The increasing order of the rate of `HCN` addition of compound a-d is
(i) `HCHO`
(ii) `CH_(3)COCH_(3)`
(iii) `PhCOCH_(3)`
(iv) `PhCOPh`

Options

A. `(i) lt (ii) lt (iii) lt (iv)`
B. `(iv) lt (ii) lt (iii) lt (i)`
C. `(iv) lt (iii) lt (ii) lt (i)`
D. `(iii) lt (iv) lt (ii) lt (i)`

Explanation

To determine the increasing order of the rate of HCN addition to the compounds given (HCHO, CH₃COCH₃, PhCOCH₃, PhCOPh), we need to analyze the structure of each compound and the steric hindrance involved in the addition reaction. Here’s a step-by-step solution:

### Step 1: Identify the Compounds
1. **HCHO (Formaldehyde)**: This is an aldehyde with no alkyl groups attached to the carbonyl carbon.
2. **CH₃COCH₃ (Acetone)**: This is a ketone with two methyl groups attached to the carbonyl carbon.
3. **PhCOCH₃ (Acetophenone)**: This is a ketone with one phenyl group and one methyl group attached to the carbonyl carbon.
4. **PhCOPh (Benzophenone)**: This is a ketone with two phenyl groups attached to the carbonyl carbon.

### Step 2: Analyze the Reactivity
- **HCHO**: The carbonyl carbon is less sterically hindered because it has two hydrogen atoms. Thus, it is the most reactive towards HCN addition.

- **CH₃COCH₃**: The carbonyl carbon is attached to two methyl groups. Although it has some steric hindrance, it is still less hindered compared to the compounds with phenyl groups. Therefore, it is the second most reactive.

- **PhCOCH₃**: The presence of one phenyl group introduces more steric hindrance than the two methyl groups in acetone. Hence, it is less reactive than acetone but more reactive than benzophenone.

- **PhCOPh**: This compound has two phenyl groups, which create significant steric hindrance around the carbonyl carbon, making it the least reactive towards HCN addition.

### Step 3: Order the Reactivity
Based on the analysis:
1. HCHO (most reactive)
2. CH₃COCH₃
3. PhCOCH₃
4. PhCOPh (least reactive)

### Conclusion
The increasing order of the rate of HCN addition to the compounds is:
**PhCOPh < PhCOCH₃ < CH₃COCH₃ < HCHO**

### Final Answer
**The increasing order of the rate of HCN addition is: PhCOPh < PhCOCH₃ < CH₃COCH₃ < HCHO.**

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