Working with different units in chemistry

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FactorNameUnitCommon examples
106megaM
103kilokkg
10-1deciddm
10-2centiccm
10-3millimmm, mg
10-6microμμm, μg
10-9nanonnm

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