Question

A slightly bruised apple will rot extensively in 3.0 days at room temperature (26.0 degree C). If it is kept in a refrigerator at 1.5 degree C it takes 16 days for the apple to rot to the same extent. What is the activation energy for the reaction that causes rotting? (J/mol)

Answer 1

In (k2/k1) = [Ea/R] [ (1/T1) - (1/T2)]

Ea = [R ln (k2/k1) ] / [(1/T1) - (1/T2)] -- Eq (1)

k1 = 1/16 (rots 1/16 of the way per day)

k2 = 1/3 (rots 1/3 of the way per day)

R = 8.314 J mol^-1 K^-1

T1 = 1.5 oC = 1.5 + 273 K = 274.5 K

T2 = 26 oC = 26 + 273 K = 299 K

Substitute all the values in eq (1),

Ea = [R ln (k2/k1) ] / [(1/T1) - (1/T2)] -- Eq (1)

= [ 8.314 In(1/3/1/16)] / [ (1/274.5) – (1/299)]

     = 46623 J/mol

Ea = 46623 J/mol

Therefore,

activation energy for the reaction that causes rotting = 46623 J/mol