T H E CONSTANTS O F EBULLIOSCOPY C R E I G S. HOYT
ASD
CARL K. F I N K
Depai tment oJ Chemzstry, Groze C i t y College, Groze City, Pennsylvanza Receized September 8 , 1936
The ebullioscopic method for the determination of molecular weights in solution has been the subject of a tremendous volume of study, both theoretically and experimentally. I n spite of this, the values of the ebullioscopic constants of various solvents as given by different sourceq vary widely. The most consistent and accurate values in use today are those of Rosanoff and Dunphy ( 5 ) . On the assumption that the slope of the vapor pressure curve of the solution is the same as that of the solvent over a short range and the further assumption that the lams of Henry and Raoult are valid for very dilute solutions, they derive the ebullioscopic constant from the simple mathematical expression for Raoult’s law.
If dp/dP
=
n/N
then dp/dT
=
p/dT,n/N
Now, when n = 1 and N = 1000/M, d T = Ka and Kb
=
dT =
PM 1000 dp/dT
The gas laws were then utilized to conrert the expression into
Kb =
RT 1 0 0 0 *dp,’dT ~
on the assuniption that the gas laws accurately represent the behavior of saturated vapors a t the boiling point. This introduces a n error of from 0.5 to 5.0 per cent in the calculated constant, which may be eliminated by applying the Berthelot correction to the gas constant. This is unnecessary, however, when the original form of the equation is employed. As a consequence of the assumptions inherent in the derivation of the equation, this constant is correct only when the solution is very dilute. It constitutes a limiting value of the function which is approached more closely the more dilute the solution. 453
454
CREIG S. HOYT AND CARL K. F I S K
The thermodynaniic cycle at the boiling point has been utilized to derive the boiling-point constant. If proper corrections are mad? for the failure of the gas laws to represent adequately the .tate of vapors at the boiling point, the values should be same a% tho.? obtained by Rosaiioff and Dunphy. I n the limiting case, where the concentration of the solution is so small that the heat of e\-aporation of a mole of solvent from a n infinite amount of the solution ib equal to the latent heat of vaporization,
Kb
=
~
ET2 1000 L,
(3)
where T i s the boiling point of the solution on the ab-olute scale and L, is the latent heat of vaporization. The gas constant R must be corrected by the Berthelot equation, and failure t o do so accounts for much of the discrepancy in earlier results. VARIATION O F EBULLIOSCOPIC COXSTANT WITH BAROMETRIC P R E S S U R E
The variation in the ebullioscopic constant with change in barometric pressure becomes important when determinations of molecular weight are made a t altitudes where the barometric pressure may differ from standard pressure b y 40 mm. or more. hIenzies and Kright (4) state that the variation is approximately 0.03 per cent for all solvents, based on the value at 760 mm. Rosanoff and Dunphy hare furnished a table of variations for each 10 mm. change but, owing to a n unfortunate misprint in the original article and the fact that their constants are based on 100 g. of solvent, the corrections as quoted are often in error by one decimal place (2). Moreover, the values as given by these authors in certain cases are otherwise seriously in error. The variation may be calculated by differentiating Kb with respect to T .
Kb
=
RT' ~
1000L, 2RT dKb/dT = ___ 1000 L, 2RT dKb/dp = 1000L,.dp, d T Table 1 gives the values of the ebullioscopic constant of a number of solvents calculated from equation 1 and from equation 3 and the variation in the ebullioscopic constant with change in barometric pressure, using the slope of the vapor pressure curve gireii by Rosanoff and Dunphy. It is apparent that the constant for all solvents decreases approximately 0.025 per cent for each mm. decrease in barometric pressure. T h k is in good agreement with the value given for benzene by Waihburn and Read (6).
455
COSSTASTS O F EBULLIOSCOPT EXPERIMESTAL
The experiniental deterniinations of the ebullioscopic constant were made with the apparatus designed by llenzies and Kright (1). I n the TABLE 1 Calculated z'alues o j the ebullioscopic constant
'
SOLTEST
SLOPE O F 5 APOR PRESSURE CUR5 E
CORRECTION P E R MY.
Eq. 3
dpldT
Carbon tetrachloride. . . . 0.0306 Cyclohexane. , . . . , . . . . . 0.0301 Ethanol. , . . . . . . . . . . , , 0,0379
n-Heptane n-Hexane Iodobenzene
* Data
0 0292 0 0313 0 0239
77 13 98 42 68 59 188.47 64 67 125 80 36 00 100 00
1
87 63' 1 919 76 35* 1 900
85 76 538 7*
~
2 3 2 8 0 4 2 0
77 43 75 53 83 02 04 505
~
i
1.71 2.54 6 12 2 34 4 06 3 64 5 02 2 79 1 19 2 10 2 68 3 43 2 80 8 87 0 84 1 25 2 06 0 510
1
0.0004 0.0007 0.0016 0 0006 0.0011 0.00'09 0.0013 0.0007 0.0003 0.0005 0 0007 0 0008 0.0007 0.0021 0.0002 0.0010 0.0005 0.0001
from Matthen-s: J. A m . Chem. Soc. 48, 562 (1926)
TABLE 2 Experimental determination o j ebullioscopic constants
'
SOLVEST
Acetone . . , . . . . . . . . . . . . . . . . , . . . . . . . Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . Benzene . . , . , . . . . . . . . . . . . . . . . . . . Be t i ze ne . . . . . . .. .. , ..... . . Car bo i i tetrachloride . . . . . . . . . . . . . , Carbon tetrachloride.. . . . . . . . . . . . , , , . . , LIethanol.. . , , , , , , , , , . , , . . . . . . . . . . . . . . . . Methanol. . . . . . . . . . . . . . . . . . , . . . ,
, , , ,
MOLESOF SOLVENT
, ,
.1
0.3087 0.7774
MOLES OF SOLCTE
Tb
Kb
0.000985 0,000961 0.0010% 0.000952 0.000769 0.001626 0 ,001075 0 001011
0.0730 0.0690 0,1040 0.0933 0.0809 0.1776 0.0360 0.0354
1 733 1.743 2.537 2.534 5 077 5 068 0 835 0 837
original form, as described by these investigators, the solution was drawn by the pump from the bottom of the boiling vessel. Bancroft and Davis (1) haye shown that in the Cottrell apparatus superheating occurs when the
456
C R E I G S. HOYT AND CARL K . F I N K
pump is placed close to the bottom. By shortening the pump in the apparatus of RIenzies and Wright so that it drew the solution from close t o the surface and plugging t h e efflux end loosely with a plug of glass wool, superheating was eliminated and a steady stream of solution in equilibrium with its vapor flowed over the lower bulb of the differential thermometer. The whole apparatus was placed inside a case with a plate glass window, and the readings were taken with a telescope located several feet away. The use of a micro burner in place of the Bunsen burner gave good control of the boiling rate. Benzil was chosen as solute, since its boiling point is sufficiently high so t h a t its vapor pressure is negligible at the boiling point of any solvent used. The sample was recrystallized several times from alcohol and melted sharply at 95°C. The solvents were chosen t o cover a wide range of internal pressures in order to test the effect when solutions were not ideal (3). Table 2 shows the experimental values for acetone, benzene, carbon tetrachloride, and methanol. SUMMARY
A recalculation of the values of the ebullioscopic constants by the equation of Rosanoff and Dunphy has been made for eighteen common solvents. These agree closely with those calculated from the usual thermodynamic equation, provided the gas constant is corrected by the Berthelot equation. Experimental values check the theoretical when superheating is eliminated. Where any appreciable difference occurs between the two values, t h a t calculated by the equation of Rosanoff and Dunphy is to be preferred. REFERENCES (1) BANCROFT A N D DAVIS:J. Phys. Chem. 33, 591 (1930). (2) GETMASA N D D ~ X I E: LOutlines ~ of Theoretical Chemistry, 5th edition. TViley and Sons, Inc.. Yew York (1931). (3) HILDEBRASD: Solubility, 211d edition. T h e Chemical Catalog Co , I n r York (1936). (4) MESZIES~ K WRIGHT: D J. 4 m . Cheni SOC.43, 2309 (1921). ( 5 ) ROSASOFF A N D DUNPHI-: J. Am. Chem. SOC.36, 1411 (1911). (6) WASHBURN AXD R E ~ DJ : Am. Chem. Soc. 41, 729 (1919).
John
New
