Exploring the Link between Equilibrium and Kinetics
The equilibrium constant Kc for the reaction of hydrogen with iodine is 57.0 at 700 K, and the reaction is endothermic (ΔE = 9 kJ).
\mathrm{H}_2(g)+\mathrm{I}_2(g) \underset{k_{\mathrm{r}}}{\stackrel{k_{\mathrm{f}}}{\rightleftharpoons}} 2 \mathrm{HI}(g) \quad K_{\mathrm{c}}=57.0 \text { at } 700 \mathrm{~K}(a) Is the rate constant k_f for the formation of HI larger or smaller than the rate constant k_r for the decomposition of HI?
(b) The value of k_r at 700 K is 1.16 × 10^{-3} M^{-1} \ s^{-1} . What is the value of k_f at the same temperature?
(c) How are the values of k_f, \ k_r, and K_c affected by an increase in temperature?
STRATEGY
To answer these questions, make use of the relationship K_c = k_f/k_r. Also, recall that the temperature dependence of a rate constant increases with increasing value of the activation energy (Section 12.10).
(a) Because K_c = k_f/k_r = 57.0, the rate constant for the formation of HI (forward reaction) is larger than the rate constant for the decomposition of HI (reverse reaction) by a factor of 57.0.
(b) Because K_c = k_f/k_r,
k_{\mathrm{f}}=\left(K_c\right)\left(k_{\mathrm{r}}\right)=(57.0)\left(1.16 \times 10^{-3} \mathrm{M}^{-1} \mathrm{~s}^{-1}\right)=6.61 \times 10^{-2} \mathrm{M}^{-1} \mathrm{~s}^{-1}(c) Because the reaction is endothermic, E_a for the forward reaction is greater than E_a for the reverse reaction. Consequently, as the temperature increases, k_f increases by more than k_r increases, and therefore K_c = k_f/k_r increases