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study examples carefully14. Other GCSE chemical calculations - SOLUTION DILUTION CALCULATIONSstudy examples carefully

soluble salt preparation from insoluble base-acid neutralisationQuantitative chemistry calculations Diluting solutions. Help for problem solving dilution calculations. How do you do solution dilution calculations? Using dilution factors to solve concentration problems - fully worked out example calculations for diluting solutions. Online practice exam chemistry CALCULATIONS and solved problems for KS4 Science GCSE/IGCSE CHEMISTRY and basic starter chemical calculations for A level AS/A2/IB courses.  These revision notes and practice questions on how to do solution dilution chemical calculations and worked examples should prove useful for the new AQA, Edexcel and OCR GCSE (91) chemistry science courses.

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study examples carefully14. Other GCSE chemical calculationsstudy examples carefully

14.1 % purity of a product  *  14.2a % reaction yield  *  14.2b atom economy  *  14.3 dilution of solutions

14.4 water of crystallisation calculation  *  14.5 how much of a reactant is needed?

14.3 Dilution of solutions calculations

calculating dilutions - volumes involved etc.

volumetric apparatus
  • In conjunction with this page it be important to study

  • It is important to know how to accurately dilute a more concentrated solution to a specified solution of lower concentration. It involves a bit of logic using ratios of volumes. The diagram above illustrates some of the apparatus that might be used when dealing with solutions.

  • Example 14.3.1

  • A purchased standard solution of sodium hydroxide had a concentration of 1.0 mol/dm3. How would you prepare 100 cm3 of a 0.1 mol/dm3 solution to do a titration of an acid?

    • The required concentration is 1/10th of the original solution.

    • To make 1dm3 (1000 cm3) of the diluted solution you would take 100 cm3 of the original solution and mix with 900 cm3 of water.

    • The total volume is 1dm3 but only 1/10th as much sodium hydroxide in this diluted solution, so the concentration is 1/10th, 0.1 mol/dm3.

    • To make only 100 cm3 of the diluted solution you would dilute 10cm3 by mixing it with 90 cm3 of water.

    • How to do this in practice is described at the end of Example 14.3.2 below and a variety of accurate/'less inaccurate' apparatus is illustrated above.

  • Example 14.3.2

    • Given a stock solution of sodium chloride of 2.0 mol/dm3, how would you prepare 250cm3 of a 0.5 mol/dm3 solution?

    • The required 0.5 mol/dm3 concentration is 1/4 of the original concentration of 2.0 mol/dm3.

    • To make 1dm3 (1000 cm3) of a 0.5 mol/dm3 solution you would take 250 cm3 of the stock solution and add 750 cm3 of water.

    • Therefore to make only 250 cm3 of solution you would mix 1/4 of the above quantities i.e. mix 62.5 cm3 of the stock solution plus 187.5 cm3 of pure water.

    • This can be done, but rather inaccurately, using measuring cylinders and stirring to mix the two liquids in a beaker.

    • It can be done much more accurately by using a burette or a pipette to measure out the stock solution directly into a 250 cm3 graduated-volumetric flask.

    • Topping up the flask to the calibration mark (meniscus should rest on it). Then putting on the stopper and thoroughly mixing it by carefully shaking the flask holding the stopper on at the same time!

  • Example 14.3.3

  • In the analytical laboratory of a pharmaceutical company a laboratory assistant was asked to make 250 cm3 of a 2.0 x 10-2 mol dm-3 (0.02M) solution of paracetamol (C8H9NO2).

    • (a) How much paracetamol should the laboratory assistant weigh out to make up the solution?

      • Atomic masses: C = 12, H = 1, N = 14, O = 16

      • method (i): Mr(paracetamol) = (8 x 12) + (9 x 1) + (1 x 14) + (2 x 16) = 151

      • 1000 cm3 of 1.0 molar solution needs 151g

      • 1000 cm3 of 2.0 x 10-2 molar solution needs 151 x 2.0 x 10-2/1 = 3.02g

      • (this is just scaling down the ratio from 151g : 1.0 molar)

      • Therefore to make 250 cm3 of the solution you need 3.02 x 250/1000 = 0.755 g

    • method (ii): Mr(paracetamol) = 151

      • moles = molarity x volume in dm3

      • mol paracetamol required = 2.0 x 10-2 x 250/1000 = 5.0 x 10-3 (0.005)

      • mass = mol x Mr = 5.0 x 10-3 x 151 = 0.755 g

    • (b) Using the 2.0 x 10-2 molar stock solution, what volume of it should be added to a 100cm3 volumetric flask to make 100 cm3 of a 5.0 x 10-3 mol dm-3 (0.005M) solution?

      • The ratio of the two molarities is stock/diluted = 2.0 x 10-2/5.0 x 10-3 = 4.0 or a dilution factor of 1/4 (0.02/0.005).

      • Therefore 25 cm3 (1/4 of 100) of the 2.0 x 10-2 molar solution is added to the 100 cm3 volumetric flask prior to making it up to 100 cm3 with pure water to give the 5.0 x 10-3 mol dm-3 (0.005M) solution.

      • There are more questions involving molarity in (c) doc b section 7. introducing molarity and (c) doc b section 12. on dilution

  • Example 14.3.4

    • You are given a stock solution of concentrated ammonia with a concentration of 17.9 mol dm-3 (conc. ammonia! ~18M!)

    • (a) What volume of the conc. ammonia is needed to make up 1dm3 of 1.0 molar ammonia solution?

      • Method (i) using simple ratio argument.

      • The conc. ammonia must be diluted by a factor of 1.0/17.9 to give a 1.0 molar solution.

      • Therefore you need (1.0/17.9) x 1000 cm3 = 55.9 cm3 of the conc. ammonia.

      • If the 55.9 cm3 of conc. ammonia is diluted to 1000 cm3 (1 dm3) you will have a 1.0 mol dm-3 (1M) solution.

      • Method (ii) using molar concentration equation - a much better method that suits any kind of dilution calculation involving molarity.

        • molarity = mol / volume (dm3), therefore mol = molarity x volume in dm3

        • Therefore you need 1.0 x 1.0 = 1.0 moles of ammonia to make 1 dm3 of 1.0M dilute ammonia.

        • Volume = mol / molarity

        • Volume of conc. ammonia needed = 1.0 / 17.9 = 0.0559 dm3 (55.9 cm3) of the conc. ammonia is required,

        • and, if this is diluted to 1 dm3, it will give you a 1.0 mol dm-3 dilute ammonia solution.

    • (b) What volume of conc. ammonia is needed to make 5 dm3 of a 1.5 molar solution?

      • molarity = mol / volume (dm3), therefore mol = molarity x volume in dm3

      • Therefore you need 1.5 x 5 = 7.5 moles of ammonia to make 5 dm3 of 1.5M dilute ammonia.

      • Volume (of conc. ammonia needed) = mol / molarity

      • Volume of conc. ammonia needed = 7.5 / 17.9 = 0.419 dm3 (419 cm3) of the conc. ammonia is required,

      • and, if this is diluted to 5 dm3, it will give you a 1.5 mol dm-3 dilute ammonia solution.

  • -

Above is typical periodic table used in GCSE science-chemistry specifications in doing chemical calculations, and I've 'usually' used these values in my exemplar calculations to cover most syllabuses


  1. What is relative atomic mass?, relative isotopic mass and calculating relative atomic mass

  2. Calculating relative formula/molecular mass of a compound or element molecule

  3. Law of Conservation of Mass and simple reacting mass calculations

  4. Composition by percentage mass of elements in a compound

  5. Empirical formula and formula mass of a compound from reacting masses (easy start, not using moles)

  6. Reacting mass ratio calculations of reactants and products from equations (NOT using moles) and brief mention of actual percent % yield and theoretical yield, atom economy and formula mass determination

  7. Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations (relating reacting masses and formula mass)

  8. Using moles to calculate empirical formula and deduce molecular formula of a compound/molecule (starting with reacting masses or % composition)

  9. Moles and the molar volume of a gas, Avogadro's Law

  10. Reacting gas volume ratios, Avogadro's Law and Gay-Lussac's Law (ratio of gaseous reactants-products)

  11. Molarity, volumes and solution concentrations (and diagrams of apparatus)

  12. How to do acid-alkali titration calculations, diagrams of apparatus, details of procedures

  13. Electrolysis products calculations (negative cathode and positive anode products)

  14. Other calculations e.g. % purity, % percentage & theoretical yield, dilution of solutions (and diagrams of apparatus), water of crystallisation, quantity of reactants required, atom economy

  15. Energy transfers in physical/chemical changes, exothermic/endothermic reactions

  16. Gas calculations involving PVT relationships, Boyle's and Charles Laws

  17. Radioactivity & half-life calculations including dating materials

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