For each of the following, write a series of equations for a method of synthesis from other compounds. Name all compounds involved.

a) trimethylamine from ammonia and alkanes
b) sodium ethanoate from an ester
f) phenyl 2-methylpropanoate from phenol and an appropriate alcohol.
e) N,N-dimethylethanamide from an alkene, alkane and ammonia.

For b, you can take propyl ethanoate, hydrolyze it to produce ethanoic acid and propyl alcohol, than neutralize the acid with NaOH to form the Na salt of ethanoic acid.

a) To synthesize trimethylamine from ammonia and alkanes, we can proceed through the following steps:

1. Initial Step: Combine ammonia (NH3) and an alkane (R-H) to form an amine (R-NH2) and hydrogen gas (H2).
Equation: R-H + NH3 → R-NH2 + H2

2. Methylation Step: React the amine (R-NH2) obtained from the previous step with methanol (CH3OH) and a suitable catalyst, such as sulfuric acid (H2SO4), to introduce methyl groups (CH3-) onto the amine.
Equation: R-NH2 + CH3OH → R-N(CH3)2 + H2O

3. Quaternization Step: Treat the dimethylamine (R-N(CH3)2) obtained in the previous step with formaldehyde (CH2O) and a strong base, such as sodium hydroxide (NaOH), to form quaternary ammonium salt (R-N(CH3)3+).
Equation: R-N(CH3)2 + CH2O + NaOH → R-N(CH3)3+ + H2O + NaOH^-

4. Trimethylamine Formation: Finally, treat the quaternary ammonium salt (R-N(CH3)3+) obtained in the previous step with a strong base, such as sodium hydroxide (NaOH), to release trimethylamine (N(CH3)3).
Equation: R-N(CH3)3+ + OH^- → [R-N(CH3)2H] + CH3OH

Overall Equation: R-H + 2NH3 + 2CH3OH + CH2O + NaOH → [R-N(CH3)2H] + N(CH3)3 + H2O + NaOH^-

b) For the synthesis of sodium ethanoate from an ester, we can use the following steps:

1. Hydrolysis Step: React the ester (R'-COOR) with a strong base, such as sodium hydroxide (NaOH), under reflux conditions to undergo basic hydrolysis and form the corresponding sodium carboxylate (R'-COO^-Na+) and an alcohol (R'-OH).
Equation: R'-COOR + NaOH → R'-COO^-Na+ + R'-OH

2. Acidification Step: Treat the sodium carboxylate (R'-COO^-Na+) obtained in the previous step with an acid, such as hydrochloric acid (HCl), to protonate the carboxylate ion and form the sodium salt of the carboxylic acid (R'-COOH) and sodium chloride (NaCl).
Equation: R'-COO^-Na+ + HCl → R'-COOH + NaCl

Overall Equation: R'-COOR + NaOH + HCl → R'-COOH + R'-OH + NaCl

f) To synthesize phenyl 2-methylpropanoate from phenol and an appropriate alcohol, the reaction can be carried out in the following steps:

1. Esterification Step: React phenol (C6H5OH) with an appropriate alcohol, such as isobutanol (C4H9OH), in the presence of a catalyst, such as sulfuric acid (H2SO4), to form the ester phenyl 2-methylpropanoate.
Equation: C6H5OH + C4H9OH → C6H5OC(O)CH(CH3)2 + H2O

Overall Equation: C6H5OH + C4H9OH → C6H5OC(O)CH(CH3)2 + H2O

e) To synthesize N,N-dimethylethanamide from an alkene, alkane, and ammonia, we can follow these steps:

1. Hydroamination Step: React the alkene (R-CH=CH2) with ammonia (NH3) in the presence of a catalyst, such as a transition metal complex, to form the corresponding primary amine (R-CH2-CH2-NH2).
Equation: R-CH=CH2 + NH3 → R-CH2-CH2-NH2

2. N-Methylation Step: Treat the primary amine (R-CH2-CH2-NH2) obtained in the previous step with formaldehyde (CH2O) and a suitable methylating agent, such as dimethyl sulfate (CH3)2SO4, to introduce a methyl group (CH3-) onto the amine nitrogen.
Equation: R-CH2-CH2-NH2 + CH2O + (CH3)2SO4 → R-CH2-CH2-N(CH3)2 + NaOH + (CH3)2SO4^-

3. Dehydration Step: React the N-methylamine (R-CH2-CH2-N(CH3)2) obtained in the previous step with an alkane (R'-H), such as ethane (C2H6), in the presence of a dehydrating agent, such as phosphorus(V) oxide (P2O5), to remove water and form N,N-dimethylethanamide.
Equation: R-CH2-CH2-N(CH3)2 + R'-H + P2O5 → R-C(O)NH(CH3)2 + P2O4 + H2O

Overall Equation: R-CH=CH2 + NH3 + CH2O + (CH3)2SO4 + R'-H + P2O5 → R-C(O)NH(CH3)2 + P2O4 + H2O

Note: The specific compounds represented by "R" and "R'" will depend on the reactants used in the synthesis.