James P. Hoare Ford Motor Company Dearborn, Michigan
I
rrfiezing Point Measurement
Measurements of the molal freezing point depression of solutions containing a nonvolatile solute may be used to determine molecular weights and activity coefficients. This requires that the freezing points of the pure solvent and of the solution be measured. This is usually carried out by placing the solution in a double-walled vessel which is immersed in a freezing mixture contained in a widemouthed Dewar flask. By means of a differential thermometer the lowering of the freezing point from that of the pure liquid by the addition of a nonvolatile solute is determined. The freezing point values are determined from the cooling curves obtained by recording the temperature as a function of time. The ideal curve is shown in Figure 1 as curve A. The temperature a t the plateau on the curve is recorded as the true freezing point, T,". However, the more common type of cooling curve is shown in Figure 1 as curve B in which the temperature continues to fall beyond T P . This is known as supercooling. When the solid phase nucleates, the latent heat of fusion is liberated to the surroundings and the curve rises. Finally heat is drawn from the solid mass and the cooling curve falls once more. Since the maximum value, TI, recorded a t the top of the sigmoid curve B does not equal TIo, supercooling is an undesirable phenomenon and attempts are usually made to minimize it.
For some solutions, it is very difficult to separate the solid phase from the liquid phase and supercooling is inevitable. At this laboratory, a method has been used . t o measure the freezing points of such solutions which seems to give good results and which may be of interest to others. I n this method supercooling is desired and encouraged under a definite set of conditions. A dry ice-acetone freezing mixture and a Beckmann differential thermometer were used. To minimize coucentration errors due to the supercooling and to insure constant heat transfer, a steady, constant, vertical stirring was obtained by connecting the ordinary looped stirring rod to an automobile windshield-wiper motor.
Figure 2. water.
I Figure 1.
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TIME Cooling curves:
A, without, ond B, with, supercooling.
/ Journal of Chemical Educations
1
Plots of TI against AT*. for rolutiont of C r 0 1 in 1.79 H H&Ol m
E The minimum temperature, T,,, and the maximum temperature, TI (See Fig. I), were recorded and a plot of (T, - T,,)= AT,, against TI was made. It is seen from Figure 2 that such a plot gives a straight line, the slope of which is determined by the thermal properties of the system. The curves shown in Figure 2 were ohtained from measurements made on solutions of 0.15 11f and 1.00 M CrOa in 1.79 M H2SOa in water. The Beckmann thermometer was set with reference to 1.79 M H8O. in water. The intercepts a t AT,, = 0 are recorded as the freezing points, T,O, of these eolutions. I n order to find what conditions must be met to ohtain the type of curves described in Figure 2: one may consider the heat transfer relationships involved. I n the system described here, the rate of loss of heat from
the test solution to the cooling reservoir a t Tro is given by u,, where ur. = Kf(r) (TI' - Td
and where K is an overall heat transfer coefficient and f(r) is a function of the dimensions of the system and of the stirring rate. Both of these quantities are essentially constant for a given series of measurements on a given solution. Finally, TOis the temperature of the cooling bath. A freezing mixture is so chosen that (T," - T,)>(Tr0 - T,,). Then within the supercooling range T," > T > T,,, v, is essentially constant since (TI' - Td
N
(T.
