The addition of a catalyst causes the chemical reaction to go through a different mechanism (a sequence of elementary steps), in which the rate determining step (the slowest one - the one with the highest activation energy) has an activation energy lower than that for the rate determining step of the un-catalyzed reaction.
What does the above explanation mean?
In every chemical reaction, reactants become products following a specific sequence of one or more steps, called elementary reactions. These steps are collectively known as the reaction mechanism. The step with the highest activation energy is the slowest one, which consequently determines the overall rate of the reaction.
Example 1:Un-catalyzed Reaction
The un-catalyzed reaction of nitryl chloride (NO2Cl) decomposes to nitrogen dioxide (NO2) and chlorine gas (Cl2):
2NO2Cl(g) ⟶ 2NO2(g) + Cl2(g)
By looking at the balanced equation, you might think that two molecules of NO2Cl collide and, presto, you have made products but actually the reaction follows this mechanism (these specific series of steps):
Step 1: 2NO2Cl(g) ⇋ ClO2(g) + N2O(g) +ClO(g) Fast step
Step 2: N2O(g)+ClO2(g )⇋ NO2(g) + NOCl(g) Fast step
Step 3: NOCl(g) +ClO(g) ⟶ NO2(g) + Cl2(g) Slow step
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Addition of steps: 2NO2Cl(g) ⟶ 2NO2(g) + Cl2(g) Addition must match target equation
Step 3 happens to be the slowest (the one with the highest activation energy) and therefore it is the rate determining step.
Adding a catalyst to this reaction would speed up the reaction by causing the reaction to follow a mechanism different from the one shown above, in which the slowest step would have a lower activation energy than the slow step above.
Example 2: Catalyzed Reaction (Hypothetical Mechanism)
For the sake of explaining how a catalyst works to speed up the rate of the reaction, let's now assume that a catalyst, such as palladium, has been found to catalyze the reaction.
Now, the reaction follows a different mechanism:
Step 1: 2NO2Cl(g) ⟶ Cl2(g) + 2NO(g) +O2(g) Fast step (In the presence of Pd catalyst)
Step 2: 2NO(g) +O2(g) ⟶ 2NO2(g) Slow step
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Addition of steps: 2NO2Cl(g) ⟶ 2NO2(g) + Cl2(g)
The reaction now proceeds at a faster rate because step 2, the rate determining step has a lower activation energy than the slow step in the un-catayzed reaction.