
home	test	drill	game	contact

Mole-Number of Particles Calculations

Key Concepts

1 mole of any substance contains 6.022 x 10²³ particles.
6.022 x 10²³ is known as the Avogadro Number or Avogadro Constant and is given the symbol N_A or L

To find the number of particles in a mole of substance, multiply the moles by the Avogadro number:

1 mole contains 6.022 x 10²³ particles

2 moles contains 2 x 6.022 x 10²³ = 1.204 x 10²⁴

10 moles contains 10 x 6.022 x 10²³ = 6.022 x 10²⁴

0.5 moles contains 0.5 x 6.022 x 10²³ = 3.011 x 10²³

This leads to the equation: N = n x N_A
where N = number of particles in the substance
and n = moles of substance
and N_A = Avogardro Number = 6.022 x 10²³ particles mol^-1
To find the number of particles, N, in a substance: N = n x N_A
To find the moles, n, of substance, n = N/N_A

Examples

Find the number of particles

1. Find the number of ammonia, NH₃, molecules in 3.5 moles of ammonia.

Extract the data from the question:
moles of ammonia, n(NH₃) = 3.5 mol
number of ammonia molecules, N(NH₃) = ?
Write the equation: N(NH₃) = n(NH₃) x N_A
N_A is the Avogadro constant = 6.022 x 10²³ molecules mol^-1
Substitute in the vales and solve:
N(NH₃) = 3.5 x 6.022 x 10²³ = 2.1 x 10²⁴ ammonia molecules

2. Find the number of hydrogen atoms in 1.5 moles of water, H₂O.

Extract the data from the question:
moles of water, n(H₂O) = 1.5 mol
number of H atoms, N(H) = ?
Calculate the moles of H atoms present in 1.5 mol H₂O:
From the chemical formula we see that 1 molecule of water is made up of 2 atoms of hydrogen and 1 atom of oxygen.
So, 1 mole of water molecules contains 2 x 1 = 2 moles of hydrogen atoms.
Therefore 1.5 moles of water molecules contains 1.5 x 2 = 3.0 moles of hydrogen atoms.
n(H) = 3.0 mol
Calculate the number of hydrogen atoms using the equation N(H) = n(H) x N_A
N(H) = 3.0 x 6.022 x 10²³ = 1.8 x 10²⁴ hydrogen atoms.

Find the moles of substance

1. A sample of gas contains 4.4 x 10²⁴ carbon dioxide molecules.
How many moles of carbon dioxide are present in the sample?

Extract the data from the question:
Let N(CO₂) be the number of carbon dioxide molecules
N(CO₂) = 4.4 x 10²⁴ molecules
moles of CO₂, n(CO₂) = ?
Write the equation: N(CO₂) = n(CO₂) x N_A
where N_A, the Avogadro constant, = 6.022 x 10²³ molecules mol^-1
Rearrange the equation to find n(CO₂):
n(CO₂) = N(CO₂)/N_A
Substitute the values into the equation and solve:
n(CO₂) = 4.4 x 10²⁴ / 6.022 x 10²³ = 7.3 mol

2. A sample contains 2.4 x 10²² molecules of oxygen gas (O₂).
How many moles of oxygen atoms are present in the sample?

Extract the data from the question:
Let N(O₂) be the number of oxygen gas molecules
N(O₂) = 2.4 x 10²² molecules
moles of O atoms, n(O) = ?
Calculate the number of oxygen atoms present:
1 molecule of O₂ contains 2 molecules of O atoms
2.4 x 10²² O₂ molecules contains 2 x 2.4 x 10²² O atoms
N(O) = 2 x 2.4 x 10²² = 4.8 x 10²² O atoms
Write the equation: N(O) = n(O) x N_A
where N_A, the Avogadro constant, = 6.022 x 10²³ molecules mol^-1
Rearrange the equation to find n(O):
n(O) = N(O)/N_A
Substitute the values into the equation and solve:
n(O) = 4.8 x 10²² / 6.022 x 10²³ = 0.08 mol

Practice Questions

Homework Checker

For AUS-e-TUTE members:

Click on the Mole-Number of Particles drill link:
Mole-Number of Particles drill
Enter your username and password if prompted.
Click the "New Question" button to begin the drill.
Worked solutions are provided if you need some help!

Not an AUS-e-TUTE Member?

Join AUS-e-TUTE.
About AUS-e-TUTE membership
(information for students and teachers)

For AUS-e-TUTE members:

Search this Site

You can search this site using a key term or a concept to find tutorials, drills, tests, exams, learning activities (games), worksheet and quiz wizards.