Question

It is believed that the rate of at see cricket's chirping is related to temperature. Studies have shown that the activation energy for the cricket's chirping is 22kj/mol and that the cricket chirps 10 times per minute at 27 degrees Celcius. How often does the cricket chirp at 42 degrees celcius?

Answer 1

Here we need to use an equation which (I believe) is derived from the Arrhenius equation...
\[\ln(\frac{k_2}{k_1})=\frac{-E_a}{R}(\frac{1}{T_2}-\frac{1}{T_1})\]\[\ln(\frac{k_2}{10s^{-1}})=\frac{-22kJ*mol^{-1}}{8.314J*K^{-1}*mol^{-1}}(\frac{1}{315K}-\frac{1}{300K})\]\[\ln(\frac{k_2}{10s^{-1}})=-2.6461*K^{-1}(-1.5873*10^{-4})\]\[\ln(\frac{k_2}{10s^{-1}})=4.2002\]\[\frac{k_2}{10s^{-1}}=e^{4.2002}\]\[\frac{k_2}{10s^{-1}}=1.0004\]\[k_2=10.004s^{-1}\]Since, we're really only justified in keeping 2 SFs...\[k_2=10.004s^{-1}\approx 10s^{-1}\]

Answer 2

Oh! I see the mistake I made here. Let me fix that.

Answer 3

The final units just need to be in inverse minutes, not inverse seconds:

\[k_2=10mi n^ {-1}\]