GATE 2023 MT – Question 55
The enthalpy of formation of an A–B regular solution containing 80 at.% A is 3.36 kJ mol$^{-1}$. The activity coefficient of A at 500 K in a solution containing 40 at.% A is ______ (one decimal place). Given: $R=8.314$ J mol$^{-1}$ K$^{-1}$.
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Correct answer: 6.0 to 6.5
Explanation
For a regular solution, $\Delta H_{mix}=\Omega x_Ax_B$.
Hence $\Omega=3360/(0.8\times0.2)=21000$ J/mol. At $x_A=0.4$, $RT\ln\gamma_A=\Omega x_B^2=21000(0.6)^2=7560$.
Therefore $\gamma_A=\exp[7560/(8.314\times500)]=6.163$, rounding to **6.2**.