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Solutions and Mixtures

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A solution's concentration is measured as molarity: moles of solute per liter of solution. Diluting a solution means adding solvent, which spreads the same amount of solute through a larger volume, lowering the concentration. Because the moles of solute stay fixed, M₁V₁ = M₂V₂.

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
Molarity is moles of solute per liter of solution. Diluting adds pure solvent: the volume grows, the concentration drops, but the moles of solute are unchanged — which is why M₁V₁ = M₂V₂ works.
Dilution Bench · Open the sandbox →

The confusions are about what changes on dilution: the moles of solute do not change (only the volume and concentration do), and molarity is per liter of solution, not of solvent. Hold the solute amount fixed and the dilution math follows.

The work

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Lesson
Solutions and Dilution ›

Molarity and dilution both hinge on moles of solute staying fixed while volume changes. The lesson works M₁V₁ = M₂V₂ and the meaning of molarity, then closes with a ten-scenario check.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the Topic 3.7 misconceptions: dilution and molarity confusions (what changes when solvent is added), and solubility.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.

Take the diagnostic to identify your misconceptions
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