Problem on mol fraction of naphthalene

Question

At 20°C the solubility of solid naphthalene in hexane is 0.09 mol/mol of solution. Use this information and the data below to estimate the following for this system:

a) The mol fraction of naphthalene in the vapour phase in equilibrium with a saturated solution of naphthalene at 20^oC.

b) The mol fraction of naphthalene in the vapor phase in equilibrium with a liquid containing 5.0 mol% naphthalene and 95 mol% hexane at 20°C.

c) The solubility of naphthalene in hexane at 40^oc

Data:

Heat of melting of naphthalene: 4610 cal/mol
Heat of melting of hexane: 3119 cal/mol
Melting point of naphthalene: 80.2^oC
Melting point of hexane: -95^oC

Vapor pressure at 20°C:
solid naphthalene: 0.054 mmHg
liquid hexane: 122.5 mmHg

The activity coefficients of naphthalene and hexane in the liquid solution can be represented by the Regular Solution model

RT ln γ_A = αX_B²

RT ln γ_B = αX_A²

where α is a constant independent of temperature and composition.