This problem illustrates the use of a mass spectrometer to measure the enthalpy of a phase transition for the novel compound C₆₀ (buckminsterfullerene). It is taken from a paper by C.K. Mathews et al., J. Phys. Chem., 96, 3566 (1992). You do not have to look at the paper to answer the question, but you will probably find it helpful.

For the purposes of this determination, a solid sample is placed in a constant-temperature evacuated vessel with a small pinhole in it. The solid is thus essentially in equilibrium with its vapor. The small number of molecules leaking out of the chamber are ionized, passed through the spectrometer, and produce a current that is proportional to the rate of effusion through the hole (and thus also proportional to the concentration of the gas molecules in the vessel).

Below are the measurements of the signal intensity I of the C₆₀ peak as a function of temperature, which may be used to determine the enthalpy of sublimation of C_60.. Note that Mathews et al. plot the logarithm of the product IT vs. T^-1 in their determination.

T (K)	Signal intensity I (arbitrary units)
799	3.41E-01
779	1.94E-01
766	1.13E-01
760	7.67E-02
740	4.22E-02
727	2.09E-02
700	8.39E-03
675	2.59E-03
651	9.40E-04

(a) Explain why Mathews et al. plot the logarithm of the product IT vs. T^-1 (Fig. 2). (4 pts)

(b) Is the Clausius-Clapeyron equation a valid method to find an enthalpy of vaporization or sublimation for such a large molecule as C₆₀? Explain your answer. (3 pts).

(c) Determine the enthalpy of sublimation of C₆₀ from the data given above (15 pts).

(d) Is there any evidence for a large DC_P of sublimation in the data? Why or why not? (3 pts)