(i)
The desired transformation is ethanoic acid to methanamine.   

In the first reaction, ethanoic acid reacts with SOCl₂ and acetyl chloride is obtained as a product. In the second step, acetyl chloride reacts with ammonia, and an amide is obtained as a product. 

Then amide undergoes a Hoffmann bromamide reaction and then amine is obtained as a product. In this reaction, amide reacts with KOH and Br₂. 

The reactions are as follows:

(ii)

In the first reaction, hydrolysis of hexanenitrile takes place and hexanoic acid is obtained as a product. In the second reaction, the acid reacts with SOCl₂ , and the OH group is replaced by a Cl atom.

In the next step, acyl chloride reacts with ammonia, and an amide is obtained as a product. In the last step, amide undergoes a Hoffmann bromamide reaction and is converted into an amine containing 1 carbon less than the starting reactant. 

The reactions are as follows:
 

(iii)
In the first reaction, methanol reacts with PCl₅ and is converted into a methylchloride. Then, methylchloride undergoes a substitution reaction(S_N2) and an ethanenitrile is obtained as a product. 

In the next step, ethanenitrile undergoes a hydrolysis reaction and ethanoic acid is obtained as a product.
The reactions are as follows:

(iv)

In the first reaction, ethanamine reacts with NaNO₂/HCl, and diazonium salt is formed as a product. The diazonium salt obtained from primary aliphatic amine is highly unstable, and it reacts with water and forms alcohol as a product. 

In the next step, alcohol undergoes an oxidation reaction and ethanoic acid is obtained as a product. The ethanoic acid is heated with ammonia and an amide is obtained. Then in the last step, amide undergoes a Hoffmann bromamide reaction with Br₂ and NaOH, hence, methanamine is obtained as a product

The reactions are as follows:
 

(v)
In the first reaction, ethanoic acid undergoes a reduction reaction. and ethanol is obtained as a product. In the next step, ethanol reacts with PCl₅ , and ethyl chloride is obtained as the product.

In the next step, a substitution reaction occurs and propanenitrile is obtained as a product when ethyl chloride reacts with NaCN. Then in the last step CN group undergoes acid hydrolysis and is converted into an acid group. 

The reactions are as follows:

(vi)

In the first step, methanamine reacts with NaNO₂/ HCl and unstable diazonium salt is obtained. Then immediately diazonium salt reacts with water and methanol is obtained as a product.

In the next step, methanol reacts with PCl₅ and methyl chloride is obtained as a product. Then methyl chloride reacts with NaCN and ethanenitrile is obtained as a product.

The reduction of ethanenitrile in the next step gives ethanamine as a product. For this reaction, hydrogen and nickel is used as a reagent.

The reactions are as follows:
 

(vii)
In the first step, nitromethane undergoes a reduction reaction in the presence of Sn/HCl, and hence, methanamine is obtained as a product. In the next step, methanamine undergoes a carbylamine reaction, and isocyanide is obtained as a product. 

In this reaction, methanamine reacts with CHCl₃ and KOH, and isocyanide is obtained as a product,.

In the last step, the reduction of isocyanide takes place and dimethylamine is obtained as a product. 

The reactions are as follows:

(viii)

In the first reaction, propanoic acid reacts with ammonia, and an amide is obtained as a product. In the next step, amide undergoes a Hoffmann bromamide reaction, and an ethylamine is obtained as a product. 

The ethylamine reacts with NaNO₂/HCl followed by water and ethanol is obtained as a product. 

In the last step, oxidation of alcohol takes place using KMnO₄ . The reactions are as follows: