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Solutions & Dilutions

Concentration, molarity, and the dilution equation

Ten drops of ink in a bathtub still color the water — barely. Nothing about the ink changed; what changed is how much water each ink molecule has to share itself with. Concentration is not how much stuff you have, it's how crowded the stuff is. Today you learn the cleanest conservation law in chemistry: pour in all the water you want, and the solute simply refuses to leave. Only the crowding changes.

What you'll be able to do

  • Define molarity as moles per liter and distinguish amount of solute from concentration (crowding)
  • Apply C₁V₁ = C₂V₂ as a conservation statement (solute moles unchanged) to compute dilution outcomes
  • Reason through serial dilution as repeated multiplication of a fixed dilution factor

Formulas

C1V1=C2V2C_1 V_1 = C_2 V_2
Dilution equation: initial concentration × initial volume = final concentration × final volume
M=nV=moles of soluteliters of solutionM = \frac{n}{V} = \frac{\text{moles of solute}}{\text{liters of solution}}
Molarity (M) is moles of solute per liter of solution

Make a prediction

You have 10 mL of deep-blue 1.0 M CuSO₄. You pour in 90 mL of pure water — nothing removed, only water added. What happens to the concentration?

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Your prediction

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Answer: It drops to 0.1 M — same solute, ten times the volume

Concentration counts crowding: moles per liter. Pouring in water removes no solute (still 0.01 mol), but the total volume grows from 10 mL to 100 mL — ten times the room for the same particles. C₁V₁ = C₂V₂: (1.0)(10) = C₂(100), so C₂ = 0.1 M. The equation is just 'nothing escapes' written in symbols. And the trap detail: V₂ is the TOTAL volume, not the water you added.

Quiz (0/3)

If you have 50 mL of 2.0 M CuSO₄ and add 50 mL of water, what is the final concentration?

How much water must you add to 10 mL of 1.0 M solution to make 0.1 M?

After 3 serial 1:10 dilutions starting from 1.0 M, what is the final concentration?

You can now

  • Define molarity as moles per liter and distinguish amount of solute from concentration (crowding)
  • Apply C₁V₁ = C₂V₂ as a conservation statement (solute moles unchanged) to compute dilution outcomes
  • Reason through serial dilution as repeated multiplication of a fixed dilution factor

Step-by-step

  1. Select a solute and set the initial concentration with the slider.
  2. The beaker shows the solution color intensity corresponding to molarity.
  3. Add water with the slider to dilute — watch the color fade as concentration drops.
  4. The readout panel shows both predicted (C₁V₁/V₂) and actual concentration in real time.

Key formulas

  • C1V1=C2V2C_1 V_1 = C_2 V_2Dilution equation: initial concentration × initial volume = final concentration × final volume
  • M=nV=moles of soluteliters of solutionM = \frac{n}{V} = \frac{\text{moles of solute}}{\text{liters of solution}}Molarity (M) is moles of solute per liter of solution

Frequently asked questions

If you have 50 mL of 2.0 M CuSO₄ and add 50 mL of water, what is the final concentration?
C₂ = C₁V₁/V₂ = (2.0)(50)/(100) = 1.0 M.
How much water must you add to 10 mL of 1.0 M solution to make 0.1 M?
V₂ = C₁V₁/C₂ = (1.0)(10)/(0.1) = 100 mL → add 90 mL water.
After 3 serial 1:10 dilutions starting from 1.0 M, what is the final concentration?
Each 1:10 dilution divides by 10: 1.0 → 0.1 → 0.01 → 0.001 M.