The use of supercritical fluids as mobile phases in SFC depends on their properties as non polar solvents. The solubility parameter, ∂, is defined as (∆Ucohesive/Vm)1/2, where ∆Ucohesive is the cohesive energy of the solvent,

the energy per mole needed to increase the volume isothermally to an infinite value. Diethyl ether, carbon tetrachloride, and dioxane have solubility parameter ranges of7-8, 8-9, and 10-11, respectively.

(a) Derive a practical equation for the computation of the isotherms for the reduced internal energy change, ∆U (TV, vt,) defined as

∆Ut (TtVt) = Ut (TvVt) – Ut (Tvoo)/PcVc

(b) Draw a graph of U against p, .for the isotherms T, = 1, 1.2, and 1.5 in the reduced pressure range for which 0.7 < V, < 2.

(c) Draw a graph of ∂ against P, for the carbon dioxide isotherms T, = 1 and 1.5 in the reduced pressure range for which 1 < V, < 3. In what pressure range at Tf= I will carbon dioxide have solvent properties similar to those of liquid carbon tetrachloride? Hint. Use mathematical software or a spreadsheet.