How do you determine formula units in a unit cell?

In order to determine the number of formula units of a substance in a cell, you need to know the density of the substance and the edge length of the unit cell. Suppose that you are given the following problem: The density of TlCl (s) is 7.00 g/cm³, and the length of an edge of a unit cell is 385 pm. How many formula units of TlCl are in a unit cell?

Here’s how you solve the problem. Calculate the volume of the unit cell.

If the length of an edge of the cell is a, then V = a³.

V = (385 * 10⁻¹² m) ³ = 5.71 * 10⁻²⁹ m³Use the density to calculate the mass of the unit cell (The density of TlCl is the same, no matter what volume of TlCl we have).

Mass = 5.71 * 10⁻²⁹ m³ * (7.00 g/1 cm³) * (100 cm/1 m) ³ = 3.99 * 10⁻²² gUse the molar mass to convert grams to moles.

3.99 * 10⁻²² g * (1 mol/239.8 g) = 1.67 * 10 ⁻²⁴ molUse Avogadro’s number to calculate the number of formula units.

1.67 * 10 ⁻²⁴ mol * (6.022 * 10²³ formula units/1 mol) = 1.00 formula units

Therefore, 1 unit cell of TlCl contains 1 formula unit.