IGCSEChemistryCambridge (CIE)Revision Notes3. StoichiometryThe Mole & the Avogadro ConstantCalculating Concentration

Calculating Concentration (Cambridge (CIE) IGCSE Chemistry)

Revision Note

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Caroline Carroll

Written by: Caroline Carroll

Reviewed by: Stewart Hird

Units of concentration

  • A solute is a solid substance that dissolves into a liquid 

    • The amount of solute can be expressed in grams (g) or moles (mol)

  • A solvent is the liquid that a solute dissolves in 

    • The amount / volume of a solvent is measured in cm3 or dm3

  • Most chemical reactions occur between solutes which are dissolved in solvents, such as water or an organic solvent

  • A solution is the mixture formed when a solute dissolves in a solvent 

    • The amount / volume of a solution measured in cm3 or dm3 

  • Concentration refers to the amount of solute there is in a specific volume of the solvent

    • The greater the amount of solute in a given volume, the greater the concentration

    • Concentration is sometimes commonly referred to as strength

      • For example, dissolving more coffee in hot water results in a stronger coffee

  • Typically, concentration is expressed in terms of the amount of substance per dm3  

    • Therefore, the units of concentration are:

      • g / dm3 

      • mol / dm3

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Calculating concentration

Extended tier only

Calculating concentration using mass 

  • The general formula to calculate the concentration in g / dm3 is:

concentration (g / dm3) = fraction numerator mass space of space solute space left parenthesis straight g right parenthesis over denominator volume space of space solution space left parenthesis dm cubed right parenthesis end fraction

  • Concentration can also be measured in grams per cubic decimetre

    • 1 decimetre cubed (dm3) = 1000 cm3 

    • 1 decimetre cubed (dm3) is the same as 1 litre

  • You may be given data in a question which needs to be converted from cm3 to dm3 or the other way around

Converting cm3 and dm3

unit-conversion

To go from cm3 to dm3 divide by 1000. To go from dm3 to cm3 multiply by 1000

Worked Example

A student dissolved 10 g of sodium hydroxide, NaOH, in 2 dm3 of distilled water. Calculate the concentration of the solution in g / dm3.

Answer:

  • Write down the information you are given in the question:

    • Mass of solute: 10 g

    • Volume of solution: 2 dm3 

  • Calculate the concentration:

    • Concentration = fraction numerator mass space of space solute space open parentheses straight g close parentheses over denominator volume space open parentheses dm cubed close parentheses end fraction

    • Concentration = fraction numerator 10 space straight g over denominator 2 space dm cubed end fraction = 5 g / dm3 

Calculating concentration using moles

  • It is more useful to a chemist to express concentration in terms of moles per unit volume rather than mass per unit volume

  • Concentration can therefore be expressed in moles per decimetre cubed and calculated using the following equation:

concentration space left parenthesis mol divided by dm cubed right parenthesis space equals space fraction numerator number space of space moles space of space solute space left parenthesis mol right parenthesis over denominator volume space of space solution space left parenthesis dm cubed right parenthesis end fraction

  • We can modify the concentration formula to include moles

    • The units in the answer can be written as mol / dm3 (this can also be written as mol dm-3)

  • You may have to convert from g / dm3 into mol / dm3 and vice versa depending on the question

  • To go from g / dm3 to mol / dm3 

    • Divide by the molar mass in grams

  • To go from mol / dm3 to g / dm3

    • Multiply by the molar mass in grams

  • Some students find formula triangles help them to understand the relationship:

Concentration moles formula triangle, downloadable IB Chemistry revision notes

The concentration-moles formula triangle can help you solve these problems

Worked Example

Calculate the amount of solute, in moles, present in 2.5 dm3 of a solution whose concentration is 0.2 mol / dm3.

Answer:

  • Write down the information you are given in the question:

    • Concentration of solution: 0.2 mol / dm3

    • Volume of solution: 2.5 dm3 

  • Calculate the number of moles:

    • Moles = concentration x volume

    • Moles = 0.2 x 2.5 = 0.5 mol

Worked Example

Calculate the concentration of a solution of sodium hydroxide, NaOH, in mol / dm3, when 80 g is dissolved in 500 cm3 of water.

Relative atomic masses, Ar:  Na = 23;   H = 1;   O = 16

Answer:

  • Calculate the Mr of NaOH:

    • 23 + 16 + 1 = 40

  • Determine the number of moles of NaOH:

    • 40 g = 1 mole

    • So, 80 g = 2 moles

  • Convert cm3 to dm3:

    • begin mathsize 14px style 500 over 1000 end style = 0.5 dm3 

  • Calculate the concentration:

    • Concentration = moles over volume

    • Concentration = fraction numerator 2 over denominator 0.5 end fraction = 4 mol / dm3 

Worked Example

25.0 cm3 of 0.050 mol / dm3 sodium carbonate was completely neutralised by 20.00 cm3 of dilute hydrochloric acid. Calculate the concentration in mol / dm3 of the hydrochloric acid.

Na2CO3 + 2HCl → 2NaCl + H2O + CO2 

Answer:

  • Calculate the moles of sodium carbonate:

    • Moles of Na2CO3 = concentration x volume

      • Remember: The volume needs to be in dm3 

    • Moles of Na2CO3 = 0.05 x begin mathsize 14px style fraction numerator 25.0 over denominator 1000 end fraction end style = 0.00125

  • Calculate the moles of hydrochloric acid:

    • The balanced symbol equation shows that 1 mole of Na2CO3 reacts with 2 moles of HCl

    • So, 0.00125 moles of Na2CO3 reacts with 0.00250 moles of HCl

  • Calculate the concentration of hydrochloric acid:

    • Concentration = moles over volume

      • Remember: The volume needs to be in dm3 

      • 20 cm3 ÷ 1000 = 0.02 dm3 

    • Concentration = fraction numerator 0.00250 over denominator 0.02 end fraction = 0.125 mol / dm3 

Examiner Tips and Tricks

Remember: Always convert the units from cm3 to dm3 by dividing by 1000.

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    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.

    Stewart Hird

    Author: Stewart Hird

    Expertise: Chemistry Lead

    Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.