Answer
3271 K
Work Step by Step
$\Delta _{r}H^{\circ}=\Sigma n_{p}\Delta _{f}H^{\circ}(products)-\Sigma n_{r}\Delta _{f}H^{\circ}(reactants)$
$=[2\Delta _{f}H^{\circ}(CO_{2},g)]-[2\Delta _{f}H^{\circ}(CO,g)+\Delta _{f}H^{\circ}(O_{2},g)]$
$=[2(-393.509\,kJ/mol)]-[2(-110.525\,kJ/mol)+(0\,kJ/mol)]$
$=-565.968\,kJ/mol$
$\Delta _{r}S^{\circ}=\Sigma n_{p}S^{\circ}(products)-\Sigma n_{r}S^{\circ}(reactants)$
$=[2S^{\circ}(CO_{2},g)]-[2S^{\circ}(CO,g)+S^{\circ}(O_{2},g)]$
$=[2(213.74\,JK^{-1}mol^{-1})]-[2(197.674\,JK^{-1}mol^{-1})+(205.138\,JK^{-1}mol^{-1})]$
$=-173.01\,JK^{-1}mol^{-1}$
T( at which $\Delta _{r}G^{\circ}$ changes sign)=$\frac{\Delta_{r}H^{\circ}}{\Delta_{r}S^{\circ}}=\frac{-565.968\times10^{3}\,J/mol}{-173.01\,JK^{-1}mol^{-1}}$
$=3271\,K$
