Question

For a general reaction
$P_{(g)}+O_{(g)}\rightleftharpoons +S_{(g)}$, the specific rate constant is $k_{(forward)}=2.0\times 10^{-3}mo{l}^{-1}L{s}^{-1}$ at a certain temperature. Reaction starts with equimolar amounts of $P$ and $Q$. Reaching at equilibrium, it is observed that $P$ is twice that of $R$. The specific rate constant for the backward reaction is

• A. $1.5\times 10^{2}mo{l}^{-1}L{s}^{-1}$
• B. $5.0\times 10^{4}mo{l}^{-1}L{s}^{-1}$
• C. $8.0\times 10^{3}mo{l}^{-1}L{s}^{-1}$
• D. none of the above

Answer 1

Answer: (C)

$\Rightarrow x=\frac{a}{3}$
$K_c=\frac{x^2}{\left(a-x\right)\left(a-x\right)},\frac{a^2}{9\times {\left(2x\right)}^2}=\frac{{\left(3x\right)}^2}{9\times 4x^2}$
$K_c=\frac{1}{4}=0.25,$ but $K_c=\frac{k_f}{k_b}$
or $k_b=\frac{k_f}{K_c}=\frac{2\times 10^{-3}}{0.25}=8\times 10^{-3}$