Chemical Mathmatics Handout - Woodhouse College

1 Chemical Calculations 31. Introduction Rules for calculations (a) Always work from first principles - formulas (unless stated) often confuse. (b) Always show all the steps in your working, this reduces the chance of error. In examinations you get marks for knowing how to do a calculation even if your answer is wrong. (c) Never round-up or round-down a figure during a calculation - wait until you have the final answer. (d) Always give mole calculation answers to 3 decimal places. (e) Never simply write down an answer with no indication of where it came from. (If you do this in an examination you will get no marks even if the answer is correct.). (f) Never trust a calculator - try to do a rough approximation to check your answer.

2 17 =. , to check multiply 17 = about 5 (you should be able to do this in your head, NO. CALCULATORS) this gives you a rough idea of the range in which the answer lies. So, if your calculator says you know that something is wrong. Quantities of chemicals Quantity Common units Meaning Mass gram (g) Samples with the same mass give the same readings kilogram (kg) on a balance 1kg = 1000g Volume cubic centimetre (cm3) Samples with the same volume take up the same litre (l or dm3) amount of space. Two liquids with the same volume 1 litre = 1dm3 = 1000cm3 for example, fill a measuring cylinder to the same level Amount mole (mol) Samples with the same amount of a Chemical contain the same number of atoms, molecules or ions.

3 There are as many atoms in one mole of carbon as there are molecules in one mole of water. Re-arranging formula To re-arrange formula there is a simple rule: you can change any equation as much as you like as long as you always do the same thing to both sides. Mass For example, Moles = is very useful if you want to find moles but what if you want to find You need to re-arrange the formula so that is standing alone on the left-hand side of the equation. Mass Multiply both sides by Moles =. Cancel out on the right-hand side Moles = Mass Moles Mass Divide each side by Moles =. Moles Moles Mass Cancel out Moles on the left-hand side =. Moles Note that during this process we have shown how to work out Mass.

4 Chemical m, 1 worksheets Powers of 10. A lot of scientific work deals with numbers that are very large or very small. It is convenient to have a quick way of writing large numbers and small numbers. Powers of 10 do this job. Positive powers Negative powers 1. 10 = 10 10-1 = 1 10 = 102 = 10 10 = 100 10-2 = 1 (10 10) = 103 = 10 10 10 = 1000 10-3 = 1 (10 10 10) = and so on and so on Note that Note that 102 + 102 = 2 102 = 200 10-1 + 10-1 = 2 10-1 = but that but that 103 103 = 106 = 1 000 000 10-2 10-3 = 10-5 = Note also that 100 = 1. 30 Calculations involving graphs 60 Concentration time 90 120. When drawing graphs there are five points to 150. remember: Concentration mol/dm-3. 180 1.

5 Draw axes and label them carefully. 210 240 2. Use a suitable scale to give you the largest 270 possible graph on the grid provided. 300 3. Unless it is stated or observed, ( from 330 the information given it is obvious that 360 both initial readings are zero), that the graph passes through the origin, scales do not have to start at zero. 30 60 90 120 150 180 210 240 270 300 330 360. 4. Draw the best straight line or curve Time/s through the points, that on which the most number of points lie. If you have to draw more than one graph on the same axes Remember make sure that each graph is clearly A graph going from top left to bottom right has a labelled and that they are easily negative gradient.

6 Distinguishable from each other. Use different coloured pens or mark one set of points with crosses (+) and the other set with circles (o). 5. Mark clearly on your graph the information that you are required to find by drawing in A graph going from bottom left to top right has a lines to the x and y axes where appropriate positive gradient. or by drawing in gradient lines, etc. When you are working out the gradient of a graph y 2 - y1. use the formula: where x1 and y1 are x 2 - x1. the co-ordinates of the point with the lowest x value and x2 and y2 are the co-ordinates of the higher x value. Chemical m, 1 worksheets 1. Calculation of the relative molecular mass of a compound. Worked examples (a) Work out the relative molecular mass ( ) of sodium chloride, NaCl.

7 In 1 molecule of this compound there is 1 atom of sodium, Na, and 1 atom of chlorine, Cl. From your data book: the relative atomic mass ( ) of Na = , Cl = So, of NaCl = + + (b) Work out the of hydrated magnesium sulphate, In 1 molecule of this compound there is 1 mole of magnesium sulphate, containing 1 atom of magnesium, Mg, 1 atom of sulphur, S, and 4 atoms of oxygen, O, and also 7 moles of water, containing 14 atoms of hydrogen, H, and 7 atoms of oxygen, O. From your data book: Mg = ; S = ; O = ; H = So, = + + (4 ) + (14 ) + (7 ) = Questions Using your data book work out the relative molecular masses of the following compounds: (a) KBr (b) 2. Calculation of the percentage by mass of elements in a compound.

8 Worked examples (a) Calculate the percentage by mass of carbon, C, and oxygen, O, in carbon dioxide, CO2. In 1 molecule of carbon dioxide there is 1 atom of carbon, C, and 2 atoms of oxygen, O. From you data book: C = ; O = CO2 = + (2 ) = RAM C 12. %C in CO2 = 100 = 100 = RAM CO 2 44. RAM O 2 %O in CO2 = 100 = 100 = RAMCO 2 44. (b) Calculate the percentage by mass of water in hydrated aluminium chloride, In 1 molecule of hydrated aluminium chloride there is 1 molecule of aluminium chloride and 6. molecules of From your data book: AlCl3 = ; H2O = = + (6 18) = 6 RMM water 6 18. %H2O in = 100 = 100 = RMM AlCl 3 .6H 2 O Chemical m, 1 worksheets Questions Calculate the percentage by mass of (a) sulphur and oxygen in SO3.

9 (b) magnesium and nitrogen in Mg3N2. 3. Calculation of the number of moles in a given mass of a compound. Worked examples (a) Calculate the number of moles in of potassium hydroxide, KOH. K = ; H = ; O = = + + = mass Number of moles = = = RMM (b) Calculate the number of moles in of hydrated barium chloride, Ba = ; Cl = ; H = ; O = = + (2 ) + (4 ) + (2 ) = mass Number of moles = = = RMM Questions Calculate the number of moles in (a) of sodium chloride. (b) of calcium carbonate 4. Calculation of the formula of a compound. Worked examples (a) What is the formula of the oxide formed when of sodium combine with of oxygen? Na = ; O = Moles of Na = = ; Moles of O = = Mole ratio must be a whole number so divide both answers by the smallest number of moles.

10 Moles of Na = = 2; Moles of O = = 1. Formula is Na2O. Chemical m, 1 worksheets (b) Calculate the empirical (lowest mole ratio) formula of a compound containing magnesium, sulphur and oxygen. Assume 100g of compound, mass of Mg = , S = , O = Mg = ; O = ; S = Moles Mg = = ; Moles O = = ; Moles S = = ;. Divide by the smallest number of moles Ratio moles Mg = = 1 : Moles O = = 4 : Moles S = = 1. Formula is MgSO4. (c) A hydrocarbon (a compound containing carbon and hydrogen only) contains carbon. Its relative molecular mass is Calculate (i) its empirical formula, (ii) its molecular formula. Assume 100g; Mass of C = ; Mass of H = - = C = ; H = (i) Moles of H = = ; Moles of C = = Divide by the smallest number of moles Ratio moles H = = 3 : Moles C = = 1.