Assertion: `(C_(2)H_(5))_(3)N` is less basic than trimethylamine `(CH_(3))_(3)N`
Reason: Due to hyperconjugation of `C_(2)H_(5)` is less than methyl.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. if assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that triethylamine \((C_2H_5)_3N\) is less basic than trimethylamine \((CH_3)_3N\).
- Basicity in amines is influenced by the availability of the lone pair of electrons on the nitrogen atom for donation.

2. **Structure of Triethylamine**:
- Triethylamine has three ethyl groups attached to the nitrogen atom.
- The nitrogen atom has a lone pair of electrons that can be donated to accept protons (H⁺).

3. **Structure of Trimethylamine**:
- Trimethylamine has three methyl groups attached to the nitrogen atom.
- Similar to triethylamine, the nitrogen atom has a lone pair available for donation.

4. **Inductive Effect**:
- Both ethyl and methyl groups exhibit a +I (inductive) effect, which increases the electron density on the nitrogen.
- However, the +I effect of ethyl groups is stronger than that of methyl groups due to the larger size and greater electron-releasing ability of the ethyl group.

5. **Steric Hindrance**:
- Triethylamine has larger ethyl groups compared to the smaller methyl groups in trimethylamine.
- The presence of three bulky ethyl groups around the nitrogen creates steric hindrance, which makes it more difficult for the nitrogen to donate its lone pair of electrons.

6. **Conclusion on Basicity**:
- Although triethylamine has a stronger +I effect, the steric hindrance from the bulky ethyl groups reduces its basicity.
- Therefore, triethylamine is indeed less basic than trimethylamine.

7. **Understanding the Reason**:
- The reason provided states that the basicity difference is due to hyperconjugation of \(C_2H_5\) being less than that of methyl.
- This statement is incorrect because the basicity difference is primarily due to steric hindrance, not hyperconjugation.

8. **Final Evaluation**:
- The assertion is true (triethylamine is less basic than trimethylamine).
- The reason is false (the basicity difference is not due to hyperconjugation).

### Answer:
- The correct option is that the assertion is true, but the reason is false.