The mole - Higher
Introducing the mole, the unit of measurement for the number of particles in a substance
It is often useful in chemistry to know the number of atomThe smallest part of an element that can exist., ionElectrically charged particle, formed when an atom or molecule gains or loses electrons. or moleculeA collection of two or more atoms held together by chemical bonds. involved in a chemical reaction. The moleThe amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12 (contains the Avogadro's constant 6.0 ×10²³ number of particles). is the unit for amount of substance. It is abbreviated to mol.
1 mol is the amount of substance that contains the same number of particles as there are atoms in 12.0 g of carbon-12.
Since atoms are so very small and have very little massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g)., the number of atoms in 12.0 g of carbon-12 is huge. It is equal to the Avogadro constantThe number of particles in one mole of particles, 6.02 × 10²³ per mole.:
The Avogadro constant = 6.022 Ă— 1023 atoms per mole.
Calculating the number of particles
The number of particles of a substance can be calculated using:
- the Avogadro constant
- the amount of substance in mole
number of particles = Avogadro constant Ă— amount (mol)
Example
Calculate the number of water molecules in 0.5 mol of water.
Number of water molecules = 6.022 Ă— 1023 Ă— 0.5
= 3.011 Ă— 1023
It is important to be clear about the particles involved. For example, 3.011 Ă— 1023 water molecules contain 9.033 Ă— 1023 atoms. This is because a water molecule, H2O, contains three atoms.
Question
Calculate the number of oxygen atoms in 0.5 mol of oxygen molecules, O2.
Number of atoms = 2 Ă— 0.5 Ă— 6.022 Ă— 1023
= 6.022 Ă— 1023
Masses of atoms
The Avogadro constant can be used to calculate the mass of an atom in grams:
\(mass\ of\ atom\ (g)\ =\ \frac{A_{r}\ of\ element}{Avogadro\ constant}\)
Example
Calculate the mass of a magnesium atom.
(relative atomic massThe mean relative mass of the atoms of the different isotopes in an element. It is the number of times heavier an atom is than one-twelfth of a carbon-12 atom., Ar = 24.3)
\(mass\ of\ Mg\ atom\ =\ \frac{24.3}{6.022 Ă— 10^{23}}\)
= 4.04 Ă— 10-23 g
It is important to give the final answer to the lowest number of significant figureGiving a number to a specified number of significant figures is a method of rounding. For example, in the number 7483, the most significant, or important, figure is 7, as its value is 7000. To give 7483 correct to one significant figure (1 sf), would be 7000. To 2 sf, it would be 7500. used in the calculation. In this example, this is the same number of significant figures as the Ar value.
Question
Calculate the mass of a carbon atom. (Relative atomic mass, Ar = 12.0)
\(mass\ of\ C\ atom\ =\ \frac{12.0}{6.022 Ă— 10^{23}}\)
= 1.99 Ă— 10-23 g
Masses of molecules
The Avogadro constant can be used to calculate the mass of a molecule in grams:
\(mass~of~molecule~(g) = \frac{M_{r}~of~substance}{Avogadro~constant}\)
Example
Calculate the mass of a bromine molecule. (relative formula massThe sum of the relative atomic masses of the atoms in a chemical formula., Mr = 159.8)
\(mass\ of\ bromine\ molecule\ (g)\ = \frac{159.8}{6.022 Ă— 10^{23}}\)
= 2.654 Ă— 10-22 g
This answer is given to 4 significant figures because both numbers used in the calculation are given to 4 significant figures.
Question
Calculate the mass of a water molecule. (Relative formula mass, Mr = 18.0)
\(mass\ of\ water\ molecule\ (g)\ = \frac{18.0}{6.022 Ă— 10^{23}}\)
= 2.99 Ă— 10-23g