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General Chemistry I · Aqueous Reactions

Dilution

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

Dilution is adding more solvent to a solution, which lowers its concentration while keeping the number of moles of solute unchanged. Because moles of solute before dilution equal moles after (n₁ = n₂), and n = M × V, we get the dilution equation M₁V₁ = M₂V₂: the product of molarity and volume is constant. Dilution is how chemists take a concentrated stock solution and produce a weaker working solution safely and precisely.

Why this matters

Dilution is routine in every lab, clinic, and factory: pharmacists dilute stock drugs to patient doses, technicians dilute concentrated reagents for assays, and water-treatment operators adjust chemical dosing. A dilution error — using the wrong volume or confusing solvent with solution volume — can mean an ineffective or dangerously concentrated result, so the M₁V₁ = M₂V₂ check is a daily safety calculation.

The college version

Key Ideas

The conservation of moles

  • Adding solvent changes the volume and concentration, but the solute particles are the same — none are added or removed.
  • n(before) = n(after), i.e., M₁V₁ = M₂V₂.

Deriving the equation

  • Moles = Molarity × Volume: n₁ = M₁V₁ and n₂ = M₂V₂.
  • Since n₁ = n₂, we set M₁V₁ = M₂V₂.

Stock vs. working solution

  • Stock solution: concentrated, stored for repeated use.
  • Working solution: diluted from stock for the actual experiment.
  • Always add concentrated stock to water (never water onto concentrated acid) for safety.

Equations and Variables

  • Dilution equation: M₁V₁ = M₂V₂
    • M₁, V₁ = initial molarity and volume; M₂, V₂ = final molarity and volume.
  • Volume units may be mL or L, as long as they match on both sides.

How It Works (Problem-Solving Method)

  1. Identify the three knowns among M₁, V₁, M₂, V₂.
  2. Check that units match (both volumes in mL, or both in L).
  3. Rearrange M₁V₁ = M₂V₂ to solve for the unknown.
  4. Compute the result with correct significant figures.
  5. State the procedure: measure V₁ of stock, then dilute with solvent to total volume V₂.

Worked Example

What volume of 6.0 M HCl stock is needed to prepare 250.0 mL of 0.50 M HCl?

  • Known: M₁ = 6.0 M, M₂ = 0.50 M, V₂ = 250.0 mL. Unknown: V₁.
  • Rearrange: V₁ = M₂V₂ / M₁ = (0.50 M × 250.0 mL) / 6.0 M.
  • V₁ = 20.83 mL ≈ 21 mL (to 2 significant figures).
  • Procedure: measure ~21 mL of 6.0 M HCl, then dilute with water to a final volume of 250.0 mL.

Concentration check: Diluting 100.0 mL of 2.00 M NaCl to 500.0 mL:

  • M₂ = M₁V₁ / V₂ = (2.00 M × 100.0 mL) / 500.0 mL = 0.400 M. (Five-fold dilution → one-fifth the concentration.)

Common Confusions

  • "Dilution reduces the number of moles of solute." — No; moles are conserved. Only the concentration falls.
  • "V₂ is the volume of water added." — V₂ is the final total solution volume. The water added = V₂ − V₁.
  • "M₁V₁ = M₂V₂ works only in liters." — Any matching volume units work (mL with mL), because the units cancel.
  • "You can mix M and mL arbitrarily." — The equation still holds dimensionally (both sides are mol·(mL/L)·L), but keep the same volume unit on both sides to avoid slip-ups.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a cup of strong orange juice concentrate. If you pour it into a bigger pitcher and add water, the juice gets weaker — but you didn't remove any orange. The "orange-ness per cup" (concentration) went down, while the total orange stayed the same. The dilution equation just says: strength × amount = strength × amount, before and after. The catch: the final "amount" is the whole pitcher after adding water, not just the water you poured — same "solution volume, not solvent volume" rule from molarity.

Key takeaways

  • Dilution conserves moles of solute: n₁ = n₂.
  • M₁V₁ = M₂V₂ (units must match).
  • Concentration drops; moles stay constant.
  • V₂ = V₁ + solvent added (final solution volume).
  • Stock solution is concentrated; working solution is the diluted one.
  • Moles conserved during dilution: n₁ = n₂.
  • Dilution equation: M₁V₁ = M₂V₂.
  • V₂ is final solution volume, not added solvent.
  • Solve for the unknown, keeping volume units consistent.

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Define dilution and explain that it conserves moles of solute.
  • Derive and apply the dilution equation M₁V₁ = M₂V₂.
  • Calculate the volume of concentrated stock solution needed to prepare a dilute solution.
  • Explain why dilution lowers concentration but not the amount of solute.

Sources & references

  1. Chemistry LibreTexts, "13.7: Solution Dilution."
  2. OpenStax, "3.3 Molarity." *Chemistry 2e*.
  3. Chemistry LibreTexts, "13.6: Specifying Solution Concentration — Molarity."

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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