APFIVE Activation Energy From Rate Constants
The table shows the rate constant, k, for a reaction at different temperatures. Using the data and the Arrhenius equation, $$\ln{(k_2/k_1)} = -\frac{E_a}{R}(1/T_2 - 1/T_1)$$, estimate the activation energy, $E_a$, in J/mol. Use R = 8.314 J/(mol·K).
| Temperature (K) | k (s^-1) |
|---|---|
| 290 | 0.0020 |
| 300 | 0.0050 |
| 310 | 0.0120 |
A
Approximately $$1.2 \times 10^4\,J/mol$$.
B
Approximately $$6.7 \times 10^3\,J/mol$$, which likely results from a misapplication of the temperature conversion in the Arrhenius equation.
C
Approximately $$6.7 \times 10^4\,J/mol$$.
D
Approximately $$1.2 \times 10^5\,J/mol$$.
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