Maths for A Level Biology - updated edition

than 100 cm 3 . The way to do it is to dissolve the glucose in, say 70 cm 3 of water and when it is fully dissolved, make up the volume to 100 cm 3 . If you need 50 cm 3 4% salt solution, you may have to calculate how much salt you need. Always work things out from ϐirst principles. This is how: 1 Initial statement about solution 100 cm 3 4% salt solution has 4 g salt 2 Find how much in 1 cm 3 1 cm 3 4% salt solution has 4 100  g salt 3 Find how much in the volume you want to make 50 cm 3 4% salt solution has 4 100 × 50 g salt 4 Final answer = 2 g salt 2.3.2 Using moles For some reason, students are often frightened by moles. Perhaps they had a bad experience at GCSE. This section will show you how logical the calculations are and how you can do them easily. The table on the right shows the atomic masses of some atoms common in biological molecules. The relative molecular mass is the sum of the masses of all the atoms in a molecule. Often the word ‘relative’ is not used, because it is assumed that all atomic masses are relative to the mass of carbon, which is 12. Relative molecular mass has the symbol M r . This table shows some calculations of M r : Name Formula Calculation M r water H 2 O 1 + 1 + 16 18 carbon dioxide CO 2 12 + 16 + 16 44 methane CH 4 12 + (1 × 4) 16 urea CO(NH) 2 12 + 16 + 2(14 + 1) = 12 + 16 + 30 58 glucose C 6 H 12 O 6 (12 × 6) + (1 × 12) + (16 × 6) = 72 + 12 + 96 180 A mole is a mass. It is the relative molecular mass ( M r ) given in grams. So if you have 18 g water or 180 g glucose, in each case, you have 1 mole of the substance. 2.3.3 Molarity The concentration of a solution can be expressed in terms of the mass of solute in a given volume. If the mass were in grams, the concentration could be given as g/dm 3 . If the mass were in moles it could be given as moles/dm 3 . The number of moles in 1 dm 3 is the solution’s molarity. The M r of glucose is 180 and one mole of glucose has a mass of 180 g. If 1 dm 3 of a solution contains 180 g glucose, the solution has a concentration of 1 mol/ dm 3 or 1mol dm −3 . In the past, the unit M, meaning ‘molar’ has been used, but the current convention is to use mol/dm 3 or mol dm −3 , where mol is the abbreviation for mole. 1mmol is read as ‘1 millimole’. Milli- as a preϐix means 10 −3 . A solution of concentration 1mmol dm −3 contains 10 −3 moles in each dm 3 . QUICKFIRE 2.9 a) How many moles in 58g urea? b) How many moles in 32g methane? c) How many g in 2 moles carbon dioxide? Pointer 1 mol/dm 3 is the same as 1mol dm −3 . QUICKFIRE 2.10 Glucose has an M r of 180. How many grams would you need in 1dm 3 to make a solution that has a concentration of 1mol dm −3 ? QUICKFIRE 2.8 a) What is the mass of sucrose in 100 cm 3 of a 1% solution? b) What is the mass of lead nitrate in 10 cm 3 of a 1% solution? c) What is the mass of sodium chloride in 50 cm 3 of a 0.1% solution? d) What is the mass of maltose in 200 cm 3 of a 2% solution? Element Atomic mass C 12 H 1 O 16 N 14 2 Processed numbers 43