# The equilibrium constant $K_c$ for the reaction of $H_2$ with $I_2$ is 57.0 at 700 K $H_2(g) + I_2(g) \rightleftharpoons 2HI$; $K_c$ = 57 at 700K. select correct statement:

(a) rate constant $k_f$ for the formation of HI is smaller than that of rate constant $k_b$ for the dissociation of HI

(b) $k_f > k_b$

(c) addition of catalyst increases value of $K_c$.

(d) addition of catalyst decreases value of $K_c$.

Toolbox:
• Rate of reaction = Equilibrium Constant $\times$ Product of concentration of reactants / products in the reaction
• $R_x = k_x [A] [B]$ where $R_x$ = rate of reaction, $k_x$ = equilibrium constant and, A and B are reactants or products
• At equilibrium, Rate of Forward reaction = Rate of backward reaction. $R_f = R_b.$

Answer: $k_f > k_b$

For forward reaction, $R_f = k_f [H_2][I_2]$

For backward reaction, $R_b = k_b [HI]^2$

At equilibrium, $R_f = R_b$
$\Rightarrow k_f [H_2] [I_2] = k_b [HI]^2$
$\Rightarrow \frac{k_f}{k_b} = \frac{[HI]^2}{[H_2][I_2]} = K_c$ = 57

As, $K_c$ = 57
$k_f = 57 \times k_b$
$\therefore k_f > k_b$