To produce ethylbenzene (PhEt) using anhydrous AlCl3 as a catalyst, the correct reaction is option 'C': H2C = CH2 + C6H6.

Explanation:

Anhydrous AlCl3 is a Lewis acid catalyst and is commonly used in Friedel-Crafts alkylation reactions. In these reactions, an alkyl halide is reacted with an aromatic compound in the presence of a Lewis acid catalyst to form a new carbon-carbon bond.

The reaction pathway for the formation of ethylbenzene using anhydrous AlCl3 as a catalyst is as follows:

Step 1: Activation of the catalyst
AlCl3 reacts with a Lewis base, which can be the alkyl halide or the aromatic compound, to form a complex. In this case, AlCl3 reacts with the alkyl halide (H2C = CH2) to form a complex.

Step 2: Formation of the carbocation
The alkyl halide (H2C = CH2) undergoes homolytic cleavage to generate a carbocation intermediate. The carbocation formed in this case is the ethyl carbocation (H3C - CH2+).

Step 3: Reaction with the aromatic compound
The carbocation intermediate (H3C - CH2+) reacts with the aromatic compound (C6H6) through electrophilic aromatic substitution. The carbocation is attacked by the electron-rich benzene ring, resulting in the formation of ethylbenzene (PhEt).

Step 4: Regeneration of the catalyst
After the reaction, the catalyst AlCl3 is regenerated by reacting with a Lewis base, which can be a byproduct or excess alkyl halide.

Overall reaction:
H2C = CH2 + C6H6 → H3C - CH2C6H5 (ethylbenzene)

In this reaction, the alkene (H2C = CH2) acts as the alkylating agent, and the aromatic compound (C6H6) acts as the substrate. The Lewis acid catalyst, anhydrous AlCl3, facilitates the reaction by activating the alkene and stabilizing the carbocation intermediate.

Thus, the correct option for the reaction that produces ethylbenzene using anhydrous AlCl3 as a catalyst is option 'C': H2C = CH2 + C6H6.