Effect of a Catalyst & Energy Profiles

How a Catalyst Works

A catalyst is a substance that increases the rate of a reaction without itself being consumed in the overall reaction. A small amount can speed up the conversion of large amounts of reactant, and it is recovered chemically unchanged at the end.

The secret: a catalyst provides an alternative reaction pathway with a lower activation energy $E_a$. Because $k = A e^{-E_a/RT}$, lowering $E_a$ increases $k$ exponentially — so even a modest reduction in the barrier can produce a large rate increase.

A catalyst does NOT:

• get consumed (it is regenerated),
• change the enthalpy change $\Delta H$ of the reaction,
• change the position of equilibrium (it speeds up forward and backward reactions equally),
• supply the energy of activation — it lowers the barrier rather than adding energy.

Energy Profile Diagrams

A potential-energy vs reaction-coordinate diagram shows the energy barrier the reaction must cross. The catalysed path has a lower peak.

The two key readings:

• The activation energy is lowered ($E_a^{cat} < E_a$), so more molecules can react → faster rate.
• The reactant and product energy levels are unchanged, so $\Delta H$ and the equilibrium constant are unchanged. A catalyst helps equilibrium be reached faster, not shifted.

Types and Examples of Catalysis

• Homogeneous catalysis — catalyst and reactants in the same phase (e.g. acid-catalysed ester hydrolysis; oxidation of SO$_2$ by NO in the lead-chamber process).
• Heterogeneous catalysis — catalyst in a different phase, usually a solid catalyst with gaseous/liquid reactants (e.g. iron in the Haber process for NH$_3$; platinum in catalytic converters; finely divided nickel in the hydrogenation of oils).
• Enzymes are highly specific biological catalysts (e.g. amylase, which catalyses starch hydrolysis).

Key Point: A catalyst changes only the rate (kinetics), never the thermodynamics ($\Delta H$, $\Delta G$, $K$). It lowers $E_a$ for both the forward and reverse reactions by the same amount.

[JEE Tip] A classic trap: "Does a catalyst change the equilibrium constant?" — No. It lowers the activation energy of both directions equally, so it only makes equilibrium arrive sooner; the value of $K$ is untouched.

Solved Examples

Example 1: How a catalyst speeds a reaction

Explain, using the Arrhenius equation, how a catalyst increases the rate.

Solution: A catalyst provides an alternative path with a lower activation energy $E_a$. Since $k = A e^{-E_a/RT}$, a smaller $E_a$ makes $e^{-E_a/RT}$ larger, so $k$ and the rate increase — without changing $A$ or $T$.

Example 2: Effect on enthalpy

Does a catalyst change the $\Delta H$ of a reaction?

Solution: No. The catalyst lowers the energy barrier but the reactant and product energy levels are unchanged, so $\Delta H$ stays the same.

Example 3: Effect on equilibrium

Does a catalyst shift the position of equilibrium?

Solution: No. A catalyst lowers $E_a$ for the forward and reverse reactions by the same amount, speeding both equally. Equilibrium is reached faster, but the equilibrium constant $K$ and the position of equilibrium are unchanged.

Example 4: Homogeneous vs heterogeneous

Classify (a) acid hydrolysis of an ester and (b) the Haber process (Fe catalyst) as homogeneous or heterogeneous catalysis.

Solution: (a) Acid and ester are both in solution → homogeneous catalysis. (b) Solid iron with gaseous N$_2$/H$_2$ → heterogeneous catalysis.

Example 5: Why a small amount suffices

Why can a small amount of catalyst speed up the reaction of a large amount of reactant?

Solution: The catalyst is not consumed — it is regenerated at the end of each cycle and used again and again. So a small quantity can process a large amount of reactant repeatedly.

Example 6: Activation energies of forward and reverse

A catalyst lowers the forward activation energy by 20 kJ mol$^{-1}$. By how much does it lower the reverse activation energy?

Solution: By the same 20 kJ mol$^{-1}$. Because $\Delta H = E_a(\text{forward}) - E_a(\text{reverse})$ is unchanged, both barriers drop equally, so the catalyst does not alter $\Delta H$.

Example 7: Enzyme catalysis

What kind of catalyst is an enzyme, and give one property.

Solution: An enzyme is a biological catalyst (a protein). A key property is high specificity — each enzyme typically catalyses one particular reaction (e.g. amylase acts on starch).

Example 8: Reading an energy profile

On an energy-profile diagram, what feature is lowered by a catalyst, and what stays the same?

Solution: The catalyst lowers the peak (the activation-energy barrier). The reactant and product energy levels (and hence $\Delta H$) stay the same.

Example 9: Catalyst and rate constant

A catalyst lowers $E_a$ from 75 to 50 kJ mol$^{-1}$. Qualitatively, what happens to $k$?

Solution: Since $k = A e^{-E_a/RT}$, reducing $E_a$ makes the exponent less negative, so $e^{-E_a/RT}$ increases and $k$ increases — the reaction goes faster. (At room temperature a 25 kJ mol$^{-1}$ drop increases $k$ by a very large factor.)

Example 10: Catalytic converter

What catalyst type operates in a car's catalytic converter, and what does it do?

Solution: A heterogeneous catalyst (platinum/palladium/rhodium on a solid support). It speeds the conversion of harmful exhaust gases (CO, unburnt hydrocarbons, NO$_x$) into less harmful CO$_2$, H$_2$O and N$_2$ by lowering their activation energies.