A given sample of milk turns sour at room temperature `(27^(@) C)` in 5 hours . In a refrigerator at `-3^(@) C` , it can be stored 10 times longer . The energy of activation for the souring of milk is

Options

A. `2.303xx10 " R kJ mol"^(-1)`
B. `2.303xx5 " R kJ mol"^(-1)`
C. `2.303xx3 " R kJ mol"^(-1)`
D. `2.303xx2.7 " R kJ mol"^(-1)`

Answer

D

Explanation

(D) At -`3^(@)` C the milk sample can be stored 10 times longer as compared to `27^(@)` C .
`:. (k_(27^(@)C))/(k_(-3^(@)C))=(k_(300K))/(k_(270K))=10`
` "log"(k_(2))/(k_(1))=(E_(a))/(2.303xxR)[(1)/(T_(1))-(1)/(T_(2))]`
or log ` 10=(E_(a))/(2.303xxR)[(1)/(270)-(1)/(300)]`
or `1=(E_(a))/(2.303xxR)[(10-9)/(2700)]`
`1=(E_(a))/(2.303xxR)xx(1)/(2700)`
or `E_(a)=2.303xx2700" RJ mol"^(-1)`
`= 2.303xx2.7 " R kJ mol"^(-1)`