Answer:

Variable oxidation states:
- Transition metals have the ability to exhibit multiple oxidation states due to the presence of incompletely filled d orbitals.
- This property allows them to easily gain or lose electrons during chemical reactions, making them excellent catalysts.
- The variable oxidation states of transition metals enable them to participate in redox reactions, where they can both accept and donate electrons.
- This ability to change oxidation states is crucial for many catalytic processes, as it allows the transition metal to readily switch between different forms, facilitating the reaction.

Explanation:
Transition metals are known for their catalytic activity, which is the ability to increase the rate of a chemical reaction without being consumed in the process. This is due to their unique electronic structure, specifically the presence of incompletely filled d orbitals.

The variable oxidation states of transition metals arise from the fact that d orbitals can hold different numbers of electrons. In a transition metal atom, the d orbitals can be either completely filled or partially filled, depending on the number of electrons present. This allows the transition metal to readily gain or lose electrons, leading to the formation of different oxidation states.

The ability to change oxidation states is crucial for catalytic activity. In a catalytic reaction, the transition metal acts as a catalyst by providing an alternative reaction pathway with lower activation energy. This lowers the energy barrier for the reaction, allowing it to proceed at a faster rate. The transition metal catalyst can undergo reversible oxidation and reduction reactions, enabling it to interact with reactant molecules and facilitate the reaction.

For example, in the Haber-Bosch process, which is used to produce ammonia from nitrogen and hydrogen, iron is commonly used as a catalyst. Iron can exist in different oxidation states, such as Fe2+ and Fe3+, and can readily switch between these states during the reaction. This allows the iron catalyst to interact with both nitrogen and hydrogen molecules, facilitating the formation of ammonia.

In summary, the variable oxidation states of transition metals are associated with their catalytic activity. This property allows transition metals to participate in redox reactions and easily gain or lose electrons, enabling them to act as catalysts in a wide range of chemical reactions.