Acetone boils at under a pressure of

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Interacting systems, real gases and phase equilibria

Thermal Physics, Ch Phase coexistence and the Clausius-Clapeyron relation

Problem

Acetone boils at Tb=329.2 KT_b = 329.2\,\mathrm{K} under a pressure of 101.3 kPa101.3\,\mathrm{kPa}, where its latent heat of vaporisation is L=29.1 kJ mol−1L = 29.1\,\mathrm{kJ\,mol^{-1}}, taken as constant over the few kelvin used below. Treat the vapour as an ideal gas; the liquid's molar volume is 0.074 L mol−10.074\,\mathrm{L\,mol^{-1}}, negligible beside the vapour's. Take R=8.314 J mol−1 K−1R = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}. ((a)) Find the entropy of vaporisation of acetone per mole at 329.2 K329.2\,\mathrm{K}. ((b)) Find the molar volume change Δv\Delta v on vaporising at 329.2 K329.2\,\mathrm{K} and 101.3 kPa101.3\,\mathrm{kPa}, and hence the slope dp/dT\mathrm{d}p/\mathrm{d}T of the vaporisation line there, in kPa K−1\mathrm{kPa\,K^{-1}}. ((c)) A distillation flask is pumped down so that the pressure above the boiling acetone is 92.0 kPa92.0\,\mathrm{kPa}. Using the slope of part (b) as constant over this small interval, find the temperature at which the acetone boils. ((d)) The chemical potential of an ideal-gas vapour at fixed temperature depends on pressure as μ(T,p)=μ(T,p0)+kBTln⁡(p/p0)\mu(T,p) = \mu(T,p_0) + k_BT\ln(p/p_0) per particle. The liquid and its vapour at 101.3 kPa101.3\,\mathrm{kPa} have equal μ\mu at 329.2 K329.2\,\mathrm{K}. Calculate, per mole, how far the vapour's chemical potential at 92.0 kPa92.0\,\mathrm{kPa} and 329.2 K329.2\,\mathrm{K} lies below the liquid's, and state which way molecules therefore move. ((e)) A separate temperature-composition diagram at 101.3 kPa101.3\,\mathrm{kPa} is given for acetone-toluene mixtures, treated as ideal. At 355 K355\,\mathrm{K} the tie line joins a liquid of acetone mole fraction xL=0.35x_L = 0.35 to a vapour of acetone mole fraction xV=0.62x_V = 0.62. A closed vessel holds 4.00 mol4.00\,\mathrm{mol} of overall acetone mole fraction x0=0.50x_0 = 0.50 at 355 K355\,\mathrm{K}. How many moles are in the vapour phase?

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