Conversions:a) Methane to ethaneb) But-2-ene to ethanalc) Sodium benzoate to chlorobenzened) Benzene to m-dinitrobenzenee) Ethyne to benzene sulphonic acid

a) Converting methane to ethane typically involves a process known as hydrodehalogenation. The reaction can be summarized as follows:

CH₄ + Cl₂ → CH₃Cl + HCl (chlorination of methane)
CH₃Cl + Cl₂ → CH₂Cl₂ + HCl (dichlorination of methane)
CH₂Cl₂ + Cl₂ → CHCl₃ + HCl (trichlorination of methane)
CHCl₃ + Cl₂ → CCl₄ + HCl (tetrachlorination of methane)
CCl₄ + H₂ → CHCl₃ + HCl (hydrodehalogenation)
CHCl₃ + H₂ → CH₃Cl + HCl (hydrodehalogenation)
CH₃Cl + H₂ → CH₃CH₃ + HCl (hydrodehalogenation)

By repeating the hydrodehalogenation steps, methane (CH₄) can be gradually converted to ethane (C₂H₆).

b) Converting but-2-ene to ethanol involves a hydration reaction. Here's the reaction:

CH₃CH=CHCH₃ + H₂O → CH₃CH₂CH₂OH

In this reaction, but-2-ene (CH₃CH=CHCH₃) reacts with water (H₂O) to produce ethanol (CH₃CH₂CH₂OH).

c) Converting sodium benzoate to chlorobenzene can be achieved through a substitution reaction known as the Sandmeyer reaction. Here's the reaction:

C₆H₅COONa + Cl₂ + HCl → C₆H₅Cl + NaCl + H₂O

In this reaction, sodium benzoate (C₆H₅COONa) reacts with chlorine (Cl₂) and hydrochloric acid (HCl) to yield chlorobenzene (C₆H₅Cl), sodium chloride (NaCl), and water (H₂O).

d) Converting benzene to m-dinitrobenzene involves a nitration reaction. Here's the reaction:

C₆H₆ + 3HNO₃ → C₆H₃(NO₂)₃ + 3H₂O

In this reaction, benzene (C₆H₆) reacts with nitric acid (HNO₃) to produce m-dinitrobenzene (C₆H₃(NO₂)₃) and water (H₂O).

e) Converting ethyne (also known as acetylene) to benzene sulfonic acid involves a reaction called sulfonation. Here's the reaction:

HC≡CH + H₂SO₄ → C₆H₅SO₃H

In this reaction, ethyne (HC≡CH) reacts with sulfuric acid (H₂SO₄) to yield benzene sulfonic acid (C₆H₅SO₃H).