Introduction:
The Friedel-Crafts alkylation reaction is an important organic reaction that involves the introduction of an alkyl group onto an aromatic ring. It is named after its discoverers, Charles Friedel and James Crafts. The reaction is typically carried out using a catalyst, which facilitates the reaction and increases the yield of the desired product.

Catalyst Used:
The catalyst used in the Friedel-Crafts alkylation reaction is anhydrous aluminium chloride (AlCl3). It acts as a Lewis acid catalyst, meaning that it can accept a pair of electrons from a Lewis base to form a coordinate covalent bond. In this reaction, the catalyst helps in the formation of a carbocation intermediate, which is crucial for the alkylation process.

Mechanism:
The reaction proceeds through the following steps:

1. Activation of the catalyst: Anhydrous aluminium chloride is added to the reaction mixture to activate it. It coordinates with the alkyl halide, making it more electrophilic and reactive.

2. Formation of the carbocation intermediate: The alkyl halide undergoes a nucleophilic attack by the Lewis base generated from the benzene ring. This leads to the formation of a carbocation intermediate. The formation of a carbocation is facilitated by the presence of the Lewis acid catalyst.

3. Rearrangement (if applicable): In some cases, the carbocation intermediate may undergo a rearrangement to form a more stable carbocation. This rearrangement can occur through a hydride shift or a methyl shift.

4. Attack by the benzene ring: The carbocation intermediate is then attacked by the benzene ring, which acts as a nucleophile. The benzene ring donates a pair of electrons to the carbocation, resulting in the formation of a new carbon-carbon bond.

5. Regeneration of the catalyst: After the reaction is complete, the catalyst can be regenerated by reacting it with a suitable compound, such as water or an alcohol.

Advantages of using anhydrous aluminium chloride:
- Anhydrous aluminium chloride is a widely used catalyst in the Friedel-Crafts alkylation reaction due to its high reactivity and selectivity.
- It can activate a wide range of alkyl halides and facilitate the formation of the carbocation intermediate.
- The catalyst can be easily separated from the reaction mixture.
- It is relatively inexpensive and readily available.

Conclusion:
In conclusion, the catalyst used in the Friedel-Crafts alkylation reaction is anhydrous aluminium chloride. It plays a crucial role in activating the alkyl halide, facilitating the formation of the carbocation intermediate, and increasing the yield of the desired alkylbenzene product. The use of this catalyst allows for the efficient and selective introduction of alkyl groups onto aromatic rings.