R.J. SIME
800
AND
N W. GREGORY
much more difficult to obtain precise results in these more viscous solutions than in water. We do not yet understand the factors which cause this difficulty. In concluding, it should be noted that a t these low concentrations of potassium chloride, we have avoided the difficulties which would be
[CONlRIBUTION FROM
THE
VOl. 82
encountered in considering the migration of all the components in this three component system. Acknowledgment.-This work was supported i n part by the Atomic Energy Commission under Cow tract AT (30-1) 1375. NEW HAVEN,CONN.
DEPARTMENT O F CHEMISTRY
AT THE
UNIVERSITY OF WASHINGTON]
Vapor Pressure of Chromium(I1) Bromide BY R. J. SIMEAND N. W. GREGORY RECEIVED AUGUST24, 1959 The vapor pressure of CrBrp(s) has been measured over the temperature interval 837-1083°K., and thermodynamic properties of the monomeric and dimeric forms have been evaluated relative t o the solid.
T h e vapor pressure of CrBr2 has been measured between 972 and 1083'K. by the transpiration method and in the vicinity of S39'K. by the torsion effusion method. Experimental Part The experimental methods and apparatus have been described in earlier papers.'n2 Argon was used as a carrier gas in transpiration experiments; flow rates between 13 and 60 ml./min. gave the same vapor pressures. The quantity of CrBrz transported was determined spectrophotometrically, after oxidation to chromate, as described in an earlier ~ was prepared in a quartz tube by study on c r B r ~ . CrBrz reaction of HBr with powdered chromium metal a t 780". It was purified by sublimation in high vacuum: analysis gave a chromium content corresponding to 99.374 CrBrz. With the radiant heating technique employed,2 the torsion effusion cell could be heated only to 568" a t which the vapor pressure of CrBrn is near the lower limit of the sensitivity of the apparatus. Hence torsion measurements were limited t o this one temperature and t o a cell with and 3.72 X moderately large orifices ( A , = 2.80 X 10-3 cm."). The sample was introduced into the cell (in a dry box) through the effusion orifices. Calibration of the apparatus has been described earlier.2
Results and Discussion Results are shown in Fig. 1. The solid line is drawn through the calculated transpiration pressures when the monomer is assumed the only vaporizing species; the dotted line represents the same data if the dimer were the only vapor species. The monomer line is seen to be in better agreement with the absolute pressures obtained by the torsion effusion method (the points grouped a t the lowest temperature). We were unable to confirm independently that the torsion pressures shown are a good approximation to equilibrium vapor pressures (steady-state pressures in effusion cells with moderately large orifices will be below equilibrium values if the condensation coefficient is small) 2,4 by repeating the measurement with a cell with smaller orifices since the latter would give a deflection a t 568' too small for accurate measurement. Hence the torsion points (Fig. 1) are regarded as lower limiting values; they do correlate well with the transpiration data, however, which suggests they are close to equilibrium. The solid line may (1) R. 0. MacLaren arid N. W. Gregory, J . Phys. C h e m , 59, 184 (1955). (2) R. J. Sime a n d N. W.Gregory, ibid., 6 4 , 86 (1960). (3) R. J. S h e a n d N. W. Gregory, THIS JOURNAL,83, 93 (1SGO). (4) J. H.Stern a n d N. W. Gregory, J . Phys. Chem.. 61, 122G (1957).
be represented by the equation (837-1083°K.) log P m m . = -12050T-'
4- ll.OG
which, without further knowledge of the mode of vaporization, gives the standard (atm.) free energy of sublimation equation A P = 55,100
- 37.4T
Recently Schoonmaker, Friedman and Porter6 have carried out a mass spectrometric analysis of the vapor in equilibrium with CrBrz a t 931'K. Their results indicate about 20% of the vapor to be in the form CrzBr4 a t this temperature. They also measured the vapor pressure a t this one temperature by conventional effusion technique and report AFo = 17.2 for the reaction (1)
CrzBr4(g) = 2CrBrz(g)
and, from an estimated AS0 of 32 e.u., calculate AH0 for (1) as 47 kcal. Using their standard free energy and estimated entropy changes for (l), we have calculated the partial pressures of monomer and dimer for each of our measured vapor pressures ( A P = -RT In K I = 47,000 -32 T., assumed; ACp for (1) neglected). Data are summarized in Table I. P a m represents TABLE I
x
OK.
072 1000 1021 1024 1024 1048 1083
Pam 104, atm
Pm
x
lo',
K~ x 104 atm. Transpiration data 2 G7 4 5 0 603 0 3 1 26 -5 28 S GO 17 2 2 41 9 20 17 7 2 48 9 20 17 8 2 46 1.5 0 32 4 4 55 84 0 32 4 12 8
Pd
x
ntm
0 1 3 3 3 6 21
lo6,
7G 64 44 41 44 73 8
Torsion effusion data
vt x 837 837 838 841
109
0.00007 ,00775 ,00538 ,00640
0.0528 ,0528 ,0546 0676 t
0 055
. Of39 ,049 ,059
0.0057 ,0085 ,0048 ,0050
the apparent pressure of monomer, ;.e., as shown in Fig. 1, the pressure calculated from the number of grams of chromium halide transported, assuming ( 5 ) R. C. Schoonmaker, A. N.Friedman and R. F. Porter, private communication; J. C h e m . Phys. in press,
THEVAPOR PRESSURE OF CHROMIUM(II) BROMIDE
Feb. 20, 1960
L,
801
T. Eff
1.20
1.10
1.00
8
I 0 0 O/ To K , Fig. 1.-Vapor
1.20
1.15
pressure of chromium( 11) bromide.
the vapor to be only CrBrz(g). Actually Pam = k(n, -I- 2nd) = P m $- 2Pd, where k is a proportionality constant, n m and ??,d represent the actual number of moles of monomer and dimer, respectively, in the volume of vapor taken and Pm and Pd the partial pressure of each form. We may write Kl = Pm2/'Pdand 2Pd = Pam- Pm and thus from calculated values of K , and Pam a t each temperature a quadratic equation for Pm may be solved and Pd subsequently evaluated. The torsion data were treated in a similar manner, starting with actual measured total pressure, Pt = Pm f Pd. The relationship of P , and Pd and their variation with temperature is shown in Fig. 2, which also includes for comparison the single pressure measurement by Schoonmaker, Friedman and Porter. The lines drawn lead to the equations (837-1083' K.1 CrBrz(s) = CrBrz(g) A P = 52300 2CrBrp(s) = CrzBrl(g) A P = 58000
- 33.9T - 36.6T
(2) (3)
We suggest an uncertainty in AHo for (2) of *3 kcal.; that for (3) is somewhat larger because of the small concentration of dimer and the estimations involved in the calculation of the dimer pressures.
I
1.10
'
1
1.05
'
I
1.00
'
I
.95
'
1
.9C
1000 T - ' Fig. 2.-CrBro
and CrZBrc pressures over solid CrBra.
The entropy of solid CrBrz a t 298OK. may be estimated from Latimer's tablese (32 e.u.); assuming the heat capacity of CrBrz to be about the same as CrC12' the entropy of solid CrBrz a t 1000°K. is estimated to be 54 e.u. and the entropy of CrBr2(g), from the entropy of sublimation, 88 e.u. This value seems quite reasonable from statistical thermodynamic considerations, although the vibrational contribution is so large that a quantitative estimate is difficult. Translational and rotational contributions alone, assuming CrBrz(g) is linear with a Cr-Br distance of 2.2 A., total 69 e.u., leaving 19 e.u. to be accounted for by vibrational and electronic states. Frequencies observed for somewhat similar molecules, e.g., ZnBr,, CdBrz, HgC12, HgBr2,ssuggest that the vibrational contribution can easily be this large. Acknowledgment.-This work was supported in part by financial assistance from the Office of Ordnance Research, U. S. Army. SEATTLE, WASHINGTON ( 6 ) W. M . Latimer, Tam J O U R N A L , 73, 1480 (1051). (7) H. A. Doerner, Bur. Mines Bull. 577, 1937. (8) W.Klemperer, J . Chcm. Phys., as, I006 (1056).
