4. Show that the Gibbs-Duhem equation can be written for a binary mixture as: \[ x_{A}\left(\frac{\partial \ln \gamma_{A}}{\partial x_{A}}\right)_{P, T}+\left(1-x_{A}\right)\left(\frac{\partial \ln \gamma_{B}}{\partial x_{A}}\right)_{P, T}=0 \]
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The Gibbs-Duhem equation for a binary mixture is given by: \[ x_A d\mu_A + x_B d\mu_B = 0 \] where \(x_A\) and \(x_B\) are the mole fractions of components A and B, and \(\mu_A\) and \(\mu_B\) are their respective chemical potentials. Show more…
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