Thermodynamics and Thermochemistry - Result Question 87

####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:

  1. 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.



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