Reaction involved

Addition of $HCN$ to carbonyl compounds is a nucleophilic addition reaction: $R_2C=O + HCN \rightarrow R_2C(OH)CN$

The rate depends mainly on how susceptible the carbonyl carbon is to nucleophilic attack.

Factors affecting rate

The rate of nucleophilic addition to aldehydes/ketones increases when:

• the carbonyl carbon is more electrophilic
• steric hindrance around the carbonyl carbon is less

Thus:

• Aldehydes react faster than ketones because they have less steric hindrance and less $+I$ effect.
• Aromatic ketones/aldehydes are less reactive than aliphatic ones because the phenyl group conjugates with the carbonyl group, reducing the positive character on the carbonyl carbon.
• More phenyl groups attached to the carbonyl make it still less reactive.

Compare the given compounds

• A: $HCHO$ (formaldehyde)
  Most reactive: no alkyl/aryl groups, least steric hindrance, maximum electrophilicity.

• B: $CH_3COCH_3$ (acetone)
  A simple aliphatic ketone. Less reactive than formaldehyde, but more reactive than aryl ketones.

• C: $PhCOCH_3$ (acetophenone)
  One phenyl group conjugated with carbonyl, so less reactive than acetone.

• D: $PhCOPh$ (benzophenone)
  Two phenyl groups conjugated with carbonyl, maximum resonance stabilization and steric hindrance among these, hence least reactive.

Increasing order of rate

Therefore, $PhCOPh < PhCOCH_3 < CH_3COCH_3 < HCHO$ i.e. $D < C < B < A$

Match with options

This corresponds to Option C.

Comparison with stored answer

Stored correct answer: C
Derived answer: C
Hence, they agree.