The Mole Concept
Senior 2 · Chemistry
The Mole Concept
Lesson 1 of 5
20 min
At Kimironko market nobody sells rice grain by grain. Rice is sold by the kilogram, eggs by the tray of 30, and paper by the ream of 500 sheets. Counting in bundles makes large numbers manageable.
Atoms are so small that even a single drop of water, about 0.05 g, contains roughly 1.7 × 1021 water molecules: 1 700 000 000 000 000 000 000 of them. Chemists therefore count particles in a much bigger bundle, the mole. The mole links the invisible world of atoms to the masses you can weigh on a balance, and it is the basis of every calculation in this unit.
By the end of this lesson you will be able to define the mole and convert between moles and numbers of particles.
The mole (symbol mol) is the unit of amount of substance. One mole of any substance contains 6.02 × 1023 particles. This number is the Avogadro constant, written NA or L:
NA = 6.02 × 1023 particles per mole (6.02 × 1023 mol−1)
The particles can be atoms, molecules, ions or electrons, so always say which. One mole of carbon contains 6.02 × 1023 carbon atoms; one mole of water contains 6.02 × 1023 water molecules.
If n is the number of moles and N is the number of particles:
N = n × NA and n = N ÷ NA
How many atoms are there in 2.5 mol of iron?
Solution. N = 2.5 × 6.02 × 1023 = 15.05 × 1023 = 1.51 × 1024 atoms.
A sample contains 3.01 × 1022 molecules of carbon dioxide. How many moles is this?
Solution. n = 3.01 × 1022 ÷ 6.02 × 1023 = 0.0500 mol.
How many atoms, and how many hydrogen atoms, are there in 0.5 mol of water?
Solution. 0.5 mol of H2O is 0.5 × 6.02 × 1023 = 3.01 × 1023 molecules. Each molecule has 3 atoms (2 H and 1 O), so there are 3 × 3.01 × 1023 = 9.03 × 1023 atoms, of which 2 × 3.01 × 1023 = 6.02 × 1023 are hydrogen atoms. In moles: 0.5 mol of water contains 1 mol of H atoms and 0.5 mol of O atoms.
How many ions are there in 1 mol of calcium chloride, CaCl2?
Solution. Each formula unit contains one Ca2+ and two Cl−: 3 ions. 1 mol of CaCl2 therefore contains 3 mol of ions = 3 × 6.02 × 1023 = 1.81 × 1024 ions.
To multiply numbers in standard form, multiply the front numbers and add the powers: (2 × 103) × (3 × 104) = 6 × 107. To divide, divide the front numbers and subtract the powers: (6 × 1023) ÷ (2 × 1020) = 3 × 103. Always give the answer with the front number between 1 and 10.
Tip
The mole bridge. Going from moles to particles, multiply by 6.02 × 1023. Going from particles to moles, divide. Before you start, write down which particle you are counting: "1 mol of O2 molecules contains 2 mol of O atoms."
Try each item before you read the solution.
How many atoms are there in 0.20 mol of copper?
Solution: 0.20 × 6.02 × 1023 = 1.20 × 1023 atoms.
How many moles of carbon are there in 1.204 × 1024 carbon atoms?
Solution: 1.204 × 1024 ÷ 6.02 × 1023 = 2.00 mol.
How many oxygen atoms are there in 2 mol of carbon dioxide?
Solution: Each CO2 molecule has 2 O atoms, so 2 mol of CO2 contains 4 mol of O atoms: 4 × 6.02 × 1023 = 2.41 × 1024 atoms.
Which contains more atoms: 1 mol of helium (He) or 0.5 mol of oxygen gas (O2)?
Solution: Neither. 1 mol of He is 6.02 × 1023 atoms. 0.5 mol of O2 molecules contains 2 × 0.5 = 1 mol of O atoms, also 6.02 × 1023. They contain the same number of atoms.
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