The Temperature Dependence of the Vapor Pressure of Carbon Tetrachloride

This experiment gives you the opportunity to examine the thermodynamics of a pure system, namely CCl4. In particular, you will study the phase diagram of this system, which is rather simple because there is only a single chemical component,  Thus it is sufficient to plot the vapor pressure as a function of temperature.  Then, by using the Clapeyron equation you will be able to extract the enthalpy of sublimation and vaporization, and the temperature of the phase transitions.

Theory
We would liek to derive the condition that pressure P and temperature T must obey in order for two phases to be in equilibrium. As always, we start form the fundamental requirem=ent that for two phases and tto be in equilibrium their chemical potentials must be equal:

ua=ub  (1)

Now the chemical potential of a pure substance is just the molar Gibbs free energy.  By taking the differential of the above eqaution we obtain:

dua=dub  (2)

which leads to

dGma=dGmb  (3)

 and so

-Sma dT + VmadP = -Smb dT + Vmb dP  (4)

can rearrange to

dP/dT = (Smb - Sma)/(Vmb - Vma) = delSm/delVm  (5)

Now delSm for a phase transition is just Hm/T, and we can approximate delVm as RT/P, since we are looking at the difference in volume between a gas (large) and a condensed phase (small).  These substitutions result in the Clausius-Clapeyron equation:

dP/dT = delHm/T(RT/P)  (6)

which most conveniently is written as

dlnP/d(1/T) = -delHm/R  (7)

Thus a plot of lnP as a function of 1/T has a slope delHm/R.  If delHm were independent of temperature, this slope would be constant.  If not, some curvature in the plot would be evident.  For extracting thermodynamic quantities it's easiest to work with the integrated form of equation 6, eventaully arriving at:

ln(P/Po) = (delH/R)*[(1/To)-(1/T)]