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. 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: Molar Mass is the mass in grams of 1 mole of a substance and is given the unit of g mol-1 molar gas volume (gas volume per mole, units dm3 mol–1 ) . This is the volume of 1 mole of a gas at a given temperature and pressure. All gases have this same volume. At room pressure (1atm) and room temperature 25oC the molar gas volume is 24 dm3 mol–1 amount = mass Mr For pure solids and gases Unit of Mass: grams Unit of amount : mol Example 1: What is the amount, in mol, in 35.0g of CuSO4? amount = mass/Mr = 35/ (63.5 + 32 +16 x4) = 0.219 mol 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’: 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 Molar Mass for a compound can be calculated by adding up the mass numbers(from the periodic table) of each element in the compound eg CaCO3 = 40.1 + 12.0 +16.0 x3 = 100.1 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. Calculation of reacting masses, gas volumes and mole concentrations Commonly in questions converting between quantities of substances reacting we will use more than just mass data. We might have the volume and concentration of a solution, or the volume of a gas. We need to adapt our existing method or reacting masses to include other quantities. Any of the equations below can be used to convert quantities into moles. amount = mass MolarMass 1. For pure solids, liquids and gases 3. For solutions Concentration = amount volume Unit of Mass: grams Unit of amount : mol Unit of concentration: mol dm-3 or M Unit of Volume: dm3 2. For Gases Gas Volume (dm3 )= amount x 24 This equation give the volume of a gas at room pressure (1atm) and room temperature 25oC. PV = nRT Or use the ideal gas equation to work out gas volumes at other temperatures and pressures PV = nRT Unit of Pressure (P):Pa Unit of Volume (V): m3 Unit of Temp (T): K n= moles R = 8.31 JK–1mol–1 Converting temperature oC  K add 273 Example 8: What is the mass of Cl2 gas that has a pressure of 100kPa, temperature 293K, volume 500cm3 . (R = 8.31 JK–1mol–1 ) 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 The ideal gas equation is a slightly more difficult way of working out a gas volume. It can calculate the volume for any temperature and pressure though so is a more useful method. The biggest problems students have with this equation is choosing and converting to the correct units, so pay close attention to the units. Ideal Gas Equation 5 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’: N Goalby chemrevise.org 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 9 : How many atoms of Tin are there in a 6.00 g sample of Tin metal? amount = mass/Ar = 6/ 118.7 = 0.05055 mol Number atoms = amount x 6.02 x 1023 = 0.05055 x 6.02 x 1023 = 3.04 x1022 Example 10 : 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 = 1.204 x1022 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. cm3  dm3 ÷ 1000 cm3  m3 ÷ 1000 000 dm3  m3 ÷ 1000 Simple mole calculations Some Simple calculations using above equations Example 6: What is the concentration of solution made by dissolving 5.00g of Na2CO3 in 250 cm3 water? amount = mass/Mr = 5 / (23 x2 + 12 +16 x3) = 0.0472 mol conc= amount/Volume = 0.0472 / 0.25 = 0.189 mol dm-3 I. Learn these equations carefully and what units to use in them. It is usually best to give your answers to 3sf. Example 7 : What is the volume in dm3 at room temperature and pressure of 50.0g of Carbon dioxide gas ? amount = mass/Mr = 50/ (12 + 16 x2) = 1.136 mol Gas Volume (dm3 )= amount x 24 = 1.136 x 24 = or 27.3 dm3 to 3 sig fig