Question

if it takes 80 h to completely recrystallize an aluminum sheet at 250 c and 6 h at 3000, calculate the activvation energy in cal/mol?

Answer 1

Arrhenius equation k = A e^-Ea/RT

where k = rate of reaction

A = collision frequency

Ea = activation energy

R= universal gas constant = 1.987 cal/K/mol

T = temperature

Arrhenius equation can be written as

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

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

Given that it takes 80 h to completely recrystallize an aluminum sheet at 250oC and 6 h at 3000oC.

Hence, Initial rate of reaction = k1 = 80 h

Final rate of reaction k2 = 6 h

Initial temperature T1 = 250oC = 250 + 273 K = 523 K

Final temperature T2 = 3000oC = 3000 + 273 K = 3273 K

Substitute all these velues in eq (1),

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

= (1.987 cal/K/mol) [ In (6/80)] / [(1/523) - (1/3273)]

= -0.0083 cal/mol

Ea = -0.0083 cal/mol

Therefore, activation energy of the reaction = -0.0083 cal/mol