The rate of a reaction triples when the temperature is raised from 300 K to 310 K. Assuming the Arrhenius equation holds with constant $E_{a}$ and $A$ , the ratio $k_{320} / k_{300}$ is (use $ln 3 = 1.0986$ )

Answer: B

From the 300 to 310 K data,

E_{a} / R = \frac{l n 3}{1/300 - 1/310} = 10217

K. Then

ln \frac{k _{320}}{k _{300}} = 10217 (0.0002083) = 2.129

, giving

8.40

. This is a little below the rule-of-thumb value 9, because the 20 K interval is not exactly twice the 10 K interval in terms of

1/ T