Answer to Question #3129 in Physical Chemistry for lfain

Question

Consider the compression at 15.6& [sup]o[/sup]C of 0.35 mol H[sub]2[/sub]O(l) from 0.10 atm to1.00 atm. Calculate the values of ΔG when the process is carried out:
(a) isothermally and reversibly and
(b) isothermally and irreversibly under a constantexternal pressure of 1.0 atm.

Answer 1

Firstly calculate the initial and final volumes of gas (using the ideal gas equation):
pV = nRT
V = nRT/p
V₁ = 0.35×0.082×288.6/0.1 = 82.83 L = 0.08282 m³
V₂ = 0.35×0.082×288.6/1 = 8.283 L = 0.008282 m³
(a) isothermally and reversibly
W = ΔG = −nRT ln(V₂/V₁) = 0.35×8.314×288.6 ln(0.008282/0.08282) = 1933.7 J
(b) isothermally and irreversibly under a constant external pressure of 1.0 atm.
W = ΔG = −p(V₂ − V₁) = 1.01 × 105(0.008282 − 0.08282) = 7528.3 J