In the start of summer, a given sample of milk turns sour at room temperature `(27^(@)C)` in `48` hours. In a refrigerator at `2^(@)C`, milk can be stored there times longer before it sours.
The activation energy of the souring of milk is `(kJ mol^(-1))`

Options

A. `30.210`
B. `30.146`
C. `30.0`
D. `35.126`

Answer

B

Explanation

At `2^(@)C (275 K)`, the reaction is theee times slower than at `27^(@)C(300 K)`. This implies that for souring of milk.
`(k_(300))/(k_(275)) = 3, T_(1) = 275 K, T_(2) = 300 K`
Applying Arrhenius equation
`log.(k_(300))/(k_(275)) = (E_(a))/(2.303 R) ((T_(2)-T_(1))/(T_(2)T_(1)))`
`log 3 = (E_(a))/(2.303 xx 8.314) ((300-275)/(275 xx 300))`
or `E_(a) = 30.146 kJ mol^(-1)`