In the reaction: `CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-OH+HCl rarr CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-Cl`
the rate-determining step is:

Options

A. `CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-OH+H_(3)O^(+)hArrCH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-underset(o+)overset(H)overset(|)O-H-H_(2)O`
B.
C.
D. all steps take place with equal ease

Explanation

To determine the rate-determining step in the reaction of a tertiary alcohol with HCl, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactants and Products**:
- The reactant is a tertiary alcohol: \( CH_3C(CH_3)_2OH \).
- The product is a tertiary alkyl chloride: \( CH_3C(CH_3)_2Cl \).

2. **Understand the Mechanism**:
- The reaction involves the protonation of the alcohol by HCl, which leads to the formation of a better leaving group (water).
- The HCl dissociates into \( H^+ \) and \( Cl^- \).

3. **Protonation of the Alcohol**:
- The \( H^+ \) from HCl attacks the hydroxyl group (-OH) of the alcohol, converting it into water (\( H_2O \)), which is a good leaving group.
- This step can be represented as:
\[ CH_3C(CH_3)_2OH + H^+ \rightarrow CH_3C(CH_3)_2OH_2^+ \]

4. **Formation of Carbocation**:
- The next step involves the loss of water (\( H_2O \)) from the protonated alcohol, leading to the formation of a carbocation.
- This is the critical step where the stability of the carbocation plays a significant role. In this case, a tertiary carbocation is formed, which is stabilized by the +I effect of the three methyl groups.
- The reaction can be represented as:
\[ CH_3C(CH_3)_2OH_2^+ \rightarrow CH_3C(CH_3)_2^+ + H_2O \]

5. **Rate-Determining Step**:
- The formation of the carbocation is the slowest step in the mechanism and thus is the rate-determining step.
- After the carbocation is formed, the \( Cl^- \) ion can quickly attack the carbocation to form the final product:
\[ CH_3C(CH_3)_2^+ + Cl^- \rightarrow CH_3C(CH_3)_2Cl \]

6. **Conclusion**:
- The rate-determining step in this reaction is the formation of the carbocation from the protonated alcohol.

### Final Answer:
The rate-determining step is the formation of the carbocation.