PYQ NEET- Chemical Thermodynamics L-10

Question: For a given reaction, $\Delta H=35.5 \mathrm{~kJ}$ $\mathrm{mol}^{-1}$ and $\Delta S=83.6 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$. The reaction is spontaneous at : (Assume that $\Delta H$ and $\Delta S$ do not vary with temperature)#

A) $T<425 \mathrm{~K}$

B) $T>425 \mathrm{~K}$

C) all temperatures

D) $\mathrm{T}>298 \mathrm{~K}$

Answer: $T>425 \mathrm{~K}$#

Solution:#

According to Gibbs-Helmholtz equation, Gibbs energy $(\Delta G)=\Delta H-T \Delta S$

Where, $\quad \Delta H=$ Enthalpy change $\Delta S=$ Entropy change $T=$ Temperature

For a reaction to be spontaneous $$ \Delta G<0 \text {. } $$ $\therefore$ Gibbs -Helmholtz equation becomes, $$ \begin{gathered} \Delta G=\Delta H-T \Delta S<0 \ \text { or, } \quad \Delta H<T \Delta S \ \text { or, } \quad T>\frac{\Delta H}{\Delta S}=\frac{35.5 \mathrm{~kJ} \mathrm{~mol}^{-1}}{83.6 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}} \ =\frac{35.5 \times 1000}{83.6}=425 \mathrm{~K} \ T>425 \mathrm{~K} \end{gathered} $$