Calculating Concentration
Section: 3. Stoichiometry | Syllabus: Cambridge AS Level Physics 9702
What is Concentration? Concentration is the amount of solute dissolved in a given volume of solution. It tells us how "strong" or "weak" a solution is. Key terms: Solute: The substance being dissolved (e.g., salt, sugar, acid) Solvent: The liquid doing the dissolving (usually water) Solution: The mixture of solute + solvent Units of Concentration There are two main ways to express concentration: Type Units Meaning Common use Mass concentration g/dm³ grams per cubic decimetre Simple solutions Molar concentration mol/dm³ moles per cubic decimetre Chemical reactions Important: 1 dm³ = 1 litre (L) = 1000 cm³ = 1000 mL Mass Concentration (g/dm³) Concentration (g/dm³) = Mass of solute (g) ÷ Volume of solution (dm³) C = m ÷ V Example 1: 20 g of sodium chloride is dissolved in 2 dm³ of water.
Calculate the concentration. C = m ÷ V C = 20 ÷ 2 = 10 g/dm³ Example 2: 5 g of sugar is dissolved in 500 cm³ of water. Calculate the concentration in g/dm³. Step 1: Convert volume to dm³ 500 cm³ = 500 ÷ 1000 = 0.5 dm³ Step 2: Calculate concentration C = 5 ÷ 0.5 = 10 g/dm³ Molar Concentration (mol/dm³) Molar concentration (also called molarity) is the number of moles of solute dissolved in 1 dm³ of solution.
Symbol: M or mol/dm³ (sometimes written as mol dm⁻³) Concentration (mol/dm³) = Moles of solute (mol) ÷ Volume of solution (dm³) C = n ÷ V Example 3: 2 moles of HCl is dissolved in 4 dm³ of solution. Calculate the concentration.
C = n ÷ V C = 2 ÷ 4 = 0.5 mol/dm³ The Concentration Triangle Three key formulas: Moles = Concentration × Volume Concentration = Moles ÷ Volume Volume = Moles ÷ Concentration Moles ------- C × V Cover the quantity you want to find: Cover Moles → n = C × V Cover C → C = n ÷ V Cover V → V = n ÷ C Converting Between Mass and Molar Concentration To convert from mass concentration to molar concentration: Step 1: Calculate moles from mass (n = m ÷ Mr) Step 2: Calculate concentration (C = n ÷ V) Example 4: A solution contains 40 g of NaOH in 2 dm³.
Calculate the concentration in mol/dm³. (Ar: Na=23, O=16, H=1) Step 1: Calculate Mr of NaOH Mr = 23 + 16 + 1 = 40 Step 2: Calculate moles n = m ÷ Mr = 40 ÷ 40 = 1 mol Step 3: Calculate concentration C = n ÷ V = 1 ÷ 2 = 0.5 mol/dm³ Working with cm³ Volumes Many questions give volumes in cm³, but concentration formulas need dm³: To convert: divide cm³ by 1000 to get dm³ Volume (dm³) = Volume (cm³) ÷ 1000 Examples: 250 cm³ = 250 ÷ 1000 = 0.25 dm³ 500 cm³ = 500 ÷ 1000 = 0.5 dm³ 25 cm³ = 25 ÷ 1000 = 0.025 dm³ Calculating Moles from Concentration and Volume Moles = Concentration × Volume n = C × V Example 5: How many moles are in 50 cm³ of 2 mol/dm³ HCl?
Step 1: Convert volume to dm³ 50 cm³ = 50 ÷ 1000 = 0.05 dm³ Step 2: Calculate moles n = C × V n = 2 × 0.05 = 0.1 mol Example 6: How many moles are in 25 cm³ of 0.1 mol/dm³ NaOH? Step 1: Convert volume 25 cm³ = 0.025 dm³ Step 2: Calculate moles n = 0.1 × 0.025 = 0.0025 mol Calculating Volume from Moles and Concentration Volume = Moles ÷ Concentration V = n ÷ C Example 7: What volume of 2 mol/dm³ HCl contains 0.5 moles?
V = n ÷ C V = 0.5 ÷ 2 = 0.25 dm³ V = 0.25 × 1000 = 250 cm³ Finding Mass from Concentration and Volume This combines multiple steps: Step 1: n = C × V (find moles) Step 2: m = n × Mr (find mass) Example 8: What mass of NaOH is in 500 cm³ of 0.5 mol/dm³ solution?
(Mr of NaOH = 40) Step 1: Convert volume 500 cm³ = 0.5 dm³ Step 2: Calculate moles n = C × V = 0.5 × 0.5 = 0.25 mol Step 3: Calculate mass m = n × Mr = 0.25 × 40 = 10 g Dilution Calculations When diluting a solution, the number of moles stays the same: C₁V₁ = C₂V₂ Where: C₁ = initial concentration V₁ = initial volume C₂ = final concentration V₂ = final volume Example 9: 100 cm³ of 2 mol/dm³ HCl is diluted to 500 cm³.
What is the new concentration? C₁V₁ = C₂V₂ 2 × 100 = C₂ × 500 200 = C₂ × 500 C₂ = 200 ÷ 500 = 0.4 mol/dm³ Common Exam Questions Type 1: Calculate concentration from moles and volume Strategy: C = n ÷ V (remember to convert cm³ to dm³!) Type 2: Calculate moles from concentration and volume Strategy: n = C × V Type 3: Calculate mass in a solution Strategy: n = C × V, then m = n × Mr Type 4: Convert between mass and molar concentration Strategy: Use Mr to convert between mass and moles Common Mistakes to Avoid Forgetting to convert cm³ to dm³: Always divide by 1000!
Using wrong formula: Check if you need n = C × V or C = n ÷ V Mixing up mass and molar concentration: Check the units (g/dm³ or mol/dm³) Not calculating Mr first: Need Mr to convert between mass and moles Wrong units in answer: Always include units (mol/dm³ or g/dm³) Calculator errors with decimals: Be careful with 0.025, 0.0025, etc.
Key Points Summary Concentration = amount of solute per unit volume Mass concentration: C = m ÷ V (units: g/dm³) Molar concentration: C = n ÷ V (units: mol/dm³) Moles = Concentration × Volume (n = C × V) Volume = Moles ÷ Concentration (V = n ÷ C) 1 dm³ = 1000 cm³ (divide cm³ by 1000 to get dm³) To find mass: calculate moles first (n = C × V), t…
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