Identify the starting compound

The given alkyne is: $\mathrm{CH_3-C\equiv C-CH_3}$ This is but-2-yne.

First reagent: $\mathrm{Na/liquid\ NH_3}$

This is the dissolving metal reduction of an alkyne.

Rule:

• Alkyne $\xrightarrow{\mathrm{Na/NH_3(l)}}$ trans-alkene

Therefore, $\mathrm{CH_3-C\equiv C-CH_3} \xrightarrow{Na/NH_3(l)} \mathrm{trans\text{-}CH_3-CH=CH-CH_3}$ i.e. trans-but-2-ene.

Second reagent: dilute $\mathrm{KMnO_4}$ at $273\,K$

Cold dilute alkaline/neutral $\mathrm{KMnO_4}$ adds two hydroxyl groups across the double bond to form a vicinal diol.

So, $\mathrm{CH_3-CH=CH-CH_3} \xrightarrow[273\,K]{dil.\ KMnO_4} \mathrm{CH_3-CH(OH)-CH(OH)-CH_3}$

Product $P$ is butane-2,3-diol.

Count oxygen atoms in $P$

In $\mathrm{CH_3-CH(OH)-CH(OH)-CH_3}$, there are two $\mathrm{-OH}$ groups.

Hence, number of oxygen atoms $= 2$.

Final answer

$\boxed{2}$

Comparison with stored answer

Stored correct answer = 2.

Our derived answer matches the stored answer.