The excess free energy of a binary solution mixture is given by [ frac{G^{mathrm{E}}}{R T}=x_{1} x_{2}left[A+Bleft(x_{1}-x_{2} ight)

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The excess free energy of a binary solution mixture is given by

\[ \frac{G^{\mathrm{E}}}{R T}=x_{1} x_{2}\left[A+B\left(x_{1}-x_{2}\right)\right] \mathrm{J} / \mathrm{mol} \]

Find the expressions for \(\gamma_{1}\) and \(\gamma_{2}\).

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