Decreasing order of reactivity in Williamson's ether synthesis of the following .
I. `Me_3"CC"H_2Br`
II. `CH_3CH_2CH_2Br`
III. `CH_2=CHCH_2Cl`
IV. `CH_3CH_2CH_2CH_2Cl`

Options

A. `IgtIIgtIV gtIII`
B. `III gtIIgtIVgtI`
C. `IgtIIIgtIIgtIV`
D. `IIgtIIIgtIVgtI`

Answer

To determine the decreasing order of reactivity in Williamson's ether synthesis for the given compounds, we need to analyze the nature of the alkyl halides involved. The compounds are:

I. `Me_3CCH_2Br` (tert-butyl bromide)
II. `CH_3CH_2CH_2Br` (n-butyl bromide)
III. `CH_2=CHCH_2Cl` (allyl chloride)
IV. `CH_3CH_2CH_2CH_2Cl` (n-butyl chloride)

### Step-by-Step Solution:

1. **Identify the Type of Halides**:
- Compound I (`Me_3CCH_2Br`) is a secondary halide (due to the tertiary carbon).
- Compound II (`CH_3CH_2CH_2Br`) is a primary halide.
- Compound III (`CH_2=CHCH_2Cl`) is an allylic halide.
- Compound IV (`CH_3CH_2CH_2CH_2Cl`) is a primary halide.

2. **Assess Reactivity Based on Bond Strength**:
- The C-Br bond is weaker than the C-Cl bond. Thus, bromides generally react faster than chlorides.
- Therefore, compounds I and II (bromides) will be more reactive than compounds III and IV (chlorides).

3. **Consider Resonance Effects**:
- Compound III (`CH_2=CHCH_2Cl`) has resonance stabilization due to the presence of the double bond adjacent to the halide. This makes it more reactive than a simple primary chloride.
- Compound IV (`CH_3CH_2CH_2CH_2Cl`) does not have such resonance stabilization and is less reactive than compound III.

4. **Evaluate Steric Hindrance**:
- Compound I (`Me_3CCH_2Br`) has significant steric hindrance due to the bulky tert-butyl group, making it less reactive in an SN2 reaction.
- Compound II (`CH_3CH_2CH_2Br`) is a primary halide and has less steric hindrance, making it more reactive than compound I.

5. **Order the Reactivity**:
- Based on the analysis, we can summarize the reactivity as follows:
- Compound II (`CH_3CH_2CH_2Br`) > Compound III (`CH_2=CHCH_2Cl`) > Compound IV (`CH_3CH_2CH_2CH_2Cl`) > Compound I (`Me_3CCH_2Br`).

### Final Decreasing Order of Reactivity:
**II > III > IV > I**