Chemguide: Support for CIE A level Chemistry ``` ``` Paper 5 Calculations Introduction You have to remember that Paper 5 is an end-of-course exam, and so you could be asked about any calculations that you have met during the whole 2 years. Having said that, there are a relatively small number of basic calculations which occur over and over again, and it is essential that you can do them so that you don't waste marks. On the whole, you will be guided through the more complicated calculations which come up from time to time. The harder the calculations, the more likely it is that not many people will be able to do them, and the effect of that is that the grade boundaries for the paper will be lower. There was a good example in November 2014 when the grade boundary for a grade A in papers 51 and 52 was only 50% and for a grade E 20%. In that sort of situation, it is really important that you don't throw away any easy marks. The very best way of practising for this is to do as many recent past papers as you can find, together with their mark schemes and Examiner's Reports. ``` ``` Calculations where you are given all the information necessary These will normally be presented as a table of experimental data and columns to be calculated from it. You will probably be told exactly how to do the calculations. What they are testing here is your ability to handle the numbers accurately. This sounds easy, but beware! There is only likely to be 1 mark for each column of figures you calculate, so be careful with your calculations. The other way to waste marks concerns significant figures and decimal places. Significant figures and decimal places Almost every Examiner's Report criticises students for wasting marks because they don't understand how to convert numbers from the calculator into, say, 3 significant figures or 2 decimal places or whatever. Suppose your calculator comes up with a number 31.364178 To convert to 3 significant figures, you just count the first three figures, ignoring any leading zeros if your number is less than 1. We'll look at an example of that in a minute. Then look at the fourth figure. If the fourth figure is 5 or greater, then you round the third figure up and remove all the figures after it. If the fourth figure is 4 or less, then you round down by leaving the third figure as it is - again removing all the figures after it. In the example above, the fourth figure is a 6, and so you round the third figure 3 up to 4. To 3 significant figures, the number is 31.4. But you could be asked to do the same sort of thing to, say, 2 decimal places. In this case, you look at the third decimal place and round the second decimal place figure in exactly the same way. In the example above, the third decimal place has a 4 in it. Because that is less than 5, you round down by leaving the preceding number as it is and removing the rest. To 2 decimal places, the answer 31.36. Don't just chop off the figures you don't want - you have to look at them carefully and decide whether to round up or down. What about a number like 0.00079864901? You would obviously not be asked to round this to 2 decimal places because that would be zero. But you could be asked to round to 3 significant figures. The leading zeros don't count as being significant, so you start counting at the 7. You should round the third figure up because it is followed by a number 5 or greater. The answer this time is 0.000799. Be careful with all this! One careless mistake will lose you the mark for accurate rounding. And be careful when you quote your answer. Suppose one of your values rounded to exactly 37. If you wrote down 37 as your answer to 3 significant figures, it is wrong. 37 is only quoted to 2 significant figures. What you should write is 37.0. Rounding errors during calculations This isn't directly relevant to the sort of calculations we are talking about which probably only have one step, but since we are looking at rounding, it is as good a place as any to discuss it. Examiner's Reports constantly moan about students rounding numbers off at every stage during a multi-step calculation, and then taking the rounded number into the next step. By the time you get to the end of the calculation, the overall effect of all this rounding can be to make your final answer slightly different from the one in the mark scheme - and therefore wrong! It is best not to round anything until you are ready to give your final answer. Then it must be rounded to whatever accuracy the question asks for. What if the question doesn't tell you to give your answer to 3 significant figures (or whatever)? The general rule is that you shouldn't give your answer to a greater degree of accuracy than the least accurate bit of data you are using. So, if you are working with numbers like 25, 27.5 and 0.316, your least accurate number is the 25 which is only quoted to 2 significant figures. Your answer can't be any more accurate than that. On the other hand, if the 25 was given as 25.0, then your final answer can be to 3 significant figures. Note:  To be strictly accurate, there is one case where what I have said above doesn't apply. Suppose one of the bits of data you are using can only be a whole number - say, if you were working out an average of 10 results, and so dividing a total by 10. Even if the 10 is only quoted to 2 figures, it is still totally accurate, and so your final degree of accuracy is only governed by the accuracy of the other numbers you are using. Common calculation types that you must be able to do Simple mole calculations I'm talking here about converting masses into moles and vice versa, simple calculations from equations involving masses, and empirical formula calculations. All this is trivial, of course, but there is one essential word of warning. Don't use relative atomic masses from memory! You must look them up in the Data Booklet you are given in the exam. There was an example in a past paper where you had to calculate the relative formula mass of a magnesium compound. The Data Booklet gives the RAM of magnesium as 24.3. Students who calculated the relative formula mass based on a remembered value for magnesium as 24 weren't given any credit for their answer. Don't make that mistake - look up every RAM you need. Calculations involving gases These might include calculations involving the molar volume of a gas which will be given you - commonly as 24 dm3 per mole at room temperature. You might, for example, be asked to work out how much gas you would get from some given reaction. This might then lead on to a decision about how much substance you had to react to give a reasonable volume of gas to collect, or to work out how much gas would be produced so that you could decide on a sensible bit of apparatus to collect it in. So it is important that you can do this sort of calculation. You might also have to use the ideal gas equation, pV = nRT. You can find a value of R from the Data Booklet in an exam. Titration calculations The questions asked are usually very straightforward. You should also be prepared to work out how much of a substance you would have to dissolve in, say, 250 cm3 to make a solution of known molar concentration. For example, how much sodium hydrogencarbonate, NaHCO3 would you have to dissolve in 250 cm3 of solution to give a 0.100 mol dm-3 solution? 1 mole of NaHCO3 weighs 84.0g. So for a 1.00 mol dm-3 solution, you would need to dissolve 84.0 g in 1000 cm3 of solution. For a 0.100 mol dm-3 solution, you would need 8.40 g in 1000 cm3 of solution. If you are only making up 250 cm3, you will only need a quarter of that: 2.10 g. Enthalpy change calculations Experiments involving enthalpy changes are a simple source of questions. What is essential is that you can calculate the amount of heat released (or, possibly, absorbed - but that is less likely) during a reaction. This involves the relationship: heat evolved = mass x specific heat x temperature rise If heat is being absorbed, then the temperature will fall, but the equation remains the same. The mass is strictly speaking the mass of everything being heated which would have to be multiplied by all the individual specific heats, but usually simplifications are used. Normally, you are measuring the amount of heat evolved by looking at the increase in temperature of a mass of liquid. For solutions, it is quite common to assume that the specific heat is the same as water, and the increase in temperature of the container is often ignored. That is fair enough if you have a container like a expanded polystyrene cup which will have negligible mass, but be aware that if you are using, say, a glass beaker this does produce errors in the calculation which you might need to comment on. This adds to errors like the amount of heat lost to the atmosphere. As a follow-on from this sort of calculation, you could be asked to do a further calculation based on a Hess's Law cycle. Make sure that you know how to do these - see learning outcome 5.2(a)(i). Rates of reaction calculations Rate of reaction experiments are another good source of questions. It is important that you know how to write a rate equation including the rate constant. It is also important that you know that for a first order reaction half-life is constant, and that you can use a graph to show the constancy of half lives in a given reaction. There will be more about this in my page about drawing graphs. You might also like to look again at learning outcome 8.1(e). You should also know the relationship between the half-life of a first order reaction and the rate constant. ``` ``` Other calculations As I said at the beginning of this page, calculations could be taken from anywhere in the course, and you should have revised those for Paper 4 anyway. This is where you really need to go back through recent examples of Paper 5 to see what is being asked, and practise actually doing Paper 5 questions. ``` ``` Go to the Paper 5 Menu . . . To return to the Paper 5 menu Go to the CIE Main Menu . . . To return to the list of all the CIE sections Go to Chemguide Main Menu . . . This will take you to the main part of Chemguide. © Jim Clark 2017