Factor | Name | Unit | Common examples |
106 | mega | M | |
103 | kilo | k | kg |
10-1 | deci | d | dm |
10-2 | centi | c | cm |
10-3 | milli | m | mm, mg |
10-6 | micro | μ | μm, μg |
10-9 | nano | n | nm |
You are expected to know this!
Let’s look at some examples …
1 kg is 1 x103 g which is 1000 g
1 mm is 1x 10-3 m which is 0.001 m (a thousandth of a metre)
1000 mm is 1 x 103 mm which is 1 m
We can convert between the units by multiplying by the appropriate factor – to convert from 10a to a factor of 10b, simply multiply by factor 10a-b
e.g. convert 7 mg into kg
1. change each into g …. 1 mg is 10-3 g and 1 kg is 103 g. We are converting 10-3 into 103
2. 10(-3)-(3) = 10-6 kg
3. so 7 mg is 7 x 10-6 kg
e.g. convert 4.32 cm into μm
1. 1cm is 10-2 m and 1 μm is 10-6 m
2. 10(-2)-(-6) = 104 μm
3. so 4.32 cm is 4.32 x 104 μm
Basically, we are either converting mass or length in chemistry so the default is g and m.
You should also know that
- 1 dm3 = 1000 cm3 = 1 litre
- 1 cm3 = 1 millilitre, ml (often laboratory glassware is still marked in l and ml)
Concentration
At GCSE the units for concentration are written as mol/dm3 which at A level becomes mol dm-3
Parts per million (ppm)
This is a way of expressing very dilute concentrations of substances. Just as per cent means out of a hundred, so parts per million or ppm means out of a million. It usually describes the concentration of something in water or soil.
1 ppm = 1 mg per litre (1 mg per dm3 ) or 1 mg per kg
It’s also really useful to know that water has a density of 1 g cm-3 which is why you can interchange mass with volume, to all intents and purposes.
e.g. 23 cm3 of water will weigh 23g
Question: A sample of mineral water is found to contain a concentration of nitrate ions (NO3–) of 25 ppm. Express this concentration in units of mol dm-3.
25 ppm = 25 mg dm-3
To convert mass into moles (for concentration) I need to first convert my mg into g.
1 mg = 1 x 10-3 g
25 mg = 25 x 10-3 g = 2.5 x 10-2 g
n = mass / Mr where Mr is the molar mass of the nitrate ion
Mr for NO3– = 62 (electrons are so tiny that gaining or losing them doesn’t affect the Mr)
n = 2.5 x 10-2 / 62 = 0.000403 mol or 4.03 x 10-4 mol
And since ppm is per litre, and 1 litre = 1 dm3, we have our answer.
25 ppm = 4.03 x 10-4 mol dm-3
Practice questions
1. Convert 3.7 nm into cm
2. Convert 0.026 kg into μg
3. Convert a sulphate (SO42- ) ion concentration of 592 ppm into mol dm-3
4. Convert a chloride (Cl– ) ion concentration of 6.2 x 10-5 mol dm-3 into ppm
Answers
1. 1 nm is 10-9 m ; 1 cm is 10-2 m; 10-9-(-2) = 10-7 so 3.7 nm is 3.7 x 10-7 cm
2. 1 kg is 103 g; 1 μg is 10-6 g; 103-(-6) = 109 so 0.026 kg is 0.026 x 109 μg which should be written as 2.6 x 107μg
3. 592 ppm = 592 mg per litre
592 mg = 592 x 10-3 g = 0.592g
n = mass / Mr and Mr for SO42- is 96.1 so n = 0.592 / 96.1 = 0.00616 mol
concentration is 6.16 x 10-3 mol dm-3
4. 6.2 x 10-5 mol dm-3 needs converting into a mass;
mass = Mr x n; mass = 6.2 x 10-5 x 35.5 = 2.201 x 10-3 g
1 mg = 1 x 10-3 g or 1 g = 1000 mg
2.201 x 10-3 x 1000 = 2.201 mg (per dm3) = 2.201 ppm