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bondistry

Dilution calculator

Use C₁V₁ = C₂V₂ to prepare a solution of the concentration you need from a stock; enter three values and the fourth is calculated instantly.

↑ calculated

RESULT · V₁

62.5mL

To prepare: measure 62.5 mL of the stock solution into a volumetric flask and add solvent up to a total volume of 250 mL (about 187.5 mL of solvent).

Step-by-step solution

  1. 01
    Diluting does not change the number of moles of solute: C₁ × V₁ = C₂ × V₂
  2. 02
    Convert the values to M and L:C₁ = 2 MC₂ = 0.5 MV₂ = 250 mL = 0.25 L
  3. 03
    Isolate the unknown: V₁ = C₂ × V₂ / C₁
  4. 04
    Substitute the values: V₁ = 0.5 M × 0.25 L / 2 M = 0.0625 L
  5. 05
    Convert to your chosen unit: 0.0625 L = 62.5 mL

What is a dilution?

Diluting means lowering the concentration of a solution by adding more solvent, usually water. Laboratories keep solutions as concentrated stocks; the weaker solution needed for an experiment is made by taking a measured volume of stock and diluting it. This avoids weighing out solid every time and reduces error.

During a dilution the amount of solute does not change — it is simply spread over a larger volume. The number of moles at the start therefore equals the number of moles at the end.

How to use the C₁V₁ = C₂V₂ formula

The number of moles is concentration times volume (n = C × V). Because it stays the same, C₁ × V₁ = C₂ × V₂. Here C₁ is the stock concentration, V₁ the volume of stock to take, C₂ the concentration you want and V₂ the final volume. When you know three of the four, rearrange the equation for the missing one.

The key rule is consistent units: both concentrations must be in the same unit (for example both in mM) and both volumes in the same unit (for example both in mL). Bondistry first converts your chosen units to M and L, does the calculation and shows the result in the unit you picked, so you can freely mix µM with M or µL with mL.

To make the solution, measure V₁ of stock into a volumetric flask and add solvent until the total volume reaches V₂. The solvent added is roughly V₂ − V₁. Because volumes do not always add up exactly when liquids mix, “make up to V₂” is more accurate than “add V₂ − V₁ of water”.

Things to watch out for

In a dilution the final concentration is always lower than the starting one. If your calculation gives C₂ > C₁, a value was probably entered incorrectly. When diluting acids, always add acid to water, never water to acid.

Worked examples

Example 1

Volume of stock to take

How many mL of a 2 M NaOH stock do you need to make 250 mL of a 0.5 M solution?

  1. 01Known: C₁ = 2 M, C₂ = 0.5 M, V₂ = 250 mL. Unknown: V₁.
  2. 02V₁ = C₂ × V₂ / C₁ = 0.5 M × 250 mL / 2 M
  3. 03V₁ = 62.5 mL
  4. 04To prepare: measure 62.5 mL of stock into a volumetric flask and make up to 250 mL with water (about 187.5 mL of water).

Answer:V₁ = 62.5 mL

Example 2

Concentration after diluting

10 mL of 1 M HCl is diluted with water to 100 mL. What is the final concentration?

  1. 01Known: C₁ = 1 M, V₁ = 10 mL, V₂ = 100 mL. Unknown: C₂.
  2. 02C₂ = C₁ × V₁ / V₂ = 1 M × 10 mL / 100 mL
  3. 03C₂ = 0.1 M = 100 mM

Answer:C₂ = 0.1 M (100 mM)