Answer :

To determine which compounds are water-soluble, we need to refer to well-established solubility rules in chemistry. Here are the solubility rules relevant to the compounds listed:

1. Sodium (Na), Potassium (K), and Ammonium (NH4) compounds: These compounds are generally soluble in water.
2. Chloride (Cl), Bromide (Br), and Iodide (I) compounds: These compounds are generally soluble in water, except when combined with Silver (Ag), Lead (Pb), and Mercury (Hg).
3. Sulfides (S) and Hydroxides (OH): These compounds are generally insoluble, except with alkali metals (like Li, Na, K) and certain alkaline earth metals.

Let's examine each compound based on these rules:

1. Li2S:
- This compound contains lithium (Li), which is an alkali metal. According to the solubility rules, compounds of alkali metals are generally soluble in water.
- Therefore, Li2S is soluble in water.

2. PbBr2:
- This compound contains lead (Pb) and bromide (Br). Although bromides are generally soluble, lead bromide is an exception.
- Therefore, PbBr2 is insoluble in water.

3. Au(OH)3:
- This compound contains hydroxide (OH), and hydroxides are generally insoluble except for those of alkali metals and some alkaline earth metals.
- Gold is neither an alkali metal nor an alkaline earth metal.
- Therefore, Au(OH)3 is insoluble in water.

4. KCl:
- This compound contains potassium (K), which is an alkali metal. Potassium compounds are generally soluble in water.
- Therefore, KCl is soluble in water.

Based on these observations, the compounds that are water-soluble are:

- Li2S
- KCl

Thus, the water-soluble compounds are:

- [tex]\( \text{Li}_2 \text{S} \)[/tex]
- [tex]\( \text{KCl} \)[/tex]

These are the compounds that dissolve in water.