What you'll learn
This topic covers how to calculate and express the amount of solute dissolved in a solvent, essential skills for practical chemistry and Paper 2/4 calculations. You'll master concentration units (g/dm³ and mol/dm³), dilution problems, and calculations involving solutions in chemical reactions. These calculations appear regularly in CIE IGCSE Chemistry papers, worth 3-6 marks per question.
Key terms and definitions
Solution — a mixture formed when a solute dissolves in a solvent to form a homogeneous mixture.
Solute — the substance that dissolves in a solvent (usually the component in smaller amount).
Solvent — the liquid in which a solute dissolves (usually the component in larger amount; in aqueous solutions, water is the solvent).
Concentration — the amount of solute dissolved in a given volume of solution, commonly expressed in g/dm³ or mol/dm³.
Molarity (mol/dm³) — the number of moles of solute per cubic decimetre (litre) of solution, the standard concentration unit for chemical calculations.
Dilution — the process of reducing the concentration of a solution by adding more solvent.
Standard solution — a solution of accurately known concentration, typically prepared by dissolving a precise mass of solute in a volumetric flask.
Volumetric analysis — quantitative analysis using carefully measured volumes of solutions, including titrations.
Core concepts
Understanding concentration units
Concentration quantifies how much solute exists in a specific volume of solution. CIE IGCSE Chemistry uses two main units:
Concentration in g/dm³ (grams per cubic decimetre)
This expresses mass of solute per volume of solution. One cubic decimetre (dm³) equals one litre (L) or 1000 cm³.
Formula: Concentration (g/dm³) = mass of solute (g) / volume of solution (dm³)
To convert between volume units:
- 1 dm³ = 1000 cm³
- To convert cm³ to dm³: divide by 1000
- To convert dm³ to cm³: multiply by 1000
Concentration in mol/dm³ (moles per cubic decimetre)
This expresses moles of solute per volume of solution, directly linking concentration to chemical equations and stoichiometry.
Formula: Concentration (mol/dm³) = moles of solute (mol) / volume of solution (dm³)
The relationship between the two units depends on the molar mass (Mr) of the solute:
Concentration (g/dm³) = Concentration (mol/dm³) × Molar mass (g/mol)
Calculating concentration from mass and volume
The fundamental calculation involves finding concentration when you know the mass of solute and volume of solution:
- Identify the mass of solute in grams
- Identify the volume of solution (convert to dm³ if necessary)
- Apply the formula: concentration = mass ÷ volume
For molar concentration, an additional step converts mass to moles:
- Calculate moles of solute: moles = mass ÷ molar mass
- Identify the volume in dm³
- Calculate concentration: mol/dm³ = moles ÷ volume
Rearranging concentration formulas
The concentration formula can be rearranged to find any of the three variables:
Standard form: Concentration = Mass / Volume (or Moles / Volume)
To find mass: Mass = Concentration × Volume
To find volume: Volume = Mass / Concentration (or Moles / Concentration)
This triangle method helps visualize rearrangements:
- Cover the quantity you want to find
- The position of the other two shows whether to multiply or divide
Dilution calculations
When water (or another solvent) is added to a solution, the number of moles of solute remains constant, but the volume increases, reducing concentration.
Key principle: Moles before dilution = Moles after dilution
This leads to the dilution formula:
c₁ × V₁ = c₂ × V₂
Where:
- c₁ = initial concentration
- V₁ = initial volume
- c₂ = final concentration
- V₂ = final volume
Units must be consistent (both volumes in the same unit; both concentrations in the same unit).
Dilution procedure:
- Calculate moles in the original solution (c₁ × V₁)
- Add the required volume of water to reach the final volume V₂
- Calculate the new concentration (moles ÷ V₂)
Concentration in chemical reactions
When solutions react, their concentrations directly determine the volumes required by stoichiometry.
Reacting volumes formula:
For reactions between solutions, the mole ratio from the balanced equation relates to concentration and volume:
n = c × V (where n = moles, c = concentration in mol/dm³, V = volume in dm³)
For a reaction: aA + bB → products
n(A) / a = n(B) / b
Therefore: c(A) × V(A) / a = c(B) × V(B) / b
This calculation type appears frequently in titration problems.
Preparing standard solutions
A standard solution has a precisely known concentration. The preparation method follows specific steps:
- Calculate the required mass of solute using: mass = concentration × volume × molar mass
- Weigh the calculated mass accurately using a digital balance
- Dissolve the solute in less than the final volume of water in a beaker
- Transfer to a volumetric flask using a funnel
- Rinse the beaker and funnel with distilled water, adding rinsings to the flask
- Add distilled water up to the graduation mark (meniscus at eye level)
- Stopper the flask and invert several times to ensure thorough mixing
Volumetric flasks provide the most accurate final volume measurement for standard solutions.
Worked examples
Example 1: Calculating concentration in g/dm³ and mol/dm³
Question: A student dissolves 5.85 g of sodium chloride (NaCl) in water to make 250 cm³ of solution. Calculate: a) The concentration in g/dm³ b) The concentration in mol/dm³ [Ar: Na = 23, Cl = 35.5]
Solution:
a) Concentration in g/dm³
Step 1: Convert volume to dm³ Volume = 250 cm³ = 250 ÷ 1000 = 0.25 dm³
Step 2: Apply the formula Concentration = mass ÷ volume Concentration = 5.85 ÷ 0.25 = 23.4 g/dm³
b) Concentration in mol/dm³
Step 1: Calculate molar mass of NaCl Mr(NaCl) = 23 + 35.5 = 58.5 g/mol
Step 2: Calculate moles of NaCl Moles = mass ÷ molar mass Moles = 5.85 ÷ 58.5 = 0.1 mol
Step 3: Calculate concentration Concentration = moles ÷ volume Concentration = 0.1 ÷ 0.25 = 0.4 mol/dm³
Example 2: Dilution calculation
Question: A technician has 50 cm³ of 2.0 mol/dm³ sulfuric acid. What volume of water must be added to produce a solution with concentration 0.5 mol/dm³?
Solution:
Step 1: Use the dilution formula c₁V₁ = c₂V₂ c₁ = 2.0 mol/dm³ V₁ = 50 cm³ c₂ = 0.5 mol/dm³ V₂ = unknown
Step 2: Rearrange to find V₂ V₂ = (c₁ × V₁) ÷ c₂ V₂ = (2.0 × 50) ÷ 0.5 V₂ = 100 ÷ 0.5 = 200 cm³
Step 3: Calculate volume of water added Volume of water = V₂ - V₁ Volume of water = 200 - 50 = 150 cm³
Example 3: Reacting volumes calculation
Question: 25.0 cm³ of 0.10 mol/dm³ sodium hydroxide solution exactly neutralizes 20.0 cm³ of sulfuric acid. H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O Calculate the concentration of the sulfuric acid in mol/dm³.
Solution:
Step 1: Calculate moles of NaOH Volume in dm³ = 25.0 ÷ 1000 = 0.025 dm³ Moles = concentration × volume Moles of NaOH = 0.10 × 0.025 = 0.0025 mol
Step 2: Use the mole ratio from the equation 1 H₂SO₄ : 2 NaOH Moles of H₂SO₄ = 0.0025 ÷ 2 = 0.00125 mol
Step 3: Calculate concentration of H₂SO₄ Volume = 20.0 cm³ = 0.020 dm³ Concentration = moles ÷ volume Concentration = 0.00125 ÷ 0.020 = 0.0625 mol/dm³
Common mistakes and how to avoid them
Mistake: Forgetting to convert cm³ to dm³ when using the concentration formula with mol/dm³. Students calculate moles correctly but divide by 250 instead of 0.25, giving an answer 1000 times too large. Correction: Always convert cm³ to dm³ by dividing by 1000 before substituting into formulas. Alternatively, use cm³ throughout but express concentration as mol/cm³, then convert the final answer.
Mistake: Confusing mass of solute with mass of solution when calculating concentration. Some students add the mass of water to the mass of solute. Correction: Concentration uses mass of solute only (the substance dissolving) and volume of the total solution (solute + solvent together).
Mistake: Using the wrong molar mass in calculations. For example, using Mr of Na (23) instead of NaCl (58.5) when the solute is sodium chloride. Correction: Identify the dissolved species carefully. The molar mass must match the complete formula of the solute.
Mistake: In dilution calculations, adding the volume of water instead of finding the total final volume. If diluting 50 cm³ to 0.5 mol/dm³, students might incorrectly use V₂ = 150 cm³ (the water added) instead of 200 cm³ (the final total). Correction: The dilution formula c₁V₁ = c₂V₂ uses total volumes before and after, not the volume added.
Mistake: Incorrectly applying mole ratios in reacting volumes. Dividing or multiplying by the wrong stoichiometric coefficient. Correction: Write out the balanced equation, identify which substance's moles you've calculated, then use the coefficient ratio systematically: moles of unknown = moles of known × (coefficient of unknown / coefficient of known).
Mistake: Rounding too early in multi-step calculations, leading to inaccurate final answers. Correction: Keep all digits in intermediate steps (use your calculator's memory function). Only round the final answer to an appropriate number of significant figures (usually 2-3 for IGCSE).
Exam technique for "Concentration of solutions and solution calculations"
Command word "Calculate" requires you to show full working. Write the formula, substitute values with units, and show each step clearly. Even if your final answer is wrong, you can earn method marks for correct working. Paper 2/4 typically award 1 mark for correct formula, 1 mark for correct substitution, 1 mark for the answer.
Units matter. Always include the correct unit with your final answer. For concentration, write g/dm³ or mol/dm³ explicitly. Omitting units often loses the final mark even when the numerical value is correct. Check the question to see which unit is required.
Significant figures and decimal places. CIE mark schemes typically accept answers within a reasonable range (usually to 2-3 significant figures). Match the precision of the data given in the question. If masses are given to 2 decimal places, give your answer to at least 2-3 significant figures.
For titration calculations, work methodically: (1) calculate moles of the known solution using n = cV, (2) use the balanced equation to find the mole ratio, (3) calculate moles of the unknown substance, (4) find concentration or volume of the unknown using rearranged formulas. Write out each step separately—examiners follow your logic through the working.
Quick revision summary
Concentration measures solute per unit volume: g/dm³ or mol/dm³. Convert cm³ to dm³ by dividing by 1000. Use c = n/V for molar concentration; calculate moles first using n = mass/Mr. Dilution keeps moles constant: c₁V₁ = c₂V₂. For reacting solutions, calculate moles (n = cV), apply the mole ratio from the balanced equation, then find the unknown concentration or volume. Always show working, include units, and convert volumes correctly. Standard solutions require accurate weighing and dilution to a precise volume in a volumetric flask.