For the reaction $A_{(g)} \rightleftharpoons 2 B_{(g)}$, the backward reaction rate constant is high

Question

For the reaction $A_{(g)} \rightleftharpoons 2 B_{(g)}$, the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500 , at 1000 K . [Given: $R=0.0831 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ ] $K_p$ for the reaction at 1000 K is

Professor PC Thomas Classes · Answer

$ 	ext {  (a) : For reaction, } A_{(g)} ightleftharpoons 2 B_{(g)} \  R=0.0831 \mathrm{~L} 	ext { atm mol }{ }^{-1} \mathrm{~K}^{-1}, T=1000 \mathrm{~K}$
$ K_c=\frac{k_f}{k_b}=\frac{k_f}{2500 k_f}=\frac{1}{2500} \  	ext { As } K_p=K_c(R T)^{\Delta n_g} \  K_p=\frac{1}{2500}(0.0831 	imes 1000)^1=0.033 \quad\left[	ext { As }, \Delta n_g=2-1=1ight]$