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Chemistry · 03 / 10

Solutions: concentration and dilution

High school foundations · Worked example and 4 exercises with solutions, at your pace.

Need a foundation?Units: numbers have dimensionsThe mole: connect mass and particlesBalance a reaction equation
UnderstandSee an exampleGuided exercise3 progressive challenges

The principle, simply

Molar concentration divides solute amount by final solution volume. Dilution preserves the sampled solute amount while increasing volume, so C₁V₁ = C₂V₂. Use the same volume unit on both sides. Dilution does not create solute or increase concentration.

C_1*V_1=C_2*V_2
THE PICTURE TO REMEMBERSolutions: concentration and dilution
  1. 01Sample solute
  2. 02Conserve amount
  3. 03Increase volume
  4. 04Reduce concentration

WORKED EXAMPLE

From principle to reasoning

To obtain 100 mL at 0.1 mol/L from 1 mol/L, calculate 10 mL of stock and reach the final 100 mL according to the supervised protocol.

Solve a problem in this subject

  1. Identify species

    Write formulas and useful states. Distinguish atoms, ions, molecules and amount of substance. Total charge is conserved.

  2. Connect quantities

    Use m = nM and C = n/V with consistent units. V is the final solution volume.

  3. Use coefficients

    Balance before building an extent table. Compare initial amounts divided by coefficients to identify the limiting reactant.

  4. Check context

    Remaining amounts cannot be negative. Check conservation, units and assumptions: dilution, medium, completion or equilibrium.

YOUR TURN

01 · Try before checking

What does a dilution factor of five do to concentration?

One hint

The factor is C₁/C₂.

Reveal and understand the solution

C₂ = C₁/5; 0.5 mol/L becomes 0.1 mol/L.

Compare method, conditions and answer; identify the exact part to revisit.

IMPROVE THROUGH PRACTICE

Three additional challenges with solutions

Start with the first challenge. Write your method before opening a hint; use the solution to find the first step that needs work.

Reflect after practising
02 · Recognise and understandLink to this exercise

Dissolve 0.02 mol to a final volume of 200 mL. Find c.

A hint to get started

Convert final volume to litres.

Step-by-step solution
  1. 200 mL = 0.200 L.
  2. c = n/V = 0.02/0.200.
  3. c = 0.10 mol/L.

Which step did you miss? Retry without help, then explain why the method works.

03 · Apply the methodLink to this exercise

Prepare 100 mL of 0.2 mol/L solution from 1 mol/L stock. What volume is needed?

A hint to get started

Dilution conserves solute amount.

Step-by-step solution
  1. c₁V₁ = c₂V₂.
  2. V₁ = 0.2 × 100/1 = 20 mL.
  3. Take 20 mL and make up to 100 mL final volume, rather than adding 100 mL water.

Which step did you miss? Retry without help, then explain why the method works.

04 · Go furtherLink to this exercise

A 0.1 mol/L solution has solute molar mass 60 g/mol. Find mass concentration.

A hint to get started

Multiply molar concentration by molar mass.

Step-by-step solution
  1. cm = cM.
  2. cm = 0.1 × 60 = 6 g/L.
  3. g/L and mol/L describe the same solution using different quantities.

Which step did you miss? Retry without help, then explain why the method works.

The trap to avoid

Final volume is not solvent volume added; follow the supervised experimental protocol.

Without notes, can you…

  • Explain the principle in your own words?
  • Rebuild the diagram and its connections?
  • Solve the exercise and justify the method?

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