Answer
$−173.3\text{ Btu/lbm}$
Work Step by Step
Obtaining properties from Table A-4E, the Gibbs function for the liquid phase is,
$$
g_f=h_f-T s_f=487.89 \mathrm{Btu} / \mathrm{lbm}-(959.67 \mathrm{R})(0.6890 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R})=-173.3\ \mathrm{Btu} / \mathrm{lbm}
$$ For the vapor phase, $$
g_g=h_g-T s_g=1202.3 \mathrm{Btu} / \mathrm{lbm}-(959.67 \mathrm{R})(1.4334 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R})=-173.3\ \mathrm{Btu} / \mathrm{lbm}
$$ For the saturated mixture with a quality of $40 \%$,$$
\begin{aligned}
& h=h_f+x h_{f g}=487.89 \mathrm{Btu} / \mathrm{lbm}+(0.40)(714.44 \mathrm{Btu} / \mathrm{lbm})=773.67\ \mathrm{Btu} / \mathrm{lbm} \\
& s=s_f+x s_{f g}=0.6890 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R}+(0.40)(0.7445 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R})=0.9868\ \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R} \\
& g=h-T s=773.67 \mathrm{Btu} / \mathrm{lbm}-(959.67 \mathrm{R})(0.9868 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R})=-173.3\ \mathrm{Btu} / \mathrm{lbm}
\end{aligned}
$$ The results agree and demonstrate that phase equilibrium exists.
