Stoichiometry
Solutions & Concentration
5th Year · 6th Year (Leaving Cert)
- ✓Define a solution, solute, solvent, and concentration.
- ✓Calculate the molarity of a solution given the mass of solute and volume of solution, and vice versa.
- ✓Perform calculations involving the dilution of solutions using the appropriate formula.
- ✓Explain the principles of volumetric analysis and titration, including the terms equivalence point and end point.
- ✓Carry out stoichiometric calculations based on titration results to determine unknown concentrations.
Key concepts
A homogeneous mixture of two or more substances. It consists of a solute dissolved in a solvent.
The substance that dissolves in a solvent to form a solution. It is typically present in the smaller quantity.
The substance that dissolves the solute to form a solution. It is typically present in the larger quantity (e.g., water in aqueous solutions).
A measure of the amount of solute dissolved in a given amount of solvent or solution. It indicates how 'strong' or 'weak' a solution is.
The most common way to express concentration in chemistry. It is defined as the number of moles of solute per litre of solution.
Molarity is expressed in moles per litre (mol L⁻¹) or simply 'M' (molar). For example, a 0.1 M solution contains 0.1 moles of solute per litre of solution.
The amount of substance. It can be calculated from mass and molar mass.
The process of reducing the concentration of a solution by adding more solvent. During dilution, the number of moles of solute remains constant.
A solution of accurately known concentration. It is typically prepared by dissolving a precisely weighed amount of a primary standard substance in a known volume of solvent.
A quantitative analytical method used to determine the concentration of an unknown solution (analyte) by reacting it with a solution of accurately known concentration (titrant). The reaction is carried out until the equivalence point is reached.
The point in a titration where the reactants have reacted completely according to their stoichiometric ratio as given by the balanced chemical equation.
The point in a titration where the indicator changes colour, signalling the completion of the reaction. Ideally, the end point should be very close to the equivalence point.
A substance, typically a weak acid or base, that changes colour over a specific pH range, used to visually determine the end point of a titration.
Key facts to remember
- 1Molarity (c) is defined as moles of solute per litre of solution (mol L⁻¹ or M).
- 2Always convert volumes to litres (L) when using the molarity formula c = n/V.
- 3The number of moles of solute remains constant during dilution, hence c₁V₁ = c₂V₂.
- 4A standard solution has an accurately known concentration and is crucial for volumetric analysis.
- 5In a titration, the equivalence point is where reactants are stoichiometrically balanced, while the end point is where the indicator changes colour.
- 6A balanced chemical equation is essential for determining the correct mole ratios in titration calculations.
- 7Molar mass (M_r) is used to convert between mass and moles (n = mass / M_r).
Worked examples
Example 1
Calculate the molarity of a solution prepared by dissolving 8.0 g of sodium hydroxide (NaOH) in enough water to make 250 cm³ of solution. (Relative molecular mass of NaOH = 40.0 g mol⁻¹)
Answer
The molarity of the NaOH solution is 0.80 M (or 0.80 mol L⁻¹).
Always ensure volume is in litres when calculating molarity.
Example 2
A 75.0 cm³ sample of 1.50 M sulfuric acid (H₂SO₄) is diluted to a final volume of 500 cm³. What is the concentration of the diluted sulfuric acid solution?
Answer
The concentration of the diluted sulfuric acid solution is 0.225 M.
The units for volume (V) must be consistent on both sides of the equation. If V₁ is in cm³, V₂ must also be in cm³.
Example 3
In a titration, 25.0 cm³ of a sodium carbonate solution (Na₂CO₃) required 20.0 cm³ of 0.100 M hydrochloric acid (HCl) for complete neutralisation. Calculate the concentration of the sodium carbonate solution. The balanced equation is: Na₂CO₃(aq) + 2HCl(aq) → 2NaCl(aq) + H₂O(l) + CO₂(g)
Answer
The concentration of the sodium carbonate solution is 0.0400 M (or 0.0400 mol L⁻¹).
Always start with a balanced chemical equation to correctly determine the stoichiometric mole ratio.
Common mistakes
- ✗Forgetting to convert volume from cubic centimetres (cm³) to litres (L) when using c = n/V.
- ✗Not using the correct stoichiometric mole ratio from the balanced chemical equation in titration calculations.
- ✗Confusing the equivalence point with the end point, or assuming they are always exactly the same.
- ✗Incorrectly calculating the relative molecular mass (M_r) of a compound.
- ✗Failing to rinse glassware (e.g., burette, pipette) correctly with the solution it will contain before use, leading to inaccurate concentrations.
Exam tips
- ★Always write down the balanced chemical equation for any reaction involved in a titration problem; this is often worth marks.
- ★Show all steps in your calculations clearly, including units, to maximise marks, even if your final answer is incorrect.
- ★Double-check all conversions, especially between cm³ and L (1 L = 1000 cm³).
- ★Clearly state your final answer with the correct units and to an appropriate number of significant figures.
- ★Practise identifying the knowns and unknowns in a problem before starting calculations to ensure you use the correct formula and approach.
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