Concept

# Duhem–Margules equation

Summary
The Duhem–Margules equation, named for Pierre Duhem and Max Margules, is a thermodynamic statement of the relationship between the two components of a single liquid where the vapour mixture is regarded as an ideal gas: : \left ( \frac{\mathrm{d}\ln P_A}{\mathrm{d}\ln x_A} \right ){T,P} = \left ( \frac{\mathrm{d}\ln P_B}{\mathrm{d}\ln x_B} \right ){T,P} where PA and PB are the partial vapour pressures of the two constituents and xA and xB are the mole fractions of the liquid. The equation gives the relation between changes in mole fraction and partial pressure of the components. Derivation Let us consider a binary liquid mixture of two component in equilibrium with their vapor at constant temperature and pressure. Then from the Gibbs–Duhem equation, we have Where nA and nB are number of moles of the component A and B while μA and μB are their chemical potentials. Dividing equation () by nA + nB, then : \frac{n_A}{n_A+n_B} \mathrm{d}\mu_A + \fr
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