A given sample of milk turns sour at room temperature \(\left(27^{\circ} \mathrm{C}\right)\) in \(5 \mathrm{~h}\). In a refrigerator at \(-3^{\circ} \mathrm{C}\), it can be stored 10 times longer. The energy of activation for the souring of milk is

Energy of activation is given by
\[
\log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right]
\]
Here, \(\quad \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}=\frac{1}{10}\)
\(\mathrm{T}_{1}=27^{\circ} \mathrm{C}=300 \mathrm{~K}\)
\(\mathrm{T}_{2}=-3^{\circ} \mathrm{C}=270 \mathrm{~K}\)
\(\therefore \quad \log \frac{1}{10}=\frac{E_{a}}{2.303 \mathrm{R}}\left(\frac{270-300}{270 \times 300}\right)\)
\(-1=-\frac{E_{a}}{2.303 R} \frac{30}{270 \times 300}\)
\(\mathrm{E}_{\mathrm{a}}=+2.303 \times 2700 \times \mathrm{R} \mathrm{J} \mathrm{mol}^{-1}\)
\(=+2.303 \times 2.7 \times \mathrm{R} \mathrm{kJ} \mathrm{mol}=1\)