Question
The factor of $$\Delta G$$ values is important in metallurgy. The $$\Delta G$$ values for the following reactions at $${800^ \circ }C$$ are given as :
$${S_2}\left( s \right) + 2{O_2}\left( g \right) \to 2S{O_2}\left( g \right);$$ $$\Delta G = - 544\,kJ$$
$$2Zn\left( s \right) + {S_2}\left( s \right) \to 2ZnS\left( s \right);$$ $$\Delta G = - 293\,kJ$$
$$2Zn\left( s \right) + {O_2}\left( g \right) \to 2ZnO\left( s \right);$$ $$\Delta G = - 480\,kJ$$
$${\text{Then}}\,\Delta G\,{\text{for the reaction :}}$$
$$2ZnS\left( s \right) + 3{O_2}\left( g \right) \to $$ $$2ZnO\left( s \right) + 2S{O_2}\left( g \right)$$
will be :
A.
$$- 357\,kJ$$
B.
$$- 731\,kJ$$
C.
$$- 773\,kJ$$
D.
$$- 229\,kJ$$
Answer :
$$- 731\,kJ$$
Solution :
$$\eqalign{
& {\text{For the reaction}} \cr
& 2\,ZnS \to 2\,Zn + {S_2};\,\Delta {G_1}^ \circ = 293\,kJ...\left( {\text{i}} \right) \cr
& 2\,Zn + {O_2} \to 2\,ZnO;\,\Delta {G_2}^ \circ = - 480\,kJ...\left( {{\text{ii}}} \right) \cr
& {S_2} + 2\,{O_2} \to 2\,S{O_2};\Delta {G_3}^ \circ = - 544\,kJ...\left( {{\text{iii}}} \right) \cr
& \Delta {G^ \circ }\,{\text{for the reaction}} \cr
& 2\,ZnS + 3\,{O_2} \to 2\,ZnO + 2\,S{O_2} \cr
& {\text{can be obtained by adding eqn}}{\text{.}}\,\left( {\text{i}} \right){\text{,}}\left( {{\text{ii}}} \right){\text{and}}\left( {{\text{iii}}} \right) \cr
& \Rightarrow \Delta {G^ \circ } = 293 - 480 - 544 = - 731\,kJ \cr} $$