A chemist runs a reaction at 65°C and determines its rate to be 0.000364 M/s. If she decreases the temperature to 25°C, what will the rate of the reaction be?
Here's what I get.
There are two ways to approach this problem.
A. Use a rule of thumb
A rule of thumb states that the rate of a reaction changes by a factor of two for every 10 °C change in temperature.
You are decreasing the temperature from 65 °C to 25 °C, a decrease of 40 °C.
Thus, the new rate will be
B. Use the Arrhenius equation
Ideally, you would know the activation energy
Then you could use the Arrhenius equation to calculate the rate at the new temperature.
#color(blue)(bar(ul(|color(white)(a/a)ln(k_2/k_1) = E_"a"/R(1/T_1 -1/T_2)color(white)(a/a)|)))" "#
Since you are changing only the temperatures, the rates are directly proportional to the rate constants, and we can write:
#ln(r_2/r_1) = E_"a"/R(1/T_1 -1/T_2)#
Let's assume that the activation energy is