equilibrium constant from temperature change

$\ln \frac{K_2}{K_1}=-\frac{\Delta H^{\circ }}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$ In other words, to solve for the $K_2$: $K_2=K_1\cdot \exp \left[-\frac{\Delta H^{\circ }}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)\right]$

The new equilibrium constant can also be ascertained by simply first solving for $\Delta S$ of the reaction, then calculating $\Delta G$ under the new temperature, and finally using $\Delta G=nRT\ln K$ to solve for the new $K$.