Question

(a) On a reaction coordinate diagram, show why a general, one-step reaction is faster when a catalyst is employed.(b) Why does a catalyst often allow a reaction to proceed at lower temperatures?

Accepted Answer

To address part (a), start by understanding that a reaction coordinate diagram plots the energy of the system (y-axis) against the progress of the reaction (x-axis). In a one-step reaction, the diagram typically shows a single energy barrier (activation energy, Ea) that must be overcome for the reaction to proceed. A catalyst lowers this activation energy, which can be represented by a smaller peak on the diagram. This lower energy barrier means the reaction occurs faster because more molecules have sufficient energy to overcome the barrier at a given temperature. For part (a), draw two reaction coordinate diagrams on the same graph. The first curve represents the uncatalyzed reaction with a higher activation energy (Ea). The second curve represents the catalyzed reaction with a lower activation energy. Ensure that the starting energy (reactants) and ending energy (products) remain the same for both curves, as a catalyst does not alter the thermodynamics of the reaction (ΔG, the free energy change). To explain part (b), recall that the rate of a reaction depends on the number of molecules with sufficient energy to overcome the activation energy barrier. This relationship is described by the Arrhenius equation: $$ k = A e^{-\frac{E_a}{RT}} $$, where $$ k  is $$the rate constant, $$ E_a  is $$the activation energy, $$ R  is $$the gas constant, and $$ T  is $$the temperature. A lower activation energy (Ea) increases the rate constant (k), even at lower temperatures. For part (b), explain that because a catalyst reduces the activation energy, the reaction can proceed efficiently at lower temperatures. This is particularly useful in industrial and biological processes where high temperatures may be impractical or damaging to sensitive materials. Summarize by emphasizing that a catalyst accelerates a reaction by providing an alternative pathway with a lower activation energy, as shown in the reaction coordinate diagram, and this reduction in activation energy allows the reaction to occur at lower temperatures while maintaining a reasonable rate.

(a) On a reaction coordinate diagram, show why a general, one-step reaction is faster when a catalyst is employed.
(b) Why does a catalyst often allow a reaction to proceed at lower temperatures?

Verified video answer for a similar problem:

Key Concepts

Reaction Coordinate Diagram

Catalysis

Temperature and Reaction Rate