The very equation of a chemical reaction is wrong.
1) Carboxylic acids and amines form salts through an acid -base reaction
RCOOH + RNH2 -> RCOO- RNH3+
If so, the equation of a chemical reaction should be:
C9H11COOH + (CH3)2NH ->
C9H11COO- (CH3)2NH+
Or
C9H12O2 + C2H7N -> C12H19NO2
2) When heated to high temperature, these salts give a useful amide product in a process called pyrolysis:
RCOO- RNH3+ -> RCONHR + H2O
If so, the equation of a chemical reaction should be:
C9H11COOH + (CH3)2NH heat-> C9H11CON(CH3)2 + H2O
Or
C10H12O2 + C2H7N -> C12H17NO + H2O
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