Catalysts influence the rate expression by modifying the rate constant, while leaving the order of the reaction unchanged.

Catalysts are substances that enhance the rate of a chemical reaction by offering an alternative pathway that requires less activation energy. Notably, catalysts are not consumed during the reaction, allowing them to be reused multiple times. The rate expression for a chemical reaction is typically represented as:

In this equation, $k$ denotes the rate constant, $[A]$ and $[B]$ are the concentrations of the reactants, and $m$ and $n$ represent the orders of reaction with respect to each reactant. Catalysts primarily affect the value of $k$.

The rate constant $k$ serves as an indicator of the reaction speed and is dependent on temperature. Generally, $k$ increases with rising temperature because higher temperatures provide more molecules with sufficient kinetic energy to surpass the activation energy barrier of the reaction. When a catalyst is introduced, it effectively reduces the activation energy, allowing more molecules to participate in the reaction at a given temperature. Consequently, this results in an increase in the value of $k$, which accelerates the reaction rate. For a deeper understanding of how temperature and molecular collisions influence reaction rates, further reading is recommended.

It is crucial to recognize that while catalysts alter the rate constant, they do not change the order of the reaction. The order of reaction with respect to a specific reactant is determined by the mechanism of the reaction, particularly the number of molecules of that reactant involved in the rate-determining step. This aspect remains unaffected by the presence of a catalyst. Thus, although the rate expression for a catalyzed reaction may yield a different value for $k$, it retains the same structural form as the rate expression for the uncatalyzed reaction.

In summary, catalysts increase the rate of a reaction by providing an alternative pathway with a lower activation energy, which results in a higher rate constant in the rate expression. However, they do not alter the order of the reaction. For additional insights into how catalysts modify energy profiles, further exploration is encouraged. Furthermore, the mathematical formulation of rate expressions and their dependence on reaction conditions can be examined in more detail in other resources.