Consider the reaction A ⇌ B at 1000K . At time t ^ ' , the...

Use $\Delta G ° = - RTlnKP$ at equilibrium

${\Delta G}_{1}^{∘} = - {RT}_{1}ln{\text{K}}_{{\text{P}}_{1}}$ ...... $( 1 )$

${\Delta G}_{2}^{∘} = - {RT}_{2}ln{\text{K}}_{\text{P}2}$ ..... $( 2 )$

${\Delta G}_{1}^{∘}{\Delta G}_{2}^{∘} = \dfrac{{\text{T}}_{1}}{{\text{T}}_{2}} \times \dfrac{{lnK}_{{\text{P}}_{1}}}{{lnK}_{{\text{P}}_{2}}}$

$=$$\begin{array}{ll}1000 \\ 2000\end{array}$$\times$$\begin{array}{ll}\ln ( 10 ) \\ \ln ( 100 )\end{array}$$$</p><p>$= \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4} = 0 . 25$