Identify the compound that will react with Hinsberg’s reagent to give a solid which dissolves in alkali.

To determine which compound reacts with Hinsberg's reagent (benzene sulfonyl chloride, $C_6{H}_{5}S{O}_{2}Cl$) to form a solid that dissolves in alkali, we look at how different types of compounds interact with it:

1. Primary Amines (1^o) react with Hinsberg's reagent to form a sulfonamide. Because the nitrogen atom in this sulfonamide is still bonded to an acidic hydrogen atom, it reacts with alkali (like NaOH or KOH) to form a soluble salt, thereby dissolving in the alkali solution.
2. Secondary Amines (2^o) react with Hinsberg's reagent to form a sulfonamide that has no acidic hydrogen atom on the nitrogen. As a result, the product is insoluble in alkali.
3. Tertiary Amines (3^o) do not react with Hinsberg's reagent under standard conditions.

Now, we analyze the provided options from the images:
- Image 0: Represents nitroethane, $C{H}_3-C{H}_2-N{O}_2$, which is a nitro compound and does not react.
- Image 1: Represents a haloalkane, 2-bromo-2-methylbutane, which does not react with Hinsberg's reagent.
- Image 2: Represents ethylamine, $C{H}_3-C{H}_2-N{H}_2$, which is a primary amine.
- Image 3: Represents a tertiary amine, N,N-diethylethanamine, which does not react.

Thus, the primary amine (ethylamine, shown in Image 2) is the correct compound.