Explicit science instruction
During an ideal dilution, solvent is added while the amount of solute remains constant. That leads to M₁V₁=M₂V₂ when both concentration terms use compatible units.
The equation is not a universal chemistry identity; it applies when solute amount is conserved between the initial aliquot and final diluted solution.
Always check direction: dilution increases volume and decreases concentration. If the calculation predicts both increasing, revisit the setup.
Vocabulary: dilution; aliquot; conserved solute; concentration; final volume.
Worked example with reasoning
25.0 mL of 2.0 M stock is diluted to 100.0 mL. M₂=(2.0×25.0)/100.0=0.50 M.
Guided question
A 10.0 mL sample of 1.5 M solution is diluted to 75.0 mL. Calculate the final molarity and perform a direction check.
Independent work
- Solve three dilution problems.
- For one, solve backward for required stock volume.
- Write the conservation statement that justifies M₁V₁=M₂V₂.
Misconception check
Dilution does not remove solute; it changes concentration by changing total volume.
Formative understanding check
Why does concentration fall during dilution even though solute moles stay constant?
Reveal response
The same solute amount is distributed through a larger solution volume.
Mentor evidence conference
Ask Archaemenes to check unit conversions, model choice, and whether the calculation matches the particle story.
Teacher guidance
Foundation: Use a before/after table.
Core: Solve forward and reverse dilution problems.
Extended: Identify cases where reaction or precipitation would invalidate the simple dilution model.