Answer
(a) $-1139\,kJ/mol$
(b) $-140.0\,kJ/mol$
(c) $-2935\,kJ/mol$
Work Step by Step
Recall: $\Delta G^{\circ}=\Sigma n_{p}\Delta G_{f}^{\circ}(products)-\Sigma n_{r}\Delta G_{f}^{\circ}(reactants)$
(a) $\Delta G^{\circ}=[2\Delta G_{f}^{\circ}(MgO,s)]-[2\Delta G_{f}^{\circ}(Mg,s)+\Delta G_{f}^{\circ}(O_{2},g)]$
$=[2(-569.6\,kJ/mol)]-[2(0)+(0)]$
$=-1139\,kJ/mol$
(b) $\Delta G^{\circ}=[2\Delta G_{f}^{\circ}(SO_{3},g)]-[2\Delta G_{f}^{\circ}(SO_{2},g)+\Delta G_{f}^{\circ}(O_{2},g)]$
$=[2(-370.4\,kJ/mol)]-[2(-300.4)+(0)]$
$=-140.0\,kJ/mol$
(c) $\Delta G^{\circ}=[4\Delta G_{f}^{\circ}(CO_{2},g)+6\Delta G_{f}^{\circ}(H_{2}O,l)]-[2\Delta G_{f}^{\circ}(C_{2}H_{6},g)+7\Delta G_{f}^{\circ}(O_{2},g)]$
$=[4(-394.4\,kJ/mol)+6(-237.2\,kJ/mol)]-[2(-32.89)+7(0)]$
$=-2935\,kJ/mol$
