Question

Question #2e1b0

Answer 1

You can say that the rate of the reaction approximately doubles for each 10 °C rise in the temperature.

Explanation:

This rule of thumb comes from the Arrhenius equation:

`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)|)))" "`

where `E_a` is the activation energy and `T_2` is the higher temperature.

For example, if `E_a = "53 kJ//mol"` and we increase the temperature from 25 °C to 35 °C, we get

`ln(k_2/k_1) = ("53 000" color(red)(cancel(color(black)("J·mol"^"-1"))))/(8.314 color(red)(cancel(color(black)("J·K"^"-1""mol"^"-1"))))(1/(298 color(red)(cancel(color(black)("K")))) -1/(308 color(red)(cancel(color(black)("K"))))) = 6400 × 1.09 × 10^"-4" = 0.70`

`k_2/k_1 = e^0.70 = 2`

That is, an increase of 10 °C in temperature doubles the rate.

The rule holds approximately at ambient temperatures for activation energies between 35 kJ/mol and 65 kJ/mol.