Question

Determine whether the reactions with the following $\Delta$H and $\Delta$S values are spontaneous or non-spontaneous. State whether the reactions are exothermic or endothermic.
(a) $\Delta$H$=-110$kJ, $\Delta$S$=+40J{K}^{-1}$ at $400$K
(b) $\Delta$H$=+40$kJ, $\Delta$S$=-120J{K}^{-1}$ at $250$K.

Answer 1

(a) Given: $\Delta H=-110$kJ
$\Delta S=40J{k}^{-1}$
$=0.04KJ{k}^{-1}$
Temperature, T$=4000$K
$\Delta G=?$
Since $\Delta H$ is $-$Ve, the reaction is exothermic
$\Delta G=\Delta H-T\Delta S$
$=-110-400\times 0.04$
$=-110-16$
$=-126$kJ
Since, $\Delta$G is negative, the reaction is spontaneous and exothermic.

(b) Given: $\Delta H=40$kJ,
$\Delta S=-120J{k}^{-1}=-0.12KJ{k}^{-1}$
Temperature, $T=250$K
$\Delta G=?$
Since $\Delta$H is $+$ve, the reaction is endothermic.
$\Delta G=\Delta H-T.\Delta S$
$=40-250\times (-0.12)$
$=40+30$
$=70$kJ.
Since $\Delta G>0$, the reaction is non-spontaneous
$\Delta G=70$kJ; The reaction is endothermic and non-spontaneous.