From the arrhenius equation, we can write,
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Where k= rate constant.
A = Arrhenius constant.
Ea =activation energy.
R= Gas constant.
T= temperature.
If we introduce an catalyst, the reaction rate constant(k) will increase by decreasing the activation energy. So, in presence of catalyst, Ea decreases and k increases.
There are two others relations to compare the presence of catalyst and that are,
螖骋鈥 = 螖贬鈥 -T螖 S鈥 补苍诲鈥︹赌︹赌︹赌︹赌1
螖贰a = 螖贬鈥 + RT. 鈥︹︹︹︹︹..2
Where every terms has their own meanings.
Now, when, catalyst is applied, Eadeceases and as per equation 2, 螖H鈥also decreases as RT is a constant value.
Now, Keq鈭, Where k and k-1 are rate constant in forward and backward direction respectively. If rate of a reaction increases which means formation of products (Forward reaction, Keqalso increases, and from , becomes more negative or more spontaneous.
With decreasing , 螖S鈥increases to make the overall reaction negative.
The order of increase and decrease for 螖贬掳螖G掳 and 螖厂掳 becomes just same as for the transition state values of enthalpy, gibes free energy and entropy.