Derive the association model for the Peng-Robinson model, using the vant Hoff formula with C P /R

Derive the association model for the Peng-Robinson model, using the van’t Hoff formula with ΔC_P/R = -1. Extend the homomorph concept by applying ω^PR = ω^homo, where ω^homo is the acentric factor for the nonassociating homomorph and ω^PR is the acentric factor substituting for the associating compound into the Peng-Robinson expression for a.

(a) For methanol, determine the values of K_a', b, a/bRT_c, x_Mc that match the critical point.

(b) Determine the vapor pressure at T_r = 0.7 for methanol assuming a hydrogen bonding energy of 15 kJ/mole, and compare to the experimental value. Infer the acentric factor and compare to the experimental value.

(c) Plot log P_r sat versus T_r =1 for the Peng-Robinson EOS and the Peng-Robinson hydrogen bonding EOS, and experiment.