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.

Pro 🔒~15 min

Solutions & Dilutions

Concentration, molarity, and the dilution equation

How it works

When a solution is diluted by adding solvent, the amount of solute (in moles) remains constant. Only the volume changes, which decreases the concentration proportionally. The dilution equation C₁V₁ = C₂V₂ expresses this conservation: C₁ is the initial molarity, V₁ is the initial volume, C₂ is the final molarity, and V₂ is the final volume (V₁ + added water). Serial dilution is a technique where each step dilutes the previous solution by a fixed ratio, useful for preparing very low concentrations. Color intensity of many solutions is proportional to concentration (Beer-Lambert Law), providing a visual indicator of dilution progress.

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Step-by-step

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

Key formulas

$C_1 V_1 = C_2 V_2$ Dilution equation: initial concentration × initial volume = final concentration × final volume
$M = \frac{n}{V} = \frac{\text{moles of solute}}{\text{liters of solution}}$ 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.