The correct order of reactivity of PhMgBr with
`Ph - overset(O)overset(||)(C ) - Ph, " " CH_(3) - overset(O)overset(||)(C ) - H, " " CH_(3) - overset(O)overset(||)(C ) - CH_(3)`
`" (I) ""(II) ""(III) "`

Options

A. `(I) gt (II) gt (III)`
B. `(III) gt (II) gt (I)`
C. `(II) gt (III) gt (I)`
D. `(I) gt (III) gt (II)`

Explanation

To determine the correct order of reactivity of PhMgBr with the given compounds, we need to analyze the electrophilicity of each carbonyl carbon in the three compounds:

1. **Identify the Compounds**:
- (I) Ph - C(=O) - Ph
- (II) CH3 - C(=O) - H
- (III) CH3 - C(=O) - CH3

2. **Understand the Reactivity**:
- The reactivity of PhMgBr (a Grignard reagent) with carbonyl compounds depends on the electrophilicity of the carbonyl carbon. The more electrophilic the carbon, the more reactive it is towards nucleophiles like PhMgBr.

3. **Analyze the Electron-Withdrawing and Electron-Donating Effects**:
- **Compound (I)**: Ph - C(=O) - Ph
- The two phenyl groups exert a resonance effect (−R effect), which stabilizes the carbonyl and decreases its electrophilicity.
- **Compound (II)**: CH3 - C(=O) - H
- The methyl group has a +I effect, which increases the electron density on the carbonyl carbon, making it more electrophilic than (I) but less than (III).
- **Compound (III)**: CH3 - C(=O) - CH3
- Here, the two methyl groups also exert a +I effect, which increases electron density even more than in (II), making the carbonyl carbon less electrophilic than in (II).

4. **Rank the Reactivity**:
- The order of decreasing electrophilicity (and thus increasing reactivity with PhMgBr) is:
- (II) > (III) > (I)
- Therefore, the order of reactivity is:
- **(II) > (III) > (I)**

5. **Conclusion**:
- The correct order of reactivity of PhMgBr with the given compounds is (II) > (III) > (I).

### Final Order:
- **(II) > (III) > (I)**