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

Options

A. `2.303xx10RkJmol^(-1)`
B. `2.303xx5RkJmol^(-1)`
C. `2.303xx3RkJmol^(-1)`
D. `2.303xx2.7RkJmol^(-1)`

Answer

D

Explanation

Milk turns sour in 5 hours at `27^(@)C`
It takes 10 times longer to sour at `-3^(@)C`
according to Arrhenius equation
`log.(k_(2))/(k_(1))=(E_(a))/(R)((1)/(T_(1))-(1)/(T_(2)))`
`k_(1)`, `k_(2)` are the rate constants
`E_(a)` is the activation constant
`T_(1)=27^(@)C=300K`
`T_(2)=-3^(@)C=270K`
After substituting in Arrhenius equation
`log.(1)/(10)=(E_(a))/(2.303R)((270-300)/(270xx300))`
`E_(a)=2.303xx2.7RkJ//mol`