At 28 ^{o}C, raw milk sours in 4 h but takes 50 h to sour in a refrigerator at 5 ^{o}C.

Estimate the activation energy in kJ/mol for the reaction that leads to the souring of milk.

We are asked to calculate for the activation energy of a chemical reaction given with two temperatures and two reaction times.

The equation that connects two given temperatures and two reaction times with the activation energy is the **two-point form of the Arrhenius equation:**

** **$\overline{){\mathbf{l}}{\mathbf{n}}{\mathbf{}}\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}\left[\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\right]}$

where: k_{1} is the rate of first reaction

k_{2} is the rate of second reaction

E_{a} is the activation energy

R is the gas constant

T_{1} is the temperature for the first reaction

T_{2} is the temperature of the second reaction