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Solution

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(a) Benzene to 1-(1-methylethyl)-4-propylbenzene

1. First benzene is treated with isopropyl (CH₃CHClCH₃) and AlCl_3, resulting in formation of isopropyl benzene by electrophilic aromatic substitution.

2. In second step, treat isopropyl benzene with propanoyl chloride (CH₃CH₂COCl) and AlCl₃, it will result in installation of (CH₃CH₂CO) group at the 4-position of isopropyl benzene. This step should not be done by propyl chloride and AlCl_3, as the resulting carbocation may rearrange and a mixture of products may be obtained.

3. Reduce the (CH3CH2CO) with LiAlH4. It will result in formation of 1-(1-methylethyl)-4-propylbenzene.

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(b) Benzene to p-chlorobenzoic acid

1. First, benzene is treated with methyl chloride and alumnium trichloride, resulting in formation of toluene by electrophilic aromatic substitution mechanism.

2. Chlorination of toluene is done by using Cl₂, AlCl₃ in dark. You will get 4-chlorotoluene as major product.

3. 4-chlorotoluene is oxidised with KMnO₄ resulting in formation of 4-chlorobenzoic acid.