Given(i) , 2Fe_2O_{3(s)} to 4Fe_{(s)} + 3O_{2 | vedclass

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(B) Given reactions are:$(i) \, 2Fe_2O_{3(s)} 	o 4Fe_{(s)} + 3O_{2(g)}; \, \Delta _rG^o = + 1487.0 \, kJ \, mol^{-1}$$(ii) \, 2CO_{(g)} + O_{2(g)}

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$-56.2$

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(B) Given reactions are:$(i) \, 2Fe_2O_{3(s)} 	o 4Fe_{(s)} + 3O_{2(g)}; \, \Delta _rG^o = + 1487.0 \, kJ \, mol^{-1}$$(ii) \, 2CO_{(g)} + O_{2(g)} 	o 2CO_{2(g)}; \, \Delta _rG^o = - 514.4 \, kJ \, mol^{-1}$To obtain the target reaction $2Fe_2O_{3(s)} + 6CO_{(g)} 	o 4Fe_{(s)} + 6CO_{2(g)}$,multiply reaction $(ii)$ by $3$:$(iii) \, 6CO_{(g)} + 3O_{2(g)} 	o 6CO_{2(g)}; \, \Delta _rG^o = 3 	imes (- 514.4) = - 1543.2 \, kJ \, mol^{-1}$Now,add reaction $(i)$ and reaction $(iii)$:$(2Fe_2O_{3(s)} + 6CO_{(g)} + 3O_{2(g)}) 	o (4Fe_{(s)} + 3O_{2(g)} + 6CO_{2(g)})$Canceling $3O_{2(g)}$ from both sides gives the target reaction:$2Fe_2O_{3(s)} + 6CO_{(g)} 	o 4Fe_{(s)} + 6CO_{2(g)}$The total $\Delta _rG^o$ is the sum of the $\Delta _rG^o$ values:$\Delta _rG^o = 1487.0 + (- 1543.2) = - 56.2 \, kJ \, mol^{-1}$

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