Primary, secondary and tertiary alcohols may be distinguished by converting them to the corresponding nitroalkanes and then treating with (a) \(\mathrm{NaNO}_{2}\) and dilute \(\mathrm{HCl}\) (b) \(\mathrm{con} \cdot \mathrm{H}_{2} \mathrm{SO}_{4}\) (c) Sn and hydrochloric acid (d) Ammonium hydroxide

To distinguish between primary, secondary, and tertiary alcohols, one must first understand their structure. Primary alcohols have the hydroxyl group attached to a carbon atom that is only bonded to one other carbon atom. Secondary alcohols have the hydroxyl group attached to a carbon atom that is bonded to two other carbon atoms. Tertiary alcohols have the hydroxyl group attached to a carbon atom that is bonded to three other carbon atoms.

Primary, secondary, and tertiary alcohols can be converted into their corresponding nitroalkanes by reacting with an inorganic nitrite such as \(\mathrm{NaNO}_{2}\) and dilute \(\mathrm{HCl}\).

Now let's analyze the reactions of nitroalkanes with the given reagents: (a) \(\mathrm{NaNO}_{2}\) and dilute \(\mathrm{HCl}\): Nitroalkanes would react with \(\mathrm{NaNO}_{2}\) and dilute \(\mathrm{HCl}\) to form alkyl halides. However, this will not show any distinct results as the alkyl halides formed from primary, secondary, and tertiary alcohols would be similar. (b) \(\mathrm{con} \cdot \mathrm{H}_{2} \mathrm{SO}_{4}\): Nitroalkanes do not show any distinguishing reaction with concentrated sulfuric acid and will not result in identifying primary, secondary, and tertiary alcohols. (c) Sn and hydrochloric acid: Nitroalkanes will react with Sn and hydrochloric acid, resulting in the formation of primary, secondary, and tertiary amines. This reaction will also not differentiate between primary, secondary, and tertiary alcohols since the corresponding amines are similar in structure. (d) Ammonium hydroxide: Nitroalkanes will react with ammonium hydroxide to form hydroxamic acids, which can form colored complexes upon treatment with ferric chloride (FeCl3). Primary, secondary, and tertiary alcohols will give rise to hydroxamic acids with different appearances, which can help differentiate between them. Based on the above analysis, the correct answer is:

(d) Ammonium hydroxide