The addition of a catalyst will lead to an increase in the rate of a reaction. A catalyst is a substance that increases the rate of a chemical reaction by providing an alternative reaction pathway with lower activation energy. Here is a detailed explanation of why the addition of a catalyst accelerates the reaction rate:

Activation Energy:
- The rate of a chemical reaction is determined by the energy barrier that must be overcome for the reaction to occur, known as the activation energy.
- Reactant molecules must acquire a certain amount of energy, called activation energy, to initiate the reaction.

Catalyst Function:
- A catalyst provides an alternative reaction pathway with a lower activation energy.
- It does not change the overall energy change or enthalpy of the reaction.
- A catalyst is not consumed during the reaction and can participate in multiple reaction cycles.

Effect of Catalyst:
- By providing a lower activation energy pathway, the catalyst allows a greater number of reactant molecules to possess the required energy to react.
- This leads to an increase in the number of effective collisions between reactant molecules, resulting in a higher reaction rate.
- In other words, a catalyst speeds up the reaction by lowering the energy barrier required for the reaction to occur.

Specific Examples:
- For example, in the presence of a catalyst, the decomposition of hydrogen peroxide into water and oxygen occurs much faster than without a catalyst.
- Similarly, in the Haber-Bosch process, the addition of an iron catalyst increases the rate of the reaction between nitrogen and hydrogen to form ammonia.

Contrasting Options:
- Decreasing temperature (option a) will generally decrease the reaction rate as it reduces the kinetic energy of the reactant molecules, making them less likely to collide effectively.
- Decreasing the concentration of reactants (option b) will also decrease the reaction rate as fewer reactant molecules are available for collisions.
- Addition of an inhibitor (option d) will decrease the reaction rate by interacting with reactant molecules and hindering their ability to react.

Conclusion:
- In summary, the addition of a catalyst provides an alternative reaction pathway with a lower activation energy, leading to an increase in the rate of the reaction.