Concept:
Arrhenius equation- Temperature Dependence and Rate constant:
- The temperature dependence of the rate of a chemical reaction can be accurately explained by the Arrhenius equation.
- It has been found that for a chemical reaction with the rise in temperature by
10∘C, the rate constant is nearly doubled.
- Mathematically, Arrhenius equation is given by,
k=Ae−‌where
A is the Arrhenius factor or the frequency factor. It is also called the preexponential factor. It is a constant specific to a particular reaction,
R is gas constant and
Ea is activation energy measured in joules/mole (
Jmol−1 ).
Activation energy (
Ea ):
- It is the minimum energy that must be supplied to the reactants to enable them to cross over the energy barrier between reactants and products.
- For fast reaction;
Ea is low.
- For slow reaction;
Ea is high.
- An alternative form of the Arrhenius equation is given by:
log(‌)=‌[‌]Where
K1 and
K2 are the rate constants for a reaction at two different temperatures
T1 and
T2.
Calculation:
Given:
K2∕K1=2 (The rate of reaction is doubled) ;
R=8.314JK−1mol−1;T1= 300K;
T2=310KAs per the Arrhenius equation,
log(‌)=‌[‌]‌log‌2=‌[‌]‌Ea=‌| log‌2×2.303×8.314×310×300 |
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Therefore,
Ea=53603J=53.6kJ∕molHence, the activation energy (
Ea ) of the reaction whose rate doubles when its temperature changes from 300 K to 310 K is
53.6KJ∕mol