Effect of a Catalyst

The Role of a Catalyst in Chemical Equilibrium

A catalyst is a substance that accelerates a chemical reaction without itself being consumed. In the context of equilibrium, its effect is often misunderstood. The key point is that a catalyst influences the rate at which equilibrium is reached, but it does not alter the position of equilibrium itself.

How does it achieve this? A catalyst provides an alternative pathway for the reaction — one that has a lower activation energy. Both the forward and the reverse reactions must pass through the same transition state. By lowering the activation energy barrier for both directions by exactly the same amount, the catalyst speeds up the forward and reverse reactions equally.

Because the catalyst does not appear in the overall balanced chemical equation, it is also absent from the equilibrium constant expression. Its only role is kinetic: it helps the system reach equilibrium faster.

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Properties of a Catalyst in Equilibrium

The textbook highlights several critical properties. Each is derived from the fundamental idea that a catalyst lowers the activation energy for both directions equally.

Property 1: A catalyst does not affect the equilibrium constant ($K$).

Proof/Reasoning:

The equilibrium constant is a thermodynamic quantity, determined solely by the difference in Gibbs free energy ($\Delta G^\circ$) between reactants and products:

A catalyst does not change $\Delta G^\circ$ because it does not alter the initial and final states of the reaction — it only changes the path between them. Since $\Delta G^\circ$ remains unchanged, $K$ remains unchanged.

Property 2: A catalyst does not affect the equilibrium composition of the reaction mixture.

Proof/Reasoning:

At equilibrium, the rates of the forward and reverse reactions are equal. A catalyst increases both rates by the same factor. If the forward rate constant $k_f$ and the reverse rate constant $k_r$ are both multiplied by the same factor $c$ (where $c > 1$), then the ratio $k_f/k_r$ — which equals $K$ — remains unchanged. Consequently, the equilibrium concentrations of reactants and products stay exactly the same as they would be without the catalyst.

Property 3: A catalyst does not appear in the balanced chemical equation or in the equilibrium constant expression.

Reasoning:

A catalyst is regenerated at the end of the reaction. It participates in the mechanism but is not a net reactant or product. Therefore, it is omitted from the stoichiometric equation and from the expression for $K$.

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Practical Application: The Haber Process

The formation of ammonia from nitrogen and hydrogen is a classic example:

This reaction is:

• Exothermic (heat is released).
• Accompanied by a decrease in the number of moles (4 moles of reactants become 2 moles of product).

According to Le Chatelier’s principle:

• Low temperature favours the exothermic forward reaction, giving a higher equilibrium yield of $\text{NH}_3$.
• High pressure favours the side with fewer moles, so high pressure also increases the yield.

However, there is a conflict: at low temperatures, the reaction rate is very slow, and it takes an impractically long time to reach equilibrium. At high temperatures, the rate is satisfactory, but the equilibrium yield of ammonia is poor because the equilibrium constant decreases with temperature.

Fritz Haber discovered that an iron catalyst allows the reaction to proceed at a satisfactory rate at a temperature where the equilibrium concentration of ammonia is still reasonably favourable. The catalyst does not change the equilibrium yield, but it makes that yield accessible in a practical time frame.

The optimum conditions for the Haber process using an iron catalyst are:

• Temperature: around 500°C
• Pressure: around 200 atm

At these conditions, the rate is fast enough for industrial production, and the equilibrium yield (though not maximal) is economically viable.

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Practical Application: The Contact Process

In the manufacture of sulphuric acid, sulphur dioxide is oxidised to sulphur trioxide:

The equilibrium constant for this reaction is enormous:

$K_c = 1.7 \times 10^{26}$ …