Consider a binary liquid mixture at constant temperature $T$ and pressure $P$. If the enthalpy change of mixing, $\Delta H = 5x_1x_2$, where $x_1$ and $x_2$ are the mole fraction of species $1$ and $2$ respectively, and the entropy change of mixing $\Delta S = -R[x_1\ln x_1+ x_2 \ln x_2]$ (with $R = 8.314 \text{ J/mol.K})$, then the minimum value of the Gibbs free energy change of mixing at $300\;K$ occur when

1. $x_1 = 0$
2. $x_1 = 0.2$
3. $x_1 = 0.4$
4. $x_1 = 0.5$