Answer
(a) $11.62\,JK^{-1}mol^{-1}$
(b) $174.7\,JK^{-1}mol^{-1}$
(c) $-620.\,JK^{-1}mol^{-1}$
Work Step by Step
Recall: $\Delta S^{\circ}_{rxn}=\Sigma n_{p}S^{\circ}(products)-\Sigma n_{r}S^{\circ}(reactants)$
(a) $\Delta S^{\circ}_{rxn}=[S^{\circ}(SO_{2},g)]-[S^{\circ}(S,rhombic)+S^{\circ}(O_{2},g)]$
$=[(248.5\,JK^{-1}mol^{-1})]-[(31.88\,JK^{-1}mol^{-1})+(205.0\,JK^{-1}mol^{-1})]$
$=11.62\,JK^{-1}mol^{-1}$
(b) $\Delta S^{\circ}_{rxn}=[S^{\circ}(MgO,s)+S^{\circ}(CO_{2},g)]-[S^{\circ}(MgCO_{3},s)]$
$=[(26.78\,JK^{-1}mol^{-1})+(213.6\,JK^{-1}mol^{-1})]-(65.69\,JK^{-1}mol^{-1})$
$=174.7\,JK^{-1}mol^{-1}$
(c) $\Delta S^{\circ}_{rxn}=[4S^{\circ}(CO_{2},g)+6S^{\circ}(H_{2}O,l)]-[2S^{\circ}(C_{2}H_{6},g)+7S^{\circ}(O_{2},g)]$
$=[4(213.6\,JK^{-1}mol^{-1})+6(69.9\,JK^{-1}mol^{-1})]-[2(229.5\,JK^{-1}mol^{-1})+7(205.0\,JK^{-1}mol^{-1})]$
$=-620.\,JK^{-1}mol^{-1}$
