Thermodynamics and Thermochemistry 1 Question 12
12. The standard reaction Gibbs energy for a chemical reaction at an absolute temperature $T$ is given by, $\Delta_{r} G^{\mathbf{o}}=A-B T$
Where $A$ and $B$ are non-zero constants.
Which of the following is true about this reaction?
(2019 Main, 11 Jan II)
(a) Endothermic if, $A<0$ and $B>0$
(b) Exothermic if, $B<0$
(c) Exothermic if, $A>0$ and $B<0$
(d) Endothermic if, $A>0$
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Solution:
- According to Gibb’s Helmholtz equation,
$$ \begin{aligned} & \Delta_{r} G^{\circ} & =\Delta_{r} H^{\circ}-T \Delta_{r} S^{\circ} \ \text { Given, } & \Delta_{r} G^{\circ} & =A-B T \end{aligned} $$
On comparing above two equations, we get,
$$ A=\Delta H^{\circ} \text { and } \Delta S^{\circ}=B $$
We know that, if $\Delta H^{\circ}$ is negative, reaction is exothermic and when it is positive, reaction is endothermic.
$\therefore$ If $A>0$, i.e. positive, reaction is endothermic.
