iodide were determined as a function of concentration a t IOo intervals from 5 to 95'.
czo
CsI(c)
-
+ aq.
=
CsI(aq)
(1)
ACpo for the reaction was computed as
ACpo
= AHs0(t2) -
tz
-
AHSO(tl) tl
(2)
where A H s o ( t ) refers to the heat - of solution at infinite dilution a t a temperature t . Cpzothen becomes -
Cplo = AC,"
+ C,"
(3)
The heat capacities of CsI(c), C P , O , over this temperature range have not been experimentally determined, but can (1) Supported in part by a grant from t h e National Science Foundation. (2) Ethyl Corporation Fellow, 1961-1962. (3) Frcmm the P h . D . Thesis of R. E . Mitchell, Purdue University, J a n , 1964, (4) C. M. Criss and J . W. Cobble, J. A m . Chem. S O L .83, , 3223 (1961). (5) J. C. Ahluwalia and J. W. Cobble, ibid.,86, 5377 (1964).
be fixed accurately enough for the present purposes from experimental heat capacity data on other cesium salts and related materiah6 Experimental Apparatus .-A submarine-type heat of solution calorimeter (CS-1) which has been previously described4was used for measurements between 5 and 55'. The sensitivity was increased by replacing the platinum resistance thermometer with a thermistor as the temperature-sensing element .b An improved calorimeter (designated as laboratory calorimeter CS-2) became available during the course of these measurements,' and the data obtained a t 55' up t o 95" were from this new device. T h e details of this calorimeter and the associated bridge are described in another communication in this series.' Electrical calibrations of the calorimetric systems were made by using a commercially available Sargent Model IT coulometer as the constant-current source. A n electronic timerS accurate to 1I~0.01sec. was used to measure the heating time; this timer was in turn powered by a 60.000-C.P.S. tuning-fork frequency standard accurate t o 10.005c;. The energy measurements were believed to be accurate to better than 0.19( even for moderately short heating times (-10 sec.). Power inputs were determined in the usual manner by measuring the voltages across the heater a t an appropriate point along the heater leads' using a Leeds and S o r t h r u p Type K-3 potentiometer with d volt box. Current measurements in the heating circuit were made using an S . B . S . calibrated 10-ohm standard resistor. Corrections for the various lead resistances were applied where necessary. ( 6 ) K . K. Kelly, U S Bureau of Mines Bulletin 584, U . S . Government Printing Office, Washington, D. C , 1960. ( 7 ) E . C Jekel, C . h l . Criss, and J W Cobble, J A m . Chrnz. Soc , 86, 5404 (1964), see also E. C Jekel, Ph.1) Thesis, Purdue University, 1964. (8) This timer was designed and built in our laboratories by R I v l . Hayes and is described by J. E. McDonald, P h 11. Thesis, Purdue Univereitv 1961.
R . E. MITCHELL AND J. W. COBBLE
5402
Vol. 86
TABLE I HEATSOF SOLUTION AND VALUES FOR CsI No. of determinations
AH., cal /mole
1 3 2 2 2
1 1 3 5 7
03 90 79 69 59
5 00" 8970 9034 f 31" 9034 i 2 9022 i 8 9030 i 1 AHs' = 9024
2 3 3 3
1 3 5 7
90 79 70 59
15 00" 8472 i 4 8444 i 14 8454 f 12 8444 i 14 AHs' = 8434
2 38 4 72 7 14 9 46 12 50
25 00" 7939 f 15 7954 f 11 7950 f 5 7942 7943 AH,' = 7920
3 3 2 1 1
2 5 4 1 1 1
a
m X 10s moles/kg of Hg0
1 2 4 7 8 9
07 30 80 50 17 74
35 11" 7566 f 48 7512 i 14 7505 f 7 7494 7526 7500 AH," = 7474
-A ~ l ' / ' a
cal./mole
No. of determinations
P,
cal./mole
55.00' 6657 f 18 6688 f 8 6695 f 11 6694 f 6 6695 f 14 AH," = 6636
3 4 4 4 1
86 70 57 40 11 11
65.00" 6273 i 37 6296 f 21 6219 f 19 6229 f 7 6337 AH,' = 6254
2 2 2 2
1 87 3 69 5 56 7 38
3 3 3 1 1
1 84 3 71 5 53 7 44 11 09
85.01" 5586 f 12 5601 f 80 5620 f 8 5612 5651 AH," = 5543
2 3 3 1
1 86 3 73 5 55 11 10
94.96" 5289 f 38 5273 f 37 5246 f 99 5307 AH." = 5198
8959 9020 9014 8998 9003
5
- 17
8455 8421 8426 8412
- 22 - 30 - 37 - 47
7917 7924 7913 7900 7896
- 18 - 25 - 35 - 43 - 45 -49
7548 7487 7470 7451 7481 7451
- 42
6 7 4 2
44 99" - 26 4 7036 i 27 1 90 7018 3 79 7083 i 7 - 36 7047 3 - 44 4 5 69 7036 7080 f 6 - 50 7 59 7092 f 4 7042 3 -61 11 36 7037 1 7098 AH," = 7043 Standard deviation of individual measurements from the average
AHa, cal./mole
89 75 64 52 27
- 11 - 14 - 20 - 24 - 27
- 23 -28 - 32
m X 108, moleq/kg of Hz0
1 3 5 7 11
1 3 5 7
74.95O 5893 f 38 5950 f 1 5954 f 11 5974 f 3 AH," = 5893
- AHI'/Za cal. / mole
- 30 - 42 - 50
- 58
- 70
- 33 - 47
- 56 - 64 - 79
-38 - 52
-64
- 73
- 42
- 59 - 73 - 83 - 101
- 49 - 68 -83
- 115
PI
cal.1 mole
6627 6646 6645 6636 6625
6240 6249 6263 6265 6258
5855 5898 5890 5901
5544 5542 5547 5529 5550
5240 5205 5163 5192
Materials.-Water used in these measurements was prepared by passing distilled water through a pair of acid-base ion-exchange columns t o remove trace ionic contaminants. Cesium iodide samples were prepared by grinding pieces of a spectroscopic grade Harshaw single crystal. The resulting powder was dried a t 400' and stored in a desiccator over magnesium perchlorate. Samples of a few hundred milligrams were weighed into thin-walled Pyrex sample bulbs, heated t o 400" for 8 hr., cooled in a vacuum desiccator, and sealed under reduced pressure (-0.1 mm.). Procedure.-Because CsI has an endothermic heat of solution over the entire temperature range under investigation, it was possible t o operate the calorimeter under nearly isothermal conditions. T h e technique used involved the addition of electrical energy a t the same time the sample was being dissolved. Particularly a t the higher temperatures, the rate of solution was so rapid t h a t it was not possible to completely eliminate temperature fluctuations by this compensation technique. However, by delaying the initiation of the chemical reaction for an appropriate time after the start of electrical heating, the small initial "overheating" could be made to balance out the small "overcooling" in the latter part of the run, and the net temperature change was rarely in excess of 1 X T h e energy equivalence of this net temperature change could he determined rather accurately by appropriate calibrations of the bridge system.
heat of solution, the adopted heat of solution a t infinite dilution, and parameters used in the extrapolations are indicated a t each temperature. Wherever possible, the standard deviations are indicated for each concentration. Calculations and Thermodynamic Data An extended form of the Debye-Hiickel theory was used to extrapolate the heats of solution to infinite dilut i ~ n . Essentially, ~ the heat of dilution of the electrolyte, @L, was taken as
Experimental Data Table I summarizes the results of 128 separate heat of solution measurements for cesium iodide. The number of replicate determinations a t each concentration, the
(9) G . N. Lewis and M. Randall, "Thermodynamics," 2nd Ed.. revised by K . S . Pitzer and I, Brewer, McGraw-Hill Book Co , New York, K . Y , 1961, p 642. (10) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd Ed., Reinhold Publishing Carp., New York, N Y , 19.58, p. 176.
where
(5) The cr(I'I2) function has been tabulated elsewhere. lo A H is the theoretical Debye-Hiickel heat slope. The
Dec. 20, 1964
STANDARD PARTIAL MOLALHEATCAPACITIES OF CsI
5403
TABLE I1 HEATCAPACITIES OF AQUEOUS AND CRYSTALLINE CESIUMIODIDE' -
tav,
10 20 30 40 50
ACPo
"C
0
-59 -51 -44 -43 -41 -40 -36 -35 -33
0 0 0 0 60 0 io 0 80 0 90 0
a
-30
CPZO
0 4 1 6 1 4 3 2 4
-46 -39 -31 -31 -28 -27 -23 -22 -20
6
0 7 2 6 9 8 7 8
TABLE I11 SMOOTHED VALUESOF THE PARTIAL MOLALHEATCAPACITY FOR AQUEOUS CESIUMIODIDE CP,O cal mole-' deg
10 20 25 30 40 50 60 70 80
-46 6 -39 0 -36 6 -34 7
-31 0
Extrapolated values
other symbols have their usual p is defined as
- 46 -50 -54
-58
8
0
IO
20
30
40
50
60
70
80
90
100
Temperoturo
viously reported by othersll; these are the only applicable data available in the literature for comparison. Table I1 is a summary of the values of ACp and Go calculated from the AH,' entries in Table I and eq. 2 and 3. The partial molal heat capacities as a function of temperature are given as closed circles in Fig. 1; the smooth curve shown was used to provide the final recommended values tabulated in Table I11 from 0 to 100'. The only other data reported in the literature are a t 25" and come from interpretation of specific heats of concentrated CsI solutions. 1 2 , 1 3 The data obtained from the smooth curve in Fig. 1 and tabulated in Table I11 are estimated to be accurate to about 0.5 cal. mole-' deg.-l between 10 and 90'; the errors in the extrapolated values a t 0 and 100' are perhaps two or three times this large. At the present time we can give no completely reasonable explanation for the apparently larger deviation of the value of a t 30' compared to the data a t other temperatures. It may be the result of an unfortunate accumulation of errors, or it may signify some real effect due to "structural" changes taking place in the solvent system in this temperature range. It is interesting to note that CsI is the first electrolyte that we haveobserved which does not display a maximum in the C', temperature curve before 80' ; if CsI has such a maximum, it is delayed until nearly 100" or even higher. Calculations from the correspondence principle14 -indicate that it should reach a maximum value of C", a t 100'. The heat capacities of CsI(aq) are more negative a t all temperatures studied than the corresponding values for NaCl(aq). This once again illustrates a pointi4 frequently overlooked in various explanations of electrolyte behavior. While the entropies of aqueous ions become more positive with increasing ionic size, the heat capacities have exactly 'the opposite trend. Yet the effect of ionic charge is exactly the same for both and $2" (ie.,increasing negative values with increasing charge).
G2"
-28 3 -25 9 -23 9 -22 6 -21 8 -21 8"
90 100 a
-1
- 57"
0
- 34
-38 42
Fig. 1.-Standard partial molal heat capacities for cesium iodide as a function of temperature: 0 , from this investigation'*; and O,I3from previously reported specific heat data.
Units in cal mole-' deg
t, o c
- 22
- 26
A function
AH,' - 2.3(13RT2v+v-(~)m dB (6)
Consequently, a plot of p against m should be linear and extrapolate to AH," a t m = 0. Our previous experience with this function has shown this procedure to be satisfactory for 1: 1 electrolytes a t dilutions below 0.05 m, even up to 100". The values of (v/2)A&+Z-l. I 1 / zand ~ p are given a t each temperature and concentration in Table I. In making the extrapolations in the manner just indicated, it is usually possible to find a range of values for AH," from these linear extrapolations which fit the experimental data equally well. Consequently, another useful aid in helping reduce the error in AH,' a t any temperature is the reasonable requirement that dpldm be a smooth function of temperature. This is a powerful aid in helping fix a unique value of AH," a t a given temperature since in effect i t is a cooperative use of the data a t neighboring temperatures. The slope that was obtained a t 25" for CsI is in excellent agreement with the heat of dilution data for closely similar CsCl pre-
c2'
G2'
1. Messner, 2 . Elrktrochem., 33, 431 (1927). (12) A. F. Kapustinskii, I I Lipilina, and 0 Ya. Samoilov, J . chim. phrs., 54, 343 (19.57). (13) M . Eigen and E. Wicke, 2 . Elektrochem , 66, 354 (19.51) (14) C . M. Criss and J. W. Cobble, J . A m . Chem. Soc., 86, 5385 (1961). (11) E. Lange and
