In an investigation of thermophysical properties of methylbenzene R.D. Goodwin (J. Phys. Chem. Ref. Data 18, XXXXXXXXXXpresented expressions for two phase boundaries. The solid–liquid boundary is...

In an investigation of thermophysical properties of methylbenzene R.D. Goodwin (J. Phys. Chem. Ref. Data 18, 1565 (1989)) presented expressions for two phase boundaries. The solid–liquid boundary is given by
p/bar = p₃/bar + 1000(5.60 + 11.727x)x where x = (T/T₃) − 1 and the triple point pressure and temperature are p₃
= 0.4362 μbar and T₃
= 178.15 K. The liquid–vapour curve is given by
ln(p/bar) = –10.418/y +21.157–15.996y + 14.015y²–5.0120y³
+ 4.7334(1—y)^1.70
where y = T/T_c
= T/(593.95 K). (a) Plot the solid–liquid and liquid–vapour phase boundaries. (b) Estimate the standard melting point of methylbenzene. (c) Estimate the standard boiling point of methylbenzene. (The equation you will need to solve to find this quantity cannot be solved by hand, so you should use a numerical approach, e.g. by using mathematical software.) (d) Calculate the standard enthalpy of vaporization of methylbenzene at the standard boiling point, given that the molar volumes of the liquid and vapour at the standard boiling point are 0.12 dm³
mol⁻¹
and 30.3 dm³
mol⁻¹, respectively.