## Chemistry: The Molecular Science (5th Edition)

Published by Cengage Learning

# Chapter 16 - Thermodynamics: Directionality of Chemical Reactions - Problem Solving Practice 16.6 - Page 714: a

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)=$\frac{\Delta_{r}H^{\circ}}{\Delta_{r}S^{\circ}}=\frac{-565.968\times10^{3}\,J/mol}{-173.01\,JK^{-1}mol^{-1}}$ $=3271\,K$

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