8303170-56-Maths-for-Chemists-1

8303170-56-Maths-for-Chemists-1 - Chem Factsheet...

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Maths for Chemists 1 C hem F actsheet www.curriculumpress.co.uk Number 56 1 This Factsheet concentrates on reviewing the basic mathematical techniques required for AS/A2 Chemistry. You will have already met the ideas involved in GCSE Maths, but this Factsheet aims to provide some fool-proof methods for applying them in chemical contexts. The topics covered are: Ratios Percentages Standard form Significant figures Later Factsheets will cover work on rearranging formulae, graphs, and exponentials and logarithms. Ratios Ratios are used in mole calculations . There are two stages in this part of the calculation: 1. Using a chemical equation to find the reacting ratio 2. Using the reacting ratio to work out moles. Stage 1 just involves looking at the numbers in the equation! eg: 4Al + 3O 2 2Al 2 O 3 Reacting ratio of Al to O 2 is 4:3 2NaOH + H 2 SO 4 Na 2 SO 4 + 2H 2 O Reacting ratio of NaOH to H 2 SO 4 is 2:1 You do have to be careful if you are looking for the reacting ratio for a particular ion rather than the entire compound. For example, 1 mole of H 2 SO 4 contains 2 moles of hydrogen ions (because of the “H 2 ” in the “H 2 SO 4 ”). So in the equation 2NaOH + H 2 SO 4 Na 2 SO 4 + 2H 2 O, the reacting ratio of OH ions to H + ions is 2:2 (the same as 1:1) Stage 2 involves the actual calculation. There are several ways to do this – if you are confident and accurate with another method, you probably do not need this one! But if you ever make mistakes, it’s worth taking a look. Example 1. 0.316 moles of aluminium react with oxygen to form aluminium oxide. Find the number of moles of oxygen gas used. Step 1: Write down your reacting ratio from the equation Al: O 2 4 : 3 Step 2: Underneath the ratio, in the right order, write down the moles you know and a ? for the moles you don’t. Line up the : to avoid mix ups 4 : 3 0.316 : ? Step 3: Draw a cross: 4 : 3 0.316 : ? Step 4: Multiply the two joined numbers and divide by the other one to find ? ? = 3 × 0.316 ÷ 4 = 0.237 moles of O 2 Exam Hint : Make sure at the end of this part of your calculation that the substance corresponding to the larger “ratio number” has the larger number of moles Example 2. 5Fe 2+ + MnO 4 + 8H + Mn 2+ + 5Fe 3+ + 4H 2 O Find the number of moles of Fe 2+ required to react with 0.123 moles of MnO 4 Step 1: Fe 2+ : MnO 4 5 : 1 ? : 0.123 Step 4: Moles of Fe 2+ = 5 × 0.123 ÷ 1 = 0.615 The questions at the end of the Factsheet gives more practice on ratio calculations NB: This is only part of the entire mole calculation! The rest of it will involve converting between moles, masses, concentrations, volumes etc. For more details on moles calculations, see Factsheets 2, 3, 7 ,23 and 59. Percentages
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This note was uploaded on 03/08/2011 for the course CHEM 101 taught by Professor Hard during the Spring '11 term at UT Arlington.

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8303170-56-Maths-for-Chemists-1 - Chem Factsheet...

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