Explanation

For an ideal solution with mole fractions xA = 0.5 and xB = 0.5, the entropy of mixing is $\Delta S_{mix} = -R(x_A \ln x_A + x_B \ln x_B) = -R(0.5 \ln 0.5 + 0.5 \ln 0.5) = -R(2 * 0.5 \ln 0.5) = -R \ln 0.5$. Since $-\ln 0.5 = \ln (1/0.5) = \ln 2$, the entropy is $R \ln 2$.