JEE PYQ: Thermodynamics Question 5
Question 5 - 2021 (26 Feb Shift 1)
For a chemical reaction $A + B \rightleftharpoons C + D$ ($\Delta H^\circ = 80$ kJ mol$^{-1}$), the entropy change $\Delta S^\circ$ depends on the temperature $T$ (in K) as $\Delta_r S^\circ = 2T$ (J K$^{-1}$ mol$^{-1}$).
Minimum temperature at which it will become spontaneous is ___ K.
Show Answer
Answer: 200
Solution
$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$. To make the process spontaneous, $\Delta G^\circ < 0$: $\Delta H^\circ - T\Delta S^\circ < 0$. $T > \dfrac{\Delta H^\circ}{\Delta S^\circ} = \dfrac{80000}{2T}$. $2T^2 > 80000$, $T^2 > 40000$, $T > 200$ K. The minimum temperature to make it spontaneous is 200 K.
BETA
