1 The mole and Avogadro’s constant

 The mole is the key concept for chemical calculations DEFINITION: The mole is the amount of substance in grams that has the same number of particles as there are atoms in 12 grams of carbon-12. Avogadro’s Number There are 6.022 x 1023 atoms in 12 grams of carbon-12. Therefore explained in simpler terms ‘One mole of any specified entity contains 6.022 x 1023 of that entity’: For most calculations we will do at AS we will use the following 3 equations moles = mass Mr 1. For pure solids and gases 2. For gases PV = nRT 3. For solutions Concentration = moles volume Learn these equations carefully and what units to use in them. Unit of Mass: grams Unit of moles : mol Unit of Pressure (P):Pa Unit of Volume (V): m3 Unit of Temp (T): K n= moles R = 8.31 Unit of concentration: mol dm-3 or M Unit of Volume: dm3 Note the different unit for volume Converting volumes cm3  dm3 ÷ 1000 cm3  m3 ÷ 1000 000 dm3  m3 ÷ 1000 Converting temperature oC  K add 273 Typical mole calculations DEFINITION: Relative atomic mass is the average mass of one atom compared to one twelfth of the mass of one atom of carbon-12 DEFINITION: Relative molecular mass is the average mass of a molecule compared to one twelfth of the mass of one atom of carbon-12 Some Simple calculations using above equations Example 2: What is the concentration of solution made by dissolving 5.00g of Na2CO3 in 250 cm3 water? moles = mass/Mr = 5.00 / (23 x2 + 12 +16 x3) = 0.0472 mol conc= moles/Volume = 0.0472 / 0.25 = 0.189 mol dm-3 Example 3: What is the mass of Cl2 gas that has a pressure of 100kPa, temperature 293K, volume 500cm3 . (R = 8.31) Example 1: What is the number of moles in 35.0g of CuSO4? moles = mass/Mr = 35.0/ (63.5 + 32.0 +16.0 x4) = 0.219 mol moles = PV/RT = 100 000 x 0.0005 / (8.31 x 293) = 0.0205 mol 100 kPa = 100 000 Pa 500 cm3 = 0.0005 m3 Mass = moles x Mr = 0.0205 x (35.5 x2) = 1.46 g Significant Figures Give your answers to the same number of significant figures as the number of significant figures for the data you given in a question. If you are given a mixture of different significant figures, use the smallest Remember the Mr must be calculated and quoted to 1dp chemrevise.org chemrevise.org 2 Avogadro’s Constant There are 6.02 x 1023 atoms in 12 grams of carbon-12. Therefore explained in simpler terms ‘One mole of any specified entity contains 6.02 x 1023 of that entity’: The mole is the amount of substance in grams that has the same number of particles as there are atoms in 12 grams of carbon-12. Avogadro’s Constant 1 mole of copper atoms will contain 6.02 x 1023 atoms 1 mole of carbon dioxide molecules will contain 6.02 x 1023 molecules 1 mole of sodium ions will contain 6.02 x 1023 ions Avogadro’s Constant can be used for atoms, molecules and ions No of particles = amount of substance (in mol) X Avogadro’s constant Example 4 : How many atoms of Tin are there in a 6.00 g sample of Tin metal? amount = mass/Ar = 6.00/ 118.7 = 0.05055 mol Number atoms = amount x 6.02 x 1023 = 0.05055 x 6.02 x 1023 = 3.04 x1022 Example 5 : How many chloride ions are there in a 25.0 cm3 of a solution of magnesium chloride of concentration 0.400 moldm-3 ? Number ions of Cl- = amount x 6.02 x 1023 = 0.0200 x 6.02 x 1023 = 1.20 x1022 (to 3 sig fig) amount= concentration x Volume = 0.400 x 0.025 = 0.0100 mol MgCl2 Amount of chloride ions = 0.0100 x2 = 0.0200 There are two moles of chloride ions for every one mole of MgCl2 Density density = mass Volume Density is usually given in g cm-3 Care needs to be taken if different units are used.