Question

Calculate $△G^o$ for the following reaction at $298\text{K}$:
$CO\left(g\right)+\left(\frac{1}{2}\right)O_2\left(g\right)\to C{O}_2\left(g\right);△H^o=-282.84\text{kJ/mol}$
Given,
$S_{C{O}_2\left(g\right)}^o=213.8{\text{J K}}^{-1}{\text{mol}}^{-1},S_{CO\left(g\right)}^o=197.9{\text{J K}}^{-1}{\text{mol}}^{-1},S_{O_2}^o=205.0{\text{J K}}^{-1}{\text{mol}}^{-1}$

• A. $+557J/mol$
• B. $-557kJ/mol$
• C. $+257kJ/mol$
• D. $-257kJ/mol$

Answer 1

The correct option is D $-257kJ/mol$

Given that the reaction is
$CO\left(g\right)+\left(\frac{1}{2}\right)O_2\left(g\right)\to C{O}_2\left(g\right);△H^o=-282.84kJ$
and, $S_{C{O}_2}^o=213.8{\text{J K}}^{-1}{\text{mol}}^{-1},S_{CO\left(g\right)}^o=197.9{\text{J K}}^{-1}{\text{mol}}^{-1},S_{O_2}^o=205.0{\text{J K}}^{-1}{\text{mol}}^{-1}$
we know that-
$△S^o=\sum S_{\text{(products)}}^o-\sum S_{\text{(reactants)}}^o$
$=\left[S_{C{O}_2}^o\right]-[S_{\left(CO\right)}^o+\frac{1}{2}{S}_{O_2}^o]$
$=213.8-[197.9+\frac{1}{2}\times 205]$
$△S^o=-86.6{\text{J K}}^{-1}{\text{mol}}^{-1}=-86.6\times {10}^{-3}{\text{kJ K}}^{-1}{\text{mol}}^{-1}$

According to Gibbs-Helmholtz equation,
$△G^o=△H^o-T△S^o$
$=-282.84-298\times (-86.6\times {10}^{-3})$
$=-282.84+25.807$
$=-257.033\text{kJ/mol}$