GATE 2025 MT – Question 50
The excess molar Gibbs free energy of a solution of elements A and B at 1000 K is $G^{XS}=-3000X_AX_B\ \mathrm{J\,mol^{-1}}$, where $X_A$ and $X_B$ are mole fractions. The activity of B in a solution containing 40 mol% B at 1000 K is ______ (rounded to two decimal places). Given: $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$.
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Correct answer: 0.34 to 0.36
Explanation
For the regular-solution expression $G^{XS}=\Omega X_AX_B$, the partial excess Gibbs energy is $RT\ln\gamma_B=\Omega X_A^2$.
Here $X_B=0.4$, $X_A=0.6$, and $\Omega=-3000$. Thus $\ln\gamma_B=-3000(0.6)^2/(8.314\times1000)=-1080/8314$.
The activity is $a_B=X_B\gamma_B=0.4\exp(-1080/8314)=0.3513\ldots$. The answer is **0.35**.