Question

The activation energy of a reaction is 55.5 kJ mol−1 and the frequency factor is 1.5×1011s−1. Calculate the rate constant of the reaction at 26 ∘C.

Answer 1

Step 1: Explanation:

Activation Energy can be calculated from Arrhenius equation

k=Ae−Ea/RT

Where, k = Rate constant, A = Frequency factor , Ea = Activation energy, R = Gas constant

T = Absolute Temperature

Step 2: Extract the data from question

k = we need to calculate   

A = 1.5 × 1011 s-1

Ea = 55.5 kJ/mol = 55500 kJ/mol

[ Note: 1 kJ = 1000 J =>  ( 55.5 kJ/mol   × 1000 J / 1 kJ ) = 55500 J/mol ]  

R = 8.314 J / mol.K

T = 26 °C = (26+273.15)K = 299.15 K

Step 3: Calculation of activation Energy

k=Ae−Ea/RT

By substituting the above value

k = 1.5 × 1011 s-1 × e-(55500 J/mol ) / (8.314 J/mol.K * 299.15 K)

k => 30.54 s-1

hence, the rate constant for the reaction at 26 °C =  30.54 s-1