Ethanol condenses onto a droplet of radius at

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Thermodynamic potentials and the formal structure of thermodynamics

Soft Matter at the Thermal Scale, Ch Nucleation and the lifetime of a metastable phase

Problem

Ethanol condenses onto a droplet of radius r=5.0 nmr = 5.0\,\mathrm{nm} at T=298 KT = 298\,\mathrm{K}. Its interfacial tension is γ=0.0227 N m−1\gamma = 0.0227\,\mathrm{N\,m^{-1}}, its density ρ=789 kg m−3\rho = 789\,\mathrm{kg\,m^{-3}} and its molar mass M=46.07 g mol−1M = 46.07\,\mathrm{g\,mol^{-1}}. Using the Kelvin equation kBTln⁡(pr/p∞)=2γvm/rk_BT\ln(p_r/p_\infty) = 2\gamma v_m/r, with molecular volume vm=M/(ρNAv)v_m = M/(\rho N_{\rm Av}), find the ratio pr/p∞p_r/p_\infty of the vapour pressure over the droplet to that over a flat ethanol surface.

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