Moles, Mass and Mr (n = m/Mr)

Definition of the Mole

The mole is a unit used to measure the amount of substance. It allows chemists to count particles like atoms, molecules, or ions by relating them to a fixed number.

One mole contains exactly 6.02 × 10²³ particles. This number is called Avogadro’s constant.

For example, 1 mole of carbon atoms contains 6.02 × 10²³ carbon atoms, and 1 mole of water molecules contains 6.02 × 10²³ water molecules.

Relative Formula Mass (Mr)

The relative formula mass, Mr, is the sum of the relative atomic masses of all the atoms in a compound or molecule.

It is a unitless number because it is a ratio compared to the mass of one atom of carbon-12.

For example, for water (H₂O):

Mr = (2 × Ar of H) + (1 × Ar of O) = (2 × 1) + (1 × 16) = 18

This means one molecule of water has a relative formula mass of 18.

Mass and Moles Relationship

The number of moles (n) of a substance is related to its mass (m) and relative formula mass (Mr) by the formula:

$n = \frac{m}{M_r}$

• $n$ = number of moles (mol)
• $m$ = mass of the substance (grams, g)
• $M_r$ = relative formula mass (unitless)

This formula allows you to calculate how many moles are in a given mass of a substance.

For instance, if you have 36 g of water (H₂O) and you know the Mr of water is 18, the number of moles is:

$$n = \frac{36}{18} = 2 \text{ mol}$$

So, 36 g of water contains 2 moles of water molecules.

Example calculation: Calculate the number of moles in 10 g of oxygen gas (O₂). Mr of O₂ = 32, so $n = \frac{10}{32} \approx 0.31 \text{ mol}$.

Calculations Using Moles

To convert between mass and moles, use the formula $n = \frac{m}{M_r}$. You can rearrange it to find mass or Mr if needed:

• $m = n \times M_r$
• $M_r = \frac{m}{n}$

The Mr is found by adding the relative atomic masses of all atoms in the formula, using the periodic table.

These calculations are essential when working with chemical equations to find out how much of each substance is involved.

For example, if you want to find the number of moles in 20 g of carbon dioxide (CO₂):

First, calculate Mr of CO₂:

$$M_r = 12 + (2 \times 16) = 44$$

Then calculate moles:

$$n = \frac{20}{44} \approx 0.45 \text{ mol}$$