## 15.109

Arrhenius Equation: $\ln k = - \frac{E_{a}}{RT} + \ln A$

Lucia H 2L
Posts: 43
Joined: Mon Nov 14, 2016 3:00 am
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### 15.109

The rate constant of the reaction O(g) + N2(g) --> NO(g) + N(g), which takes place in the stratosphere, is
9.7 x 10^10 L mol-1 s-1 at 800 deg C. The activation energy of the reaction is 315 kJ mol-1. Determine the rate constant at 700 deg C.

What is the first step here? Do you need to solve for lnA in the Arrhenius equation?

Angela G 2K
Posts: 30
Joined: Fri Sep 29, 2017 7:06 am

### Re: 15.109

You don't need lnA here. You have the rate constant at 800 deg C and the question asks for the rate constant for the same reaction at 700 deg C, so you have these two equations:

At Temp 1 = 800 C = 1073 K: $lnk_{1}=lnA-\frac{E_{a}}{RT_{1}}$
At Temp 2 = 700 C = 973 K: $lnk_{2}=lnA-\frac{E_{a}}{RT_{2}}$

Combine them and you get $lnk_{2}-lnk_{1}=lnA-\frac{E_{a}}{RT_{2}} - lnA+\frac{E_{a}}{RT_{1}}$
Simplify to get $ln\frac{k_{2}}{k_{1}}=\frac{E_{a}}{R}(\frac{1}{T_{1}}-\frac{1}{T_{2}})$

Plug in the values and solve for k2.