Benzene boils at under

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Interacting systems, real gases and phase equilibria · Interacting systems, real gases and phase equilibria

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

Problem

Benzene boils at

353.2\,\mathrm{K}

under

101.3\,\mathrm{kPa}

, where its latent heat of vaporisation is

L_{\rm vap} = 30.8\,\mathrm{kJ\,mol^{-1}}

. The vapour may be treated as an ideal gas; the liquid's molar volume,

89\,\mathrm{cm^3\,mol^{-1}}

, is negligible beside the vapour's. Take

R = 8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}

. Two phases coexist where their molar chemical potentials are equal. By stepping a small distance

(\mathrm{d}T,\mathrm{d}p)

along the coexistence line and using

\mathrm{d}\mu = -s\,\mathrm{d}T + v\,\mathrm{d}p

for each phase, derive the Clausius-Clapeyron relation for the slope of the line, and then find: ((a)) the slope

\mathrm{d}p/\mathrm{d}T

of benzene's liquid-vapour line at its normal boiling point, in

\mathrm{kPa\,K^{-1}}

; ((b)) the boiling temperature of benzene when the laboratory pressure falls to

95.0\,\mathrm{kPa}

, using that local slope as constant over the small pressure change.

Browse the problem library