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). H2(g) + I2(g) ⇔ 2 HI(g) Kc = 57.0 at 700 K (a) Is the rate constant kf for the formation of HI larger or smaller

Question

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).

[latex]\mathrm{H}_2(g)+\mathrm{I}_2(g) \underset{k_{\mathrm{r}}}{\stackrel{k_{\mathrm{f}}}{ ightleftharpoons}} 2 \mathrm{HI}(g) \quad K_{\mathrm{c}}=57.0 ext { at } 700 \mathrm{~K}[/latex]

(a) Is the rate constant [latex]k_f[/latex] for the formation of HI larger or smaller than the rate constant [latex]k_r[/latex] for the decomposition of HI?

(b) The value of [latex]k_r[/latex] at 700 K is 1.16 × [latex]10^{-3} M^{-1} \ s^{-1}[/latex] . What is the value of [latex]k_f[/latex] at the same temperature?

(c) How are the values of [latex]k_f, \ k_r[/latex], and [latex]K_c[/latex] affected by an increase in temperature?

STRATEGY

To answer these questions, make use of the relationship [latex]K_c = k_f/k_r[/latex]. Also, recall that the temperature dependence of a rate constant increases with increasing value of the activation energy (Section 12.10).

Accepted Answer

(a) Because [latex]K_c = k_f/k_r[/latex] = 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 [latex]K_c = k_f/k_r[/latex],

[latex]k_{\mathrm{f}}=\left(K_c ight)\left(k_{\mathrm{r}} ight)=(57.0)\left(1.16 imes 10^{-3} \mathrm{M}^{-1} \mathrm{~s}^{-1} ight)=6.61 imes 10^{-2} \mathrm{M}^{-1} \mathrm{~s}^{-1}[/latex]

(c) Because the reaction is endothermic, [latex]E_a[/latex] for the forward reaction is greater than [latex]E_a[/latex] for the reverse reaction. Consequently, as the temperature increases, [latex]k_f[/latex] increases by more than [latex]k_r[/latex] increases, and therefore [latex]K_c = k_f/k_r[/latex] increases

Chapter 13

Q. 13.5

Q. 13.5

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