Question

At 30C, by how much is a reactions activation energy decreased by the addition of a catalyst if the catalyst triples the reaction rate?

Answer 1

Arrhenus equation k = A e^-Ea/RT

where k = rate of reaction

A = collision frequency

Ea = activation energy

R= universal gas constant = 8.314 J/K/mol

T = temperature

k = A e^-Ea/RT

In k1= In A - Ea1/ RT ----------(1)

In k2= In A - Ea2/ RT -------(2)

(2)-(1) gives

In k2 - In k1 = In A - Ea2/ RT - In A+ Ea1/ RT

In (k2/k1) = (Ea1-Ea2) /RT

(Ea1-Ea2) = RT x In (k2/k1)

Given that At 30C, the addition of a catalyst triples the reaction rate.

Hence, k2= 3k1

T = 30oC = 303 K

Then,

(Ea1-Ea2) = RT x In (k2/k1)

= (8.314 J/K/mol) ( 303 K) In (3k1/k1)

= 2767.5 J/mol

(Ea1-Ea2) = 2767.5 J/mol

Therefore, catalyst lowers the activation energy by 2767.5 J/mol