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It is not possible to see or to weigh a single atom, so in order to count atoms, chemists compare the masses of large numbers of atoms.
The relative atomic mass (Ar) of hydrogen is 1.0. One mole of hydrogen atoms has a mass of 1g and contains a certain number of hydrogen atoms. This number of atoms is known as L.
The relative atomic mass of helium is 4.0. This means that a helium atom is four times heavier than a hydrogen atom. The same number, L, of helium atoms would have a mass of 4g. This is the mass of one mole of helium atoms.
In fact, one mole of any substance contains the same number of constituent particles. This number, L, is called the Avogadro constant.
The Avogadro constant, L = 6.022 × 1023mol-1 The Avogadro constant is the number of constituent particles in one mole of any substance.
The term ‘constituent particles’ could refer to atoms, molecules, ions or formula units depending on the structure of the given substance.
For example, neon, Ne, is a monoatomic element. Its constituent particles are single atoms. One mole of neon contains 6.022 × 1023 neon atoms.
Carbon dioxide, CO2, is a compound with a simple molecular structure. Its constituent particles are CO2 molecules. So, one mole of carbon dioxide will contain 6.022 × 1023 CO2 molecules.
We can use this information to calculate the number of atoms in one mole of carbon dioxide. Since each CO2 molecule contains three atoms (one carbon atom and two oxygen atoms), one mole of carbon dioxide contains (6.022 × 1023) × 3 = 1.8066 × 1024 atoms.
The constituent particle of an ionic compound or a substance with a macromolecular structure is one formula unit of that compound. For example, one mole of calcium oxide, CaO, contains 6.022 × 1023 formula units of CaO.
Since each formula unit of CaO contains two ions (one Ca2+ and one O2-), one mole of calcium oxide also contains (6.022 × 1023) × 2 = 1.2044 × 1024 ions.
The following equation can be used to calculate the number of constituent particles:
number of constituent particles = L × number of moles
You will always be given the value of the Avogadro constant if you need to use it in a calculation.
Example Question 1
Calculate the number of atoms in 23g of sodium, Na.
The constituent particles of sodium are Na atoms
Ar of Na = 23.0
moles of Na = = = 1 mole
number of constituent particles = (6.022 × 1023) × 1 = 6.022 × 1023 sodium atoms
Example Question 2
a. Calculate the number of molecules in 56g of nitrogen gas, N2.
The constituent particles of nitrogen are N2 molecules
Mr of N2 = (14.0 × 2) = 28.0
moles of N2 = = = 2 moles
number of constituent particles = (6.022 × 1023) × 2 = 1.2044 × 1024 N2 molecules
b. Calculate the number of nitrogen atoms in 56g of nitrogen gas, N2.
56g of N2 = 1.2044 × 1024 N2 molecules
Each N2 molecule contains two nitrogen atoms
(1.2044 × 1024) × 2 = 2.4088 × 1024 nitrogen atoms
Example Question 3
Calculate the number of ions in 29.25g of sodium chloride, NaCl.
The constituent particles of sodium chloride are NaCl formula units
Mr of NaCl = (23.0 × 1) + (35.5 × 1) = 58.5
moles of NaCl = = = 0.5 moles
(6.022 × 1023) × 0.5 = 3.011 × 1023 formula units of NaCl
Each NaCl formula unit contains two ions (one Na+ ion and one Cl– ion).
(3.011 × 1023) × 2 = 6.022 × 1023 ions
Example Question 4
Calculate the number of electrons in 120.2g of silicon dioxide, SiO2.
The constituent particles of silicon dioxide are SiO2 formula units
Mr of SiO2 = (28.1 × 1) + (16.0 × 2) = 60.1
moles of SiO2 = = = 2 moles
(6.022 × 1023) × 2 = 1.2044 × 1024 formula units of SiO2
Each SiO2 formula unit contains one silicon atom and two oxygen atoms
So, 2 moles of SiO2 contains 1.2044 × 1024 silicon atoms and 2.4088 × 1024 oxygen atoms.
Each silicon atom has 14 electrons
(1.2044 × 1024) × 14 = 1.68616 × 1025
Each oxygen atom has 8 electrons.
(2.4088 × 1024) × 8 = 1.92704 × 1025
(1.68616 × 1025) + (1.92704 × 1025) = 3.6132 × 1025 electrons
1. Which of the following statements is correct?
A. 0.5 moles of chlorine, Cl2, contains 3.001 × 1023 chlorine atoms.
B. 1.5 moles of magnesium oxide, MgO, contains 1.8066 × 1024 ions.
C. 12g of carbon, C, contains 6.022 × 1024 carbon atoms.
D. 36g of water, H2O, contains 1.2044 × 1023 molecules.
2. Which of the following contains the greatest number of atoms?
A. 27.9g of iron, Fe
B. 32.0g of oxygen, O2
C. 48.6g of magnesium, Mg
D. 111.1g of calcium chloride, CaCl2
3. Calculate the number of atoms in 1.70g of ammonia, NH3.
4. Calculate the number of protons in 10.0g of hydrogen, H2.
5. The relative atomic mass (Ar) of aluminium, Al, is 27.0. Calculate the mass, in kilograms, of one aluminium atom.
6. A sample of sodium oxide, Na2O, contains 3.011 × 1023 sodium ions, Na+. Calculate the mass, in grams, of the sodium oxide in the sample.
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