The catalytic activity of transition elements is related to their variable oxidation states, surface area, and complex formation ability. Let's discuss each of these factors in detail:

Variable Oxidation States:
Transition elements have the ability to exhibit multiple oxidation states due to the presence of partially filled d orbitals. These variable oxidation states allow transition elements to undergo redox reactions easily, making them excellent catalysts. The different oxidation states provide different electron configurations, which in turn affect the reactivity and catalytic properties of the transition elements.

Surface Area:
The catalytic activity of a substance is often dependent on its surface area. Transition elements, especially in their finely divided or nanoparticle form, have a high surface area-to-volume ratio. This increased surface area provides more active sites for reactant molecules to adsorb onto, allowing for greater interaction and higher catalytic activity. Additionally, the smaller particle size leads to increased diffusion rates, enhancing the efficiency of catalytic reactions.

Complex Formation Ability:
Transition elements have a strong tendency to form coordination complexes due to their ability to donate and accept electrons. These coordination complexes often act as catalysts by providing a suitable environment for reactant molecules to undergo chemical transformations. The presence of ligands in coordination complexes can modify the electronic structure of the metal center, influencing its catalytic activity.

The ligands can also stabilize high-energy intermediates, lower the activation energy of reactions, and increase the selectivity of catalytic processes. The coordination complexes formed by transition elements exhibit a wide range of geometries, which further enhances their catalytic versatility.

In conclusion, the catalytic activity of transition elements is influenced by their variable oxidation states, surface area, and complex formation ability. These factors allow transition elements to participate in redox reactions, provide a larger surface area for reactant adsorption, and form coordination complexes that facilitate and enhance catalytic reactions.