Rate constant calculation Using the Arrhenius equation

[Madelin Pierce]

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]

 

[Wrichik Basu]

$$\ln{k_1} = \ln{A} - \frac{E_a}{RT_1} \text{...Eqn. 1}$$ 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 put $E_a$ in Eqn1 or Eqn2, and find $A$.

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.