Question

In arrhenius equation for a certain reaction, the value of A and E_a (activation energy) are 4×10¹³ s^-1 and 98.6 kJ mol^-1 respectively. If the reaction is of first order, then at what temperature will its half life period be 10 minutes?

Answer 1

Dear Student,

A=4×10^13 s−1

Ea=98.6 kJ/mol = 98600 J/mol

t1/2= 10 min

Therefore, k=0.693÷10

=0.0693 min−1.

or,
k = 0.0693÷60
=0.001155 s−1

Now, log k = log A−Ea÷(2.303RT)

or,

Ea÷(2.303RT)=log A−log K
or,

Ea÷(2.303RT)= log (4×10^13)−log (0.001155)


=13.602+2.937

or
, Ea2.303RT=16.539
or,
T=Ea÷(2.303R×16.539)

=98600÷(2.303×8.314×16.539)

=311.4 K
Hope you got the idea