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How will you convert methane to following (a) propane (b) butane (c) methyl butanoate (d) ethanoic acid (e) ethanol?

Answer
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Hint: To convert methane into any or other organic compound, we have to apply the additional reactions, such as Wurtz synthesis, Grignard, synthesis and so forth, an addition reaction in organic chemistry, is in its simplest terms an organic reaction where two or more molecules combine to form a larger one.
To understand this question we should first know about methane and its structure.
Methane is a one-carbon compound in which the carbon is attached by single bonds to four hydrogen atoms. It is colourless, odourless non-toxic but flammable gas. It has a function as a fossil fuel, a greenhouse gas component and a metabolic of bacteria.
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Complete step by step answer:
To convert methane into propane.
(a) Propane-Propane is a three carbon alkane with the molecular formula \[{{C}_{3}}{{H}_{8}}\]. It is a gas at standard temperature and pressure.
Propane \[\left( C{{H}_{3}}C{{H}_{2}}-C{{H}_{3}} \right)\]
\[C{{H}_{4}}\xrightarrow{C{{l}_{2}}}\underset{Chloromethane}{\mathop{C{{H}_{3}}-Cl}}\,\]
\[C{{H}_{3}}-Cl\xrightarrow{C{{l}_{2}}}\underset{Chloromethane}{\mathop{C{{H}_{3}}-Cl}}\,\]
\[C{{H}_{3}}-CI\xrightarrow{Na}C{{H}_{3}}-\underset{ethane}{\mathop{C{{H}_{3}}}}\,\left( Wurtz\,synthesis \right)\]
\[C{{H}_{3}}C{{H}_{2}}-CI\xrightarrow{Li/ether}\underset{ethylithium}{\mathop{C{{H}_{3}}C{{H}_{2}}-Li}}\,\]
\[\left( C{{H}_{3}}C{{H}_{2}} \right)-CuLi+C{{H}_{3}}Cl\to \underset{\Pr opane}{\mathop{C{{H}_{3}}C{{H}_{2}}-C{{H}_{3}}}}\,\]
(b) butane is an albane with the formula \[{{C}_{4}}Hco\]. Butane is a highly flammable, colourless, easily liquefied gas that quickly vaporizes at room temperature.
To convert methane into butane
Butane \[\left( C{{H}_{3}}C{{H}_{2}}-C{{H}_{2}}C{{H}_{3}} \right)\]
\[C{{H}_{3}}C{{H}_{2}}-CI\xrightarrow{Na}\underset{\text{Butane}}{\mathop{C{{H}_{3}}C{{H}_{2}}-C{{H}_{2}}}}\,C{{H}_{3}}\left( Wurtz\,synthesis \right)\]
(c) Methyl Butanoate \[\left( {{C}_{5}}{{H}_{10}}{{O}_{2}} \right)\] – It is the methyl ester of butyric acid like most esters, it has fruity odour. It is a colourless liquid with law solubility in water.
Upon which it floats to form an oily layer.
Methyl Butanoate \[\left( {{C}_{5}}{{H}_{10}}{{O}_{2}} \right)\] \[\to \]
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{3}}CooH+C{{H}_{3}}-OH\xrightarrow{{{H}_{2}}{{O}^{+}}}\underset{\left( \text{methyl}\,\text{butanoate} \right)}{\mathop{C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Co-oC{{H}_{3}}}}\,\]
(d) Ethanoic acid \[\to \] it is chemical with a sharp smell. Ethanoic acid has many uses in industrial medical and household settings. It is also known as acetic acid.
To convert methane into ethanoic acid.
Ethanoic acid \[\left( C{{H}_{3}}CooH \right)\]
\[C{{H}_{3}}-Cl\xrightarrow{Mgldryethu}C{{H}_{3}}-MgCl\]
\[C{{H}_{3}}-MgCl\xrightarrow[2.{{H}^{+}}]{1.C{{o}_{2}}}\underset{ethanoic\,acid}{\mathop{C{{H}_{3}}-CooH}}\,\left( grignard\,synthesis \right)\]
(e) Ethanol \[\to \] ethanol is an organic chemical compound it is a simple alcohol with the chemical formula \[{{C}_{2}}{{H}_{6}}O\]. Ethanol is a volatile, flammable, collarless liquid.
Ethanol \[({{C}_{2}}{{H}_{6}})\] \[C{{H}_{3}}C{{H}_{2}}-Cl\xrightarrow{OH}\underset{ethanol}{\mathop{C{{H}_{3}}C{{H}_{2}}-oH}}\,\]


Note: To convert any organic compounds into alkane, or alkenes, first we have to know about organic compounds and reactions. Organic reactions are chemical reactions involving organic compounds. The basic organic reactions types are Addition reactions, elimination, reactions, rearrangement reactions and redox reactions etc.