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. `2.303 xx 10 R kJ * mol^(-1)`
B. `2.303 xx 5 R kJ* mol^(-1)`
C. `2.303 xx 3 R kJ * mol^(-1)`
D. `2.303 xx 2.7 R kJ* mol^(-1)`

Answer

D

Explanation

Rate of souring of milk at `27^(@)C` is 10 times faster than at `-3^(@) C` .
hence , `(k_(300))/(k_(270)) = 10 , T_(1) = 270 K , T_(2) = 300 K`
`E_(a) = 2.303 R ((T_(1) T_(2))/(T_(2) - T_(1))) log (k_(300))/(k_(270))`
`E_(a) = 2.303 R ((270 xx 300)/(300 - 270)) log 10`
`E_(a) = 2.303 R (2. 7 xx 10^(3)) J mol^(-1)`
`E_(a) = 2.303 xx 2.7 R kJ mol^(-1)`