Calculate the number of moles for each element.

We use the formula: $\text{moles} = \frac{\text{mass}}{\text{relative atomic mass}}$.
For Carbon (C):

$$\text{Moles of C} = \frac{2.4 \text{ g}}{12 \text{ g/mol}} = 0.2 \text{ mol}$$

For Hydrogen (H):

$$\text{Moles of H} = \frac{0.2 \text{ g}}{1 \text{ g/mol}} = 0.2 \text{ mol}$$

For Chlorine (Cl):

$$\text{Moles of Cl} = \frac{21.3 \text{ g}}{35.5 \text{ g/mol}} = 0.6 \text{ mol}$$

The smallest number of moles is 0.2 mol (for C and H).
For C:

$$\frac{0.2 \text{ mol}}{0.2 \text{ mol}} = 1$$

For H:

$$\frac{0.2 \text{ mol}}{0.2 \text{ mol}} = 1$$

For Cl:

$$\frac{0.6 \text{ mol}}{0.2 \text{ mol}} = 3$$

The ratio of C:H:Cl is 1:1:3.

The empirical formula of the compound is $\text{CH}_1\text{Cl}_3$.