Question

The reaction $A\left(g\right)+B\left(g\right)\rightleftharpoons C\left(g\right)+D\left(g\right)$ is elementry $2^{nd}$ order reaction. When started with equimolar amounts of A and B, at equilibrium, it is found that the concentration of A is twice that of C. Specific rate for forward reaction is $2\times {10}^{-3}mo{l}^{-1}Lse{c}^{-1}$. The specific rate constant for backward reaction is:

• A. $5.0\times {10}^{-4}{M}^{-1}se{c}^{-1}$
• B. $8\times {10}^{-3}{M}^{-1}se{c}^{-1}$
• C. $1.5\times {10}^2{M}^{-1}se{c}^{-1}$
• D. None of these

Answer 1

Answer: (B)

$8\times {10}^{-3}{M}^{-1}se{c}^{-1}$

$A\left(g\right)+B\left(g\right)\rightleftharpoons C\left(g\right)+D\left(g\right)$

$Initial$ a a 0 0
$Ateq.$ a - x a - x x x

$a-x=2x;x=a/3$

$K_c=\frac{\left[C\right]\left[D\right]}{\left[A\right]\left[B\right]}$

$\Rightarrow K_c=\frac{a^2/9}{4a^2/9}=\frac{1}{4}$

$K_c=\frac{1}{4}=\frac{2\times {10}^{-3}}{k_b}$

$K_b=8\times {10}^{-3}$ $M^{-1}se{c}^{-1}$