Question

The rate of the elementary reaction, $A_{2(g)}+B_{2(g)}\rightleftharpoons 2A{B}_{(g)}$ is given by rate $=1.7\times 10^{-18}\left[A_2\right]\left[B_2\right]$ The rate of decomposition of gaseous $AB$ to $A_2$ and $B_2$ is given by rate $=2.4\times 10^{-21}[AB{]}_2$. The equilibrium constant, for the formation of $AB$ from $A_2$ and $B_2$ is

• A. $1.4\times 10^{-3}$
• B. $2.8\times 10^{-3}$
• C. $1.4\times 10^3$
• D. $0.7\times 10^3$

Answer 1

Answer: (D)

$A_{2(g)}+B_{2(g)}\underset{k_b}{\overset{k_f}{\rightleftharpoons }}2A{B}_{(g)}$

Rate of forward reaction $\left(r_f\right)=k_f\left[A_2\right]\left[B_2\right]$

Rate of backward reaction $\left(r_b\right)=k_b[AB{]}^2$

$\therefore k_f=1.7\times 10^{-18},k_b=2.4\times 10^{-21}$

$K=\frac{k_f}{k_b}=\frac{1.7\times 10^{-18}}{2.4\times 10^{-21}}=0.708\times 10^3$