Question

For the reaction
$2A_{\left(g\right)}+B_{\left(g\right)}\to 2D_{\left(g\right)}\Delta U^{\theta }=-10.5kJand\Delta S^{\theta }=–44.1J{K}^{-1}$.
Calculate $\Delta G^{\theta }$ for the reaction, and predict whether the reaction may occur spontaneously.

Answer 1

For the given reaction,
$2A_{\left(g\right)}+B_{\left(g\right)}\to 2D_{\left(g\right)}\Delta n_g=2-\left(3\right)=–1mole$
Substituting the value of $\Delta U^{\theta }$ the expression of $\Delta H$:

$\Delta H^{\theta }=\Delta U^{\theta }+\Delta n_{g}RT=(-10.5kJ)+(-1)(8.314\times {10}^{-3}kJ{K}^{-1}mo{l}^{-1})\left(298K\right)=-10.5kJ-2.48kJ\Delta H^{\theta }=-12.98kJ$
Substituting the value of $\Delta H^{\theta }$ and $\Delta S^{\theta }$ in the expression of $\Delta G^{\theta }$:
$\Delta G^{\theta }=\Delta H^{\theta }=T\Delta S^{\theta }=-12.98kJ-\left(298K\right)(-44.1J{K}^{-1})=-12.98kJ+13.14kJ\Delta G^{\theta }=+0.16kJ$
Since $\Delta G^{\theta }$ for the reaction is positive, the reaction will not occur spontaneously.