Consider the reactions:
`(i)(CH_3)_2CH-CH_2Br overset(C_2H_5OH)to (CH_3)_2CH-CH_2OC_2H_5+HBr`
`(ii)(CH_3)_2CH-CH_2Br overset(C_2H_5O^-)to(CH_3)_2CH-CH_2OC_2H_5+Br^-`
The mechanisms of reactions (i) and (ii) are respectively :

Options

A. `S_(N^(2)) " and " S_(N^(1))`
B. `S_(N^(1)) " and " S_(N^(2))`
C. `S_(N^(1)) " and " S_(N^(1))`
D. `S_(N^(2)) " and " S_(N^(2))`

Explanation

To solve the question regarding the mechanisms of the given reactions, we will analyze each reaction step by step.

### Step 1: Analyze Reaction (i)
The first reaction is:
\[ (CH_3)_2CH-CH_2Br + C_2H_5OH \rightarrow (CH_3)_2CH-CH_2OC_2H_5 + HBr \]

1. **Identify the Reactant**: The reactant is isobutyl bromide, which is a secondary alkyl halide.
2. **Identify the Nucleophile**: The nucleophile in this reaction is ethanol (C2H5OH).
3. **Mechanism Consideration**:
- In this reaction, the bromine atom (leaving group) departs first, forming a carbocation (a positively charged ion).
- The nucleophile (ethanol) then attacks the carbocation to form the ether product.
- Since the reaction involves the formation of a carbocation and does not involve a backside attack, it suggests an SN1 mechanism.

### Step 2: Analyze Reaction (ii)
The second reaction is:
\[ (CH_3)_2CH-CH_2Br + C_2H_5O^- \rightarrow (CH_3)_2CH-CH_2OC_2H_5 + Br^- \]

1. **Identify the Reactant**: Again, the reactant is isobutyl bromide (secondary alkyl halide).
2. **Identify the Nucleophile**: The nucleophile here is the ethoxide ion (C2H5O^-), which is a strong nucleophile.
3. **Mechanism Consideration**:
- In this case, the nucleophile attacks the carbon bonded to the bromine atom directly, leading to the displacement of the bromine atom.
- This reaction occurs in a single concerted step without the formation of a carbocation, indicating an SN2 mechanism.

### Conclusion
Based on the analysis:
- Reaction (i) proceeds via an SN1 mechanism.
- Reaction (ii) proceeds via an SN2 mechanism.

Thus, the correct answer is:
**Option B: SN1 for reaction (i) and SN2 for reaction (ii).**