Of the following statements which are true for `S_(N)1` reaction.
(a) Tertiary alkyl halides react faster than secondary.
(b) The absolute confuguration of the product is oppsoite to that of the reactant when an optical active substrate is used.
(c) The reactio shows first order kinetics.
(d) The rate of reaction depends markely on the nucleophilicity of the nucleophile.
(e) The mechanism is two step.
(f) Carbocations are intermediate.
(g) Rate `= K`[Alkyl][halide]
(h) The rate of teh reaction depends on the nature of the leaving group.

Answer

To determine which statements about the \( S_N1 \) reaction are true, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement (a): Tertiary alkyl halides react faster than secondary.**
- **Analysis:** This statement is true. In \( S_N1 \) reactions, the rate is dependent on the stability of the carbocation formed. Tertiary carbocations are more stable than secondary carbocations, leading to faster reactions for tertiary alkyl halides.
- **Conclusion:** True.

2. **Statement (b): The absolute configuration of the product is opposite to that of the reactant when an optically active substrate is used.**
- **Analysis:** This statement is false. In \( S_N1 \) reactions, the product can have a racemic mixture due to the planar nature of the carbocation intermediate, leading to both retention and inversion of configuration (50% inversion and 50% retention).
- **Conclusion:** False.

3. **Statement (c): The reaction shows first-order kinetics.**
- **Analysis:** This statement is true. The \( S_N1 \) reaction is first-order because the rate-determining step involves only the alkyl halide, not the nucleophile. The rate depends solely on the concentration of the alkyl halide.
- **Conclusion:** True.

4. **Statement (d): The rate of reaction depends markedly on the nucleophilicity of the nucleophile.**
- **Analysis:** This statement is false. In \( S_N1 \) reactions, the rate is primarily dependent on the alkyl halide and not significantly on the nucleophile's strength. The nucleophile's role is to attack the carbocation after it has formed.
- **Conclusion:** False.

5. **Statement (e): The mechanism is two-step.**
- **Analysis:** This statement is true. The \( S_N1 \) mechanism involves two steps: the formation of a carbocation (rate-determining step) and the attack of the nucleophile on the carbocation.
- **Conclusion:** True.

6. **Statement (f): Carbocations are intermediate.**
- **Analysis:** This statement is true. Carbocations are indeed intermediates in the \( S_N1 \) mechanism, formed during the first step of the reaction.
- **Conclusion:** True.

7. **Statement (g): Rate = K[Alkyl][halide].**
- **Analysis:** This statement is false. The rate law for an \( S_N1 \) reaction is rate = K[Alkyl Halide], as it only depends on the concentration of the alkyl halide.
- **Conclusion:** False.

8. **Statement (h): The rate of the reaction depends on the nature of the leaving group.**
- **Analysis:** This statement is true. Both \( S_N1 \) and \( S_N2 \) reactions are influenced by the quality of the leaving group; a better leaving group increases the rate of the reaction.
- **Conclusion:** True.

### Summary of True Statements:
- True: (a), (c), (e), (f), (h)
- False: (b), (d), (g)