Question

How does the equilibrium constant change with temperature?

Answer 1

Hint : In order to answer the question, to know how the equilibrium constant changes with temperature, we should go through both the exothermic reaction and the endothermic reaction. And we will discuss more about this topic.

Complete Step By Step Answer:
Yes, the equilibrium constant varies with the change in temperature. The equilibrium constant of an exothermic reaction decreases as the temperature decreases. However, in an endothermic reaction, the equilibrium constant increases with increase in temperature.
For an exothermic reaction $(\mathrm{\Delta }Hisnegative)$ , $K$ decreases with an increase in temperature.
For an endothermic reaction $(\mathrm{\Delta }Hispositive)$ , $K$ increases with an increased temperature.
We can calculate the effect of changing temperature on the equilibrium constant by using the van't Hoff equation:
 ${\displaystyle \frac{d\ln K}{dT}}={\displaystyle \frac{\mathrm{\Delta }{H}^{\circ }}{R{T}^2}}$ , where $R$ is the Ideal Gas Constant.
 If we integrate the above equation from $T_{1}to{T}_2$ , we get-
 $\ln ({\displaystyle \frac{K_2}{K_1}})={\displaystyle \frac{\mathrm{\Delta }{H}^{\circ }}{R}}({\displaystyle \frac{1}{T_1}}-{\displaystyle \frac{1}{T_2}})$
Thus, if we know the $\mathrm{\Delta }{H}^{\circ }$ and the equilibrium constant at one temperature, we can calculate the equilibrium constant at some other temperature.

Note :
Le Chatelier's principle states that a change in temperature, pressure, or concentration of reactants in an equilibrated system will stimulate a response that partially offsets the change to establish a new equilibrium. In the case of changing temperature, adding or removing heat shifts the equilibrium.