The value of is — Solutions and Colligative Properties Chemistry Question

💡 Solution & Explanation

$\Delta G_{\text{mix}}$ per mole of solution is given by $RT (X_A \ln X_A + X_B \ln X_B)$. Here $X_A = \frac{1}{3}$, $X_B = \frac{2}{3}$, $T = 300 \text{ K}$, and $R \approx 2 \text{ cal/mol-K}$. $\Delta G_{\text{mix}} = 2 \times 300 (\frac{1}{3}\ln\frac{1}{3} + \frac{2}{3}\ln\frac{2}{3}) = 600 [-\frac{1}{3}(1.1) + \frac{2}{3}(0.7 - 1.1)] = 600 [-0.366 - 0.266] = 600 [-\frac{1.1 + 0.8}{3}] = 200 \times (-1.9) = -380 \text{ cal/mol}$. Therefore, correct answer is D.