Answer
$\Delta _{r}G^{\circ}=462.28\,kJ$
This reaction is not a good choice to produce $Si$.
Work Step by Step
$\Delta_{r}G^{\circ}=\Sigma n_{p}\Delta_{f}G^{\circ}(products)-\Sigma n_{r}\Delta _{f}G^{\circ}(reactants)$
$=[1\,mol\times\Delta_{f}G^{\circ}(Si,s)+1\,mol\times\Delta_{f}G^{\circ}(CO_{2},g)]-[1\,mol\times\Delta_{f}G^{\circ}(SiO_{2},s)+1\,mol\times\Delta_{f}G^{\circ}(C,s)]$
$=[(0)+(-394.359\,kJ)]-[(-856.64\,kJ)+(0)]$
$=462.28\,kJ$
As $\Delta _{r}G^{\circ}$ is positive, the reaction is reactant-favored (nonspontaneous) .
Therefore, this reaction is not a good choice to produce silicon.
