Maths for A Level Biology - updated edition

Sometimes a Biology examination question will ask you about concentrations, but this is not a Chemistry test so all calculations will be very straightforward. For example, you may be asked how to make a 1mol/dm 3 solution of sucrose into a solution that is 0.5mol/dm 3 : A solution that is 0.5mol/dm 3 is half the concentration of a 1mol/dm 3 solution so you are being asked how to halve a concentration. If there are x moles in a given volume, you need to put them into double that volume. So you add an equal volume of water. Then you have x moles in twice the volume, so the concentration is halved. If you had 50 cm 3 of a 1mol/dm 3 solution, you would add 50 cm 3 water. 2.3.4 Hydrogen peroxide Hydrogen peroxide is often used in biochemistry experiments to illustrate the properties of enzymes. It decomposes under the inϐluence of the enzyme catalase, into oxygen and water: 2H 2 O 2 catalase  2H 2 O + O 2 The concentration of hydrogen peroxide could be given as % or mol/dm 3 , as described above. However, the common way of expressing its concentration is to use the unit ‘vol’, which stands for volume, even though it is a measure of concentration. This is because its concentration is measured by the volume of oxygen it can generate. The higher its concentration, the more oxygen it can generate. 1 dm 3 of a concentration of 1 vol generates 1 dm 3 oxygen. 1 dm 3 of a concentration of 10 vol generates 10 dm 3 oxygen. If you had a solution of 20 vol hydrogen peroxide and you wanted a solution of 5 vol, you would need to make it 1 4 as concentrated. The number of molecules in a given volume would need to go into a volume four times as great. If you had 10 cm 3 you would need to make it up to 40 cm 3 by adding 30 cm 3 water. 2.4 Biotic indices A biotic index is a number calculated to describe a particular feature of a population. Different indices are suitable in different situations, so it is important which one is used. 2.4.1 Lincoln index The Lincoln index is used to estimate the number of animals in a population. It is sometimes called mark-recapture, summarising the method of collecting data. It is suitable for use with animals such as woodlice or voles but when it is practised in school, the Year 7s are often used. During a given time, such as 10 minutes, as many organisms as possible are captured. Let us call the number in the sample a and the total population A . They are marked in some way and released to mix at random. After a suitable time, such as one hour, 10 minutes are spent again collecting organisms. Let us call the number in the second sample B . Some will have been caught for a second time and they are marked. Let us say their number is b . QUICKFIRE 2.11 Fructose, an isomer of glucose, also has an M r of 180. How many grams of fructose would you need in 1dm 3 to make a solution that has a concentration of 1mmol dm −3 ? Pointer For hydrogen peroxide, vol is a unit of concentration. Pointer Sometimes people write vols (with an s on the end) by mistake. Make sure you don’t. QUICKFIRE 2.12 a) What volume of oxygen does 1dm 3 2 vol hydrogen peroxide produce? b) What volume of oxygen does 1dm 3 15 vol hydrogen peroxide produce? c) What volume of oxygen does 4dm 3 15 vol hydrogen peroxide produce? d) What volume of oxygen does 20 cm 3 5 vol hydrogen peroxide produce? Mathematics for Biology 44