Why is benzoic acid slightly soluble in cold water and readily soluble in hot water?

Benzoic acid is slightly soluble in cold water because the intermolecular forces between the benzoic acid molecules and water molecules are not strong enough to overcome the energy barrier required for dissolution. However, when the water is heated, the molecules gain more kinetic energy, which helps to break the intermolecular forces between the benzoic acid molecules and water molecules, allowing for easier dissolution. This is why benzoic acid is more readily soluble in hot water compared to cold water.

Benzoic acid is a weak acid, and its solubility in water is determined by the following equilibrium:

```
C6H5COOH(s) <=> C6H5COOH(aq)
```

The equilibrium constant for this reaction is very small, which means that very little benzoic acid dissolves in water at room temperature. However, as the temperature of the water increases, the equilibrium constant increases, and more benzoic acid dissolves. This is because the heat helps to break the intermolecular forces between the benzoic acid molecules and the water molecules.

In addition, hot water is less viscous than cold water, which makes it easier for the benzoic acid molecules to move around and dissolve.