Amount of Substance

The mole is one of the seven SI base units
- It is used to measure the amount of substance, not a mass
One mole is defined as follows:

The amount of substance that contains as many elementary entities as the number of atoms in 12 g of carbon-12

This amount of substance is exactly 6.02214076 × 10²³elementary entities (i.e. particles, atoms, molecules)
- At IB level, this number can be rounded to 6.02 × 10²³

One mole of gas contains a number of particles (atoms or molecules) equal to the Avogadro Constant
For example, 1 mole of sodium (Na) contains 6.02 × 10²³ atoms of sodium
The number of atoms can be determined if the number of moles is known by multiplying by N_A.
- For example: 2.0 mol of argon contains: 2.0 × N_A = 2.0 × 6.02 × 10²³ = 1.20 × 10²⁴ atoms

The number of moles, n of a substance can be calculated using the equation

$n = \frac{N}{N_{A}}$

Where:
- N = number of particles (molecules or atoms, depending on the substance)
- n = number of moles of gas (mol)
- N_A = 6.02 × 10²³ mol^–1 (Avogadro constant)

Molar Mass

One mole of any element is equal to the relative atomic mass of that element in grams
- E.g. Helium has a relative atomic mass of 4 - this means 1 mole of helium has a mass of 4 g
If the substance is a compound, add up the relative atomic masses, for example, water (H₂O) is made up of
- 2 hydrogen atoms (each with atomic mass of 1) and 1 oxygen atom (atomic mass of 16)
- So, 1 mole of water would have a mass of (2 × 1) + 16 = 18 g

The molar mass, m of a substance is defined as the mass m of the substance divided by the amount (in moles) of that substance
The molar mass is calculated as follows:

$m_{r} = \frac{m}{n}$

Where:
- m_r = molar mass in g mol^–1
- m = mass in grams (g)
- n = number of moles (mol)

Worked example

120 moles of nitrogen gas are in a container.

Calculate the number of nitrogen gas molecules in the container.

Answer:

Step 1: List the known quantities

Number of moles, n = 120

Step 2: Rearrange the number of moles equation for the number of molecules, N

$N = n N_{A}$

Step 3: Substitute in the values

$N = (6.02 \times 10^{23}) \times 120 = 7.2 \times 10^{25}$ molecules

Worked example

A container is filled with 2.6 × 10²⁰ molecules of argon gas which has a mass number of 40.

Calculate the total mass of argon in the container.

Answer:

Step 1: List the known quantities

Number of argon gas molecules, N = 2.6 × 10²⁰
Molar mass of argon, m_r = 40 g mol^–1 (same as the atomic mass)

Step 2: Calculate the number of moles of argon in the container

$n = \frac{N}{N_{A}} = \frac{2.6 \times 10^{20}}{6.02 \times 10^{23}} = 4.3 \times 10^{- 4} moles$

Step 3: Calculate the total mass of the argon in the container

$m = m_{r} \times n = 40 \times (4.3 \times 10^{- 4}) = 0.0172 g$

Examiner Tip

The value of the Avogadro constant is given on your data sheet, so you don't need to learn this value. However, it does help make calculations quicker if you do!

Take care with the units for molar mass, this is g mol^–1, so multiplying by the number of moles gives a mass in grams and not kilograms.

Amount of Substance (HL IB Physics)

Revision Note