The theoretical minimum work required to separate \(1 \mathrm{~mol}\) of a liquid mixture at \(1 \mathrm{~atm}\) containing \(50 \mathrm{~mol} \%\) each of \(n\)-heptane and \(n\)-octane into pure compounds, each at \(1 \mathrm{~atm}\), is

(a) \(-2 R T \ln 0.5\)

(b) \(-R T \ln 0.5\)

(c) \(0.5 R T\)

(d) \(2 R T\).