Question

The activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186 kJ/mol. The rate constant at 555K is 3.52 x 10-7 Lmol-1s-1. What is the rate constant at 645 K?

Short answer

9.5 x 10-5 Lmol-1s-1

Step-by-step solution

Use the Arrhenius equation for the 2 conditions.

Arrhenius equation: $k=A\exp \left(\frac{-Ea}{RT}\right).......\left(1\right)$

Taking ln both sides we get: $\ln k=\frac{-Ea}{RT}+\ln A$

Assuming A to be temperature independent, write the equation for both conditions.

$\ln \left(\frac{k_2}{k_1}\right)=\frac{E_a}{RT}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$

Given values in the question:

k1= 3.52 x 10-7 Lmol-1s-1

T1= 555 K

T2= 645 K

Ea = 186 x 103 J/mol

Substitute these values in the above equation, we get:

$\ln \left(\frac{k_2}{3.52\times {10}^{-7}}\right)=\frac{1.86\times \frac{105}{mol}}{8.314J{K}^{-1}mo{l}^{-1}}\left(\frac{1}{555}-\frac{1}{645}\right)=5.6$

So, $\frac{k_2}{3.52\times {10}^{-7}}=e^{5.6}=270$

Therefore,$k_2=\mathbf{270}\left(3.52\times {10}^{-7}\right)=9.5\times {10}^{-5}$