$419.$ The theoretical minimum work required to separate one mole of a liquid mixture at $1$ atm, containing $50$ mole $\%$ each of n$-$ heptane and n$-$ octane into pure compounds each at $1$ atm is

$-2$ RT ln $0\mathrm{.}5$

$-$RT ln $0\mathrm{.}5$

$0\mathrm{.}5$ RT

$2$ RT