IXTERACTIOS IX SALTVAPORSIN
,June, 1963
+
+
+
THE
KC1-hlgC12 SYSTEM
+
Es = ETR BROT EVIB EELECTE h i I s c (A-1)
P
=
1259
( ~ m ~ p - ~ ) ( c ’ m ~ ’ p - ~ ’ )(A-6) e-~’~
From the definition of &, it can be shown that
where
ETR = EROT = EVIB = EELECT= E M I ~ C=
(A-7) translational energy rotational energy vibrational energy electronic energy miscellaneous energy terms
and, therefore
For a perfect monatomic gas, EROT and EVIB are equal to zero. At the temperature considered, it is assumed that a negligible number of atoms are in excited electronic states, that is, all the ,-a EO. atoms are in their ground state, indicated by EELECT From the principle of equipartition of energy and the definition of a partition function
P
=
PTRPELECT PROT PVIB P ~ S (A-2) C
or Q
= - ( C C ~ ) ( m d - a ‘ ) [ e - BOPP - ( b f b ’ ) [ - ~ o
(b
PTR=
h3
(A-3)
+ b’M-’]
Since Eo generally ranges from several thousand electron volts to higher values, and p - l == 0.026 electron volt, it seems reasonable b’)p-l s,heats and entropies for the dissociation of the dimers were obtained for the three salts. Equilibrium constants were correlated as a function of temperature by means of the integrated form of the van't Hoff equation
(4)
where Kp is expressed in atmospheres and AHDO and ASDO are the enthalpy and entropy, respectively, for
97.9 94.8 94.8 94.9 95 .O 97.3 95.9 95.5 94.8 94.6 125.4 123.1 120.9 121.8 123.7 124.6 126.5 129.2 126.6 214.8 213.9 219.5 221.5 217.5
dissociation of the dimer a t the mean temperature of the experiments. It has been assumed that AHDO is independent of iemperature over the short range investigated. Table I11 gives the values of AHDO and
XlMF
=
BI
1153 1161 1282 1291 1297 1297 1298 1314 1326 1352 1255 1255 1275 1279 1301 1309 1316 1339 1346 1209 1240 1278 1320 1350
(3)
as= WB/ns=
-
OK.
Salt
MgClz CsCl a
This work.
*
45 7 f 4 . l a 40 8 f 0 . G ' 43 8 f 2.3c 32.0 f 4 . 5 a 32 2 f 3.1a 37.3 f 1 . l C Barton and Bloom.la
THE
ASDO, cal./mole OK.
29.3 i 2 . 2 ~
c
27.1 f 1.7c 18.8 f:2.05 21.0*2,5a 25.3 f l . O c Datz.6
ASDO along with the results of other investigators. The uncertainties expressed are the standard deviations as calculated from the least squares treatment of the data. It is of interest t o note that the equilibrium constant for dissociation of the dimer of KC1 is essentially equal to that for MgC12. Potassium Chloride-Magnesium Chloride Mixtures. -Vapor pressures were obtained as a function of temperature using the boiling point method for twelve mixtures of potassium chloride and magnesium chloride over the entire composition range in the temperature These data were correlated by the range 950-1150'. method of least squares. The resulting equations were used to compute the vapor pressure as a function
ECGESEE. SCHRIER A N D HERBERT AI. CLARK
1262
Vol. 67
45
40
z
? v
e
35
3
I k
30
25
20 20
40
60
80
100
Mole % KCI.
Fig. 1.-Apparent total vapor pressure ( 0 ) and observed total vapor pressure (0)of KC1-MgCl2 mixtures us. liquid composition at 1075".
0
40
20
Mole
60 KCI.
80
100
Fig. 3.-Calculated partial pressures of the components and observed total pressure for KC1-MgCL mixtures a t 1075': 0, total (b.p.) pressure; A, MgCls monomer; A, MgCls dimer; 0 , KC1 monomer; 8 , KC1 dimer; 0,KRiIgCla.
0.5
I
0.4
0
20
40
60
80
100
Mole % KCI.
0
20
40
60
80
100
Mole % KCI.
Fig. 2.-Difference between apparent total vapor pressuie :nd observed total vapor pressure us. liquid composition at 1075 .
of composition at various temperatures. Transpiration measurements were made as a function of temperature for eight mixtures of KC1 and MgClz over the entire composition range. From these data, apparent partial pressures could be obtained for each component. These pressures were calculated on the assumption that only monomers and dimers of each salt exist in the vapor and that there are no vapor phase interactions between the components. A least squares correlation
Fig. 4.-Activity coefficients of MgCl2 and KCl us. composition: 0, this work a t 1075', V, Neil" a t 800'; 8, Markov, et al.,16 at 718", A, Chu and Egan16, @, TsuchiyaZO a t 800°, O rResnikow'* at 950'; 0,TreadwellT9a t 650'.
of these data similar to that made for the boiling point measurements provided apparent vapor pressures as a function of composition for various temperatures. The lower solid curve in Fig. 1 gives the vapor pressure as a function of liquid composition as determined from boiling point measurements a t 1075'. The upper curve is a plot of the sum of the apparent partial vapor pressures, Le., the apparent total vapor pressure, as determined from transpiration measurements a t 1075'. It can be seen that the two curves do not coincide indicating that there is a vapor phase interaction between the components. It is assumed that the
June, 1963
RADIOLYSIS OF XYLEXE ISOMERS AND ETHYLBENZENE
interaction involves a mixed compound of the type (KC1),(MgC12)r, where i and j are integers. Evidence for the nature of the interaction compound is provided by Fig. 2. Here, the difference between the apparent and observed total vapor pressures shown in Fig. 1 is plotted as a function of liquid composition. ’ of each comThe maximum in the region of 50 mole % ponent is taken as evidence that the compound is of the 1: 1 type, z.e., I
