Given reactions: (i) $2\text{Zn} + \text{O}_2 \rightarrow 2\text{ZnO}; \Delta G_1^\circ = -616\text{ J}$ (ii) $2\text{Zn} + \text{S}_2 \rightarrow 2\text{ZnS}; \Delta G_2^\circ = -293\text{ J}$ (iii) $\text{S}_2 + 2\text{O}_2 \rightarrow 2\text{SO}_2; \Delta G_3^\circ = -408\text{ J}$

The target reaction is: $2\text{ZnS} + 3\text{O}_2 \rightarrow 2\text{ZnO} + 2\text{SO}_2$ This can be obtained by reversing equation (ii) and adding it to equation (i) and equation (iii): Target reaction = $-(\text{ii}) + (\text{i}) + (\text{iii})$ Therefore, by applying Hess's Law for Gibbs free energy: $\Delta G^\circ = -\Delta G_2^\circ + \Delta G_1^\circ + \Delta G_3^\circ$ $\Delta G^\circ = -(-293\text{ J}) + (-616\text{ J}) + (-408\text{ J})$ $\Delta G^\circ = 293 - 616 - 408 = -731\text{ J}$