# Rate constant calculation Using the Arrhenius equation

## Homework Statement

A reaction has a rate constant of 0.0117/s at 400.0 K and 0.689/s at 450.0 K. What is the value of the rate constant (to 1 decimal place) at 538 K?

## Homework Equations

ln k= ln A-E[a]/RT

## The Attempt at a Solution

I'm not sure how to approach this problem, although I know the arrhenius equation is involved. When I submitted it blank on the computer, the computer hinted at finding enthalpy. But I don't know how. [/B]

$$\ln{k_1} = \ln{A} - \frac{E_a}{RT_1} \text{...Eqn. 1}$$ and $$\ln{k_2} = \ln{A} - \frac{E_a}{RT_2} \text{...Eqn. 2}$$ for two different ##k_1## and ##k_2## at two different temperatures ##T_1## and ##T_2##.
Subtract Eqn1 from Eqn2:$$\ln{\frac{k2}{k1}} = - E_a R \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \text{...Eqn. 3}$$ Find ##E_a## by putting in the appropriate values.
Then use $$\ln{k} = \ln{A} - \frac{E_a}{RT}$$ and put ##T= 538K## and find ##k##, the rate constant at temperature ##T##. You already have ##E_a## and ##A##, and they remain constant.