What stays the same when we dilute a solution?
You will be able to: Use conserved solute amount to plan a dilution and interpret a concentration change.
What stays the same when we dilute a solution?
Adding water to a fixed amount of colored solution makes its color lighter. The dissolved substance is spread through more volume; adding water alone does not remove its molecules.
A useful starting point: How much solute is in each liter of solution? →
Words and symbols before equations
- Dilution
- Decreasing concentration by adding solvent.
- Aliquot
- A measured portion taken from a solution.
- Stock solution
- A solution of known concentration used to prepare another.
- Final volume
- Volume of the entire diluted solution, not just added water.
What this picture assumes
A fixed 0.100 mol of intact solute, initially in 0.250 L (0.400 M). Only solvent is added; no solute loss or reaction. Final volume, not added-water volume, is controlled.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- n = 0.1 mol; final V = 0.5 L; M = 0.2 mol/L; 6.022e+22 molecules total.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
If no solute is lost, added or chemically changed, n before equals n after. Combining this conservation statement with n = MV gives M₁V₁ = M₂V₂.
Use the volume of the stock aliquot for V₁, not the full stock bottle. V₂ is the final solution volume. Use compatible volume units on both sides.
A practical preparation measures the aliquot, transfers it, then adds solvent to the specified final-volume mark. A diluted solution can have fewer particles per sample-sized box while the total solute in the full container stays fixed.
A worked example, step by step
Prepare 100.0 mL of 0.100 M solution from 0.500 M stock. What stock volume is needed?
- Conserve solute: MstockVstock = MfinalVfinal.
- Vstock = (0.100 M)(100.0 mL)/(0.500 M) = 20.0 mL.
- Measure 20.0 mL of stock and dilute to a final volume of 100.0 mL.
- The final solution contains 0.0100 mol. Do not interpret 100.0 mL as the amount of water to add.
Dilute to the final volume. “Add 100 mL water” and “make 100 mL solution” are different instructions.
Can M₁V₁ = M₂V₂ be used without adjustment if some solute reacts away?
Compare with an explanation
No. Its simple form assumes the amount of the specified solute is conserved.
Predict. Change one thing. Explain.
Increase final volume while holding the initial 0.100 mol of solute fixed. Compare the molarity readout and the unchanged total-amount label.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
n = 0.1 mol; final V = 0.5 L; M = 0.2 mol/L; 6.022e+22 molecules total.
A fixed 0.100 mol of intact solute, initially in 0.250 L (0.400 M). Only solvent is added; no solute loss or reaction. Final volume, not added-water volume, is controlled.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using particle interactions, concentration, gas behavior or energy transfer. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionFind the stock volume needed to make 250.0 mL of 0.0400 M solution from 0.200 M stock. State the preparation instruction and the conserved solute amount.
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Compare with the answer and four-point rubric
- 1 point: Use Vstock = MfinalVfinal/Mstock.
- 1 point: Vstock = 0.0400 × 250.0/0.200 = 50.0 mL.
- 1 point: Transfer 50.0 mL stock and add solvent to 250.0 mL final volume.
- 1 point: Both the aliquot and final solution contain 0.0100 mol of the specified solute.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is conserved during simple dilution?
The amount of the specified solute.
RECALL 2What is an aliquot?
A measured portion of a solution.
RECALL 3Does dilution always decrease concentration?
Adding solvent at unchanged solute amount increases volume and decreases molarity.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
What stays the same when we dilute a solution?
- M₁V₁ = M₂V₂ when solute amount is conserved.
- Dilution changes concentration; it does not automatically change solute moles.
Remember: Dilute to the final volume. “Add 100 mL water” and “make 100 mL solution” are different instructions.
Conditions: A fixed 0.100 mol of intact solute, initially in 0.250 L (0.400 M). Only solvent is added; no solute loss or reaction. Final volume, not added-water volume, is controlled.
Refresh Kid · AP Chemistry Unit 3 · Objectives 3.7.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.7, objective 3.7.A. CED effective Fall 2024 and June 2026 clarifications checked September 16, 2026. Unit 3: Properties of Substances and Mixtures, Topics 3.1–3.13. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Colligative-property calculations and solution molality/mass-percent/volume-percent calculations are not required here. The optional speed-density model illustrates distributions; it does not require memorizing its mathematical derivation.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
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