Question

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant \[{\rm{K}}\] in terms of change in entropy is described by
(A) With increase in temperature, the value of \[{\rm{K}}\] for exothermic reaction decreases because the entropy change of the system is positive
(B) With increase in temperature, the value of \[{\rm{K}}\] for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases
(C) With increase in temperature, the value of \[{\rm{K}}\] for endothermic reaction increases because the entropy change of the system is negative
(D) With increase in temperature, the value of \[{\rm{K}}\] for exothermic reaction decreases because favourable change in entropy of the surroundings decreases

Answer 1

Hint: As we know that the equilibrium constant increases with increase in temperature when change in enthalpy is positive. For reversible reaction, change in entropy is inversely proportional to the temperature.

Complete answer
As we know that according to the van't Hoff equation, when heat is absorbed in the reaction (endothermic reaction), the equilibrium constant increases with increase in temperature.
Also, for reversible reaction, unfavourable change in entropy of the surrounding decreases as the temperature increases, this can be calculated by using the formula as-
\[{\rm{\Delta }}{{\rm{S}}_{{\rm{surr}}}}\,{\rm{ = }}\,\dfrac{{{{\rm{Q}}_{{\rm{rev}}}}}}{{\,\,\,\,\,\,\,\,\,{{\rm{T}}_{{\rm{surr}}}}}}\]
Where, \[{\rm{\Delta S}}\] is the change in entropy in the surrounding, \[\,{{\rm{T}}_{{\rm{surr}}}}\] is the surrounding temperature and \[{{\rm{Q}}_{\rm{p}}}\] is the heat at constant pressure.
So, if the temperature increases, then the value of \[{\rm{K}}\] for endothermic reaction increases and \[{\rm{K}}\] for exothermic reaction decreases.

Therefore, the correct options are option (B) and (D).

Note:
When a system absorbs heat, the molecule starts moving faster because kinetic energy increases. Hence, the disorder increases. But for the same amount of heat absorbed at low temperature, the disorder is more than at higher temperature. This shows that entropy change is inversely proportional to the temperature.