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Solutions and mixtures

Diluting a solution feels like you are adding something, but you are really just spreading the same solute through more liquid. Hold that idea — the moles of solute never change — and every dilution problem becomes one line of algebra.

§1

Concentration and dilution.

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The concentration of a solution is its molarity: moles of solute divided by liters of solution (not liters of solvent). A 2.0 M solution has 2.0 moles of solute in every liter of solution.

Diluting means adding solvent. The solute is spread through a larger volume, so the concentration drops — but the moles of solute stay the same. Nothing is added or removed except solvent.

Because moles are conserved, M₁V₁ = M₂V₂: the moles before (M₁V₁) equal the moles after (M₂V₂). This one relationship handles every dilution.

UNIT 3 TOPIC 3.7 • SOLUTIONS AND MIXTURES DILUTION BENCH Dilution adds pure solvent: solute stays the same, volume increases, concentration decreases. BEFORE DILUTION AFTER DILUTION smaller volume · higher conc. ADD SOLVENT pure solvent (no solute) larger volume · lower conc. CONCENTRATION COMPARISON (particle density) CONCENTRATED DILUTED MOLARITY EQUATION M = moles of solute liters of solution DILUTION EQUATION M₁V₁ = M₂V₂ M₁ = initial molarity V₁ = initial volume M₂ = final molarity V₂ = final volume COMMON MISTAKE Dilution does NOT add more solute. It adds solvent. CED ANCHOR Topic 3.7 · molarity relates moles of solute to volume. 1 Keep solute the same. 2 Add solvent (not solute). 3 Volume ↑ → molarity ↓. M₁V₁ = M₂V₂ moles of solute unchanged AP Chemistry · Unit 3 · Properties of Substances & Mixtures
Fig. 3.7.1 Molarity is moles of solute per liter of solution. Diluting adds pure solvent: the volume grows and the concentration drops, but the moles of solute are unchanged — which is why M₁V₁ = M₂V₂ works.
§2

Working a dilution.

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Anchor on the fixed quantity: moles of solute.

  1. Note molarity is per liter of solution. Molarity uses the total solution volume, not just the solvent added.
  2. Recognize what stays fixed. On dilution, the moles of solute do not change; only volume and concentration do.
  3. Apply M₁V₁ = M₂V₂. Set the initial moles equal to the final moles and solve for the unknown.
  4. Check the direction. Adding solvent must lower the concentration and raise the volume. If your answer says otherwise, recheck.
§3

The pieces you'll meet.

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A few definitions run every solution problem.

M
Molarity
Moles of solute per liter of solution.
solute
Solute
The substance dissolved; its moles are conserved on dilution.
solvent
Solvent
The dissolving medium; adding it dilutes the solution.
dilution
Dilution
Adding solvent to lower concentration; moles of solute unchanged.
M1V1
M₁V₁ = M₂V₂
Moles before equal moles after — the dilution equation.
solution
Solution volume
The total volume used in molarity, not the solvent volume alone.
§4

Worked example: diluting a stock solution.

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Question. You have 50.0 mL of 6.0 M HCl. You dilute it to a total volume of 300.0 mL. What is the new molarity?

Fixed quantity. The moles of HCl do not change: only water is added.

Apply M₁V₁ = M₂V₂. (6.0 M)(50.0 mL) = M₂(300.0 mL).

Solve. M₂ = (6.0 × 50.0) / 300.0 = 1.0 M. The volume grew 6-fold, so the concentration dropped 6-fold — consistent with adding solvent.

§5

Mistakes that cost real points.

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Pitfall · 01

"Adding water to a solution changes the moles of solute."

Diluting adds only solvent; the amount of solute is unchanged. What drops is the concentration, because the same moles are spread through a larger volume. Confusing 'more volume' with 'more solute' breaks the dilution logic.

Fix. Anchor on moles of solute as the conserved quantity. Only the volume and concentration change on dilution.

Pitfall · 02

"Molarity is moles of solute per liter of solvent."

Molarity is per liter of solution — solute plus solvent together — not per liter of solvent. For dilute solutions the difference is small, but the definition uses total solution volume.

Fix. Use the total solution volume in molarity, not the volume of solvent added.

Pitfall · 03

"Doubling the volume by adding water doubles the concentration."

Adding water lowers the concentration; doubling the volume halves the molarity, since the same solute now occupies twice the space. The direction is opposite to what 'adding' might suggest.

Fix. Remember dilution lowers concentration. More volume with the same solute means a smaller molarity, by M₁V₁ = M₂V₂.

§6

Skill Check.

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