P$5\mathrm{.}21$ You are interested in developing a process for converting glycerol $($a byproduct of biodiesel production$)$ to hydrogen. The gas$-$phase reaction is

$C_3{H}_8{O}_3+3H_{2}O3C{O}_2+7H_2$

You put $16\mathrm{.}3$ gmol water and $3\mathrm{.}26$ gmol glycerol into a batch laboratoryscale reactor, adjust the temperature to $200C$ and the pressure to $1\mathrm{.}2$atm. You allow the reaction to reach equilibrium, at which time you determine that the composition of the gas in the reactor is $17\mathrm{.}83$mol$\%H_{2}O,0\mathrm{.}29$mol$\%$ glycerol, $24\mathrm{.}56$mol$\%C{O}_2,$ and $57\mathrm{.}31$mol$\%H_2.$ Use these results as well as values for $hat(G{)}_f$ and $hat(H{)}_f$ from App. B to find $hat(G{)}_f(k\frac{J}{g}$mol$)$ of glycerol.