Calculations

• Mole


  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 10^23 atoms in 12 grams of carbon-12
• One mole of any specified entity contains 6.022 x 10^23 of that entity
• Equations used for most calculations at A-level


  • For pure solids, liquids and gases
  • For gases: PV = nRT
  • For solutions
• Relative atomic mass


  The average mass of one atom compared to one twelfth of the mass of one atom of carbon-12
• Relative molecular mass


  The average mass of a molecule compared to one twelfth of the mass of one atom of carbon-12
• Using Equation 1


  1. Calculate the number of moles of CuSO4 in 35.0g of CuSO4

  2. moles = mass / Mr
• Molar mass (Mr) for a compound can be calculated by adding up the mass numbers (from the periodic table) of each element in the compound
• Give your answers to the same number of significant figures as the number of significant figures for the data given in a question
• Using Equation 1


  1. Calculate the number of moles in 75.0mg of CaSO4.2H2O

  2. moles = mass / Mr
• Avogadro's Constant


  There are 6.022 x 10^23 atoms/molecules/ions in 1 mole of any specified entity
• Calculating number of atoms of tin in a 6.00 g sample of tin metal

  1. moles = mass / Ar

  2. number atoms = moles x 6.022 x 10^23
• Calculating number of chloride ions in a 25.0 cm3 solution of magnesium chloride of concentration 0.400 mol dm-3


  1. moles = concentration x volume

  2. number ions of Cl- = moles x 6.022 x 10^23
• Density


  Density is usually given in g cm-3
• Calculating number of molecules of ethanol in 0.500 dm3 of ethanol liquid

  1. mass = density x volume

  2. moles = mass / Mr

  3. number of molecules = moles x 6.022 x 10^23
• Calculating density of gold in a bar

  1. mass = moles x Mr

  2. density = mass / volume
• Molecular formula


  The actual number of atoms of each element in the compound
• Empirical formula


  The simplest ratio of atoms of each element in the compound
• Calculating empirical formula from masses of elements


  1. Divide each mass by atomic mass to get moles

  2. Divide each mole by smallest mole to get whole number ratio
• Determining water of crystallisation in hydrated calcium sulfate


  1. Weigh empty crucible

  2. Add hydrated calcium sulfate and weigh

  3. Heat strongly to remove water

  4. Allow to cool and reweigh
• Small amounts (0.100 g) should not be used as percentage uncertainties in weighing will be too high
• Large amounts (50 g) should not be used as decomposition is likely to be incomplete
• The lid improves accuracy by preventing loss of solid but should be loose fitting to allow gas to escape
• The crucible needs to be dry otherwise mass loss would be too large as water would be lost when heating
• Calculating value of x in hydrated zinc sulfate ZnSO4.xH2O


  1. Calculate mass of H2O lost

  2. Calculate moles of ZnSO4 and H2O

  3. Calculate ratio of moles to determine x
• Hydrated salt


  Contains water of crystallisation
• Calculating value of x in hydrated sodium sulfate Na2SO4.xH2O


  Use molar mass of hydrated salt to determine x
• Concentration of solutions


  Measured in mol dm-3 or M
• Calculating concentration of sodium carbonate solution

  1. moles = mass / Mr

  2. concentration = moles / volume
• A cm3 is equivalent to a cube 1cm x 1cm x 1cm, a dm3 is 10cm x 10cm x 10cm, and a m3 is 100cm x 100cm x 100cm
• To convert cm3 to dm3, divide by 1000. To convert m3 to dm3, multiply by 1000
• Solution


  A mixture formed when a solute dissolves in a solvent, commonly water as the solvent
• Molar concentration is calculated by dividing the amount in moles of the solute by the volume of the solution in dm3
• Ration


  mol dm-3 or M
• Converting volumes


  1. cm3 to dm3 ÷ 1000

  2. cm3 to m3 ÷ 1000 000

  3. dm3 to m3 ÷ 1000
• Example 11


  • Calculating the concentration of solution made by dissolving 5.00 g of Na2CO3 in 250 cm3 water
• cm3


  Equivalent to a cube 1cm x 1cm x 1cm
• dm3


  Equivalent to a cube 10cm x 10cm x 10cm = 1000 cm3
• m3


  Equivalent to a cube 100cm x 100cm x 100cm = 1000000 cm3
• 1 cm3 = 1 mL