The effect of changing the size of nano-particles on their catalytic activity in the oxidation reaction of benzene to phenol can be significant. Nano-particles, particularly metal and metal oxide nano-particles, are known to exhibit size-dependent catalytic properties. This is primarily due to the following factors:1. Surface area: As the size of the nano-particles decreases, their surface area to volume ratio increases. This leads to a higher number of active sites available for the reaction, which can enhance the catalytic activity.2. Electronic properties: The electronic properties of nano-particles can change with their size. Smaller nano-particles may have different electronic structures compared to their bulk counterparts, which can affect their ability to adsorb and activate reactants, as well as facilitate electron transfer during the reaction.3. Lattice strain: Smaller nano-particles can exhibit higher lattice strain, which can alter the binding strength between the catalyst and the reactants. This can affect the reaction rate and selectivity.4. Edge and corner sites: Smaller nano-particles have a higher proportion of edge and corner sites, which can be more reactive than the flat surfaces. This can lead to enhanced catalytic activity.In the specific case of the oxidation reaction of benzene to phenol, the size of the nano-particles can play a crucial role in determining the reaction rate and selectivity. Smaller nano-particles with higher surface area and more reactive sites can potentially lead to higher conversion rates and selectivity towards phenol. However, it is important to note that the optimal size of the nano-particles may vary depending on the specific catalyst material and reaction conditions. Therefore, it is essential to conduct experimental studies to determine the most suitable nano-particle size for the desired catalytic performance.