Question

A certain batch of fireflies were observed to "flash" at the rate of 16.9 times per minute at 25°C, and at the lower rate of 5.0 times a minute at a temperature of 15°C. Assume that the flashing is the result of an overall chemical reaction that has a single rate limiting step with the highest activation energy. Use this data to estimate the activation energy for this slowest step. You can assume that the concentrations of "reactants" in the fireflies do not depend on temperature.

Answer 1

first reaction:

the rate equation for the rate-determining step is equal to some rate constant times the concentrations of the reactants, each raised to some power.

since the concentrations are the same at both temperatures, the ratio of the rates is equal to the ratio of the rate constants.

the rate constant becomes lower at 15 deg Celsius because it usually has the form:

rate constant = A * exp (- Ea/RT)

so when T decreases, the exponential factor becomes smaller, and the rate constant becomes smaller.

Answer 2

continuing, the ratio of the two rates:

rate1/rate2
= k1/k2
= exp(-Ea/RT1) / exp(-Ea/RT2)

k1 is the rate constant at the higher temp (T1), Ea is the activation energy, and R is the gas constant.

Answer 3

taking the log:

ln(rate1/rate2)
=-Ea/R (1/T1 - 1/T2)

we know the temps and the rates and the gas constant, so we can plug these in to find Ea, the activation energy.

i might have messed up somewhere, so feel free to correct me.