Which of the following characteristics of the transition metals is associated with their catalytic property activity?

variable oxidation states

The correct answer is option 2. variable oxidation states.

The catalytic activity of transition metals is primarily associated with their ability to exhibit variable oxidation states. Let us break down each characteristic:

1. Color of hydrated ion: While the color of hydrated ions of transition metals can vary due to the presence of d-electrons, it is not directly related to their catalytic activity.

2. Variable oxidation states: Transition metals have the unique ability to exist in multiple oxidation states. This property is crucial for catalysis because it allows them to readily accept and donate electrons during chemical reactions, making them effective catalysts for a wide range of reactions.

3. High enthalpy of atomization: This characteristic refers to the energy required to separate the atoms of a substance in the gas phase. While transition metals generally have high enthalpies of atomization due to strong metallic bonding, this property is not directly related to their catalytic activity.

4. Paramagnetic behavior: Transition metals often exhibit paramagnetic behavior due to the presence of unpaired electrons in their d-orbitals. While this property is a consequence of their electronic configuration, it is not directly linked to their catalytic activity.

Therefore, the characteristic of transition metals associated with their catalytic property/activity is: 2. Variable oxidation states