How many of the following amines will undergo diazotisation?
`underset((I))("tert-butylamine"), underset((II))("Ethanamine"),underset((III))("Aniline"),underset((IV))("N-methylaniline"),underset((V))("p-toluidine"),underset((VI))("m-chloroaniline"),underset((VII))("2-phenylethanamine")`

Answer

To determine how many of the given amines will undergo diazotization, we need to identify which of these amines are aromatic primary amines. Diazotization typically occurs with aromatic primary amines when they are treated with nitrous acid (HNO2), leading to the formation of diazonium salts.

Let's analyze each of the given amines step by step:

1. **tert-butylamine (I)**:
- Structure: (CH3)3CNH2
- Type: Tertiary amine (not primary) and non-aromatic.
- Conclusion: Will NOT undergo diazotization.

2. **Ethanamine (II)**:
- Structure: C2H5NH2
- Type: Primary amine (but non-aromatic).
- Conclusion: Will NOT undergo diazotization.

3. **Aniline (III)**:
- Structure: C6H5NH2
- Type: Primary amine and aromatic.
- Conclusion: Will undergo diazotization.

4. **N-methylaniline (IV)**:
- Structure: C6H5N(CH3)2
- Type: Aromatic but secondary amine (not primary).
- Conclusion: Will NOT undergo diazotization.

5. **p-toluidine (V)**:
- Structure: C6H4(CH3)NH2 (where the methyl group is at the para position).
- Type: Primary amine and aromatic.
- Conclusion: Will undergo diazotization.

6. **m-chloroaniline (VI)**:
- Structure: C6H4ClNH2 (where the chlorine is at the meta position).
- Type: Primary amine and aromatic.
- Conclusion: Will undergo diazotization.

7. **2-phenylethanamine (VII)**:
- Structure: C6H5CH2CH2NH2
- Type: Primary amine but non-aromatic (the amine is attached to a carbon chain).
- Conclusion: Will NOT undergo diazotization.

Now, let's summarize the findings:
- Amines that will undergo diazotization:
- Aniline (III)
- p-toluidine (V)
- m-chloroaniline (VI)

Thus, the total number of amines that will undergo diazotization is **3**.

### Final Answer: 3