Dilution Calculator

The Dilution Equation

C₁ × V₁ = C₂ × V₂

Where:

• C₁ — concentration of the stock (concentrated) solution.
• V₁ — volume of stock solution needed.
• C₂ — concentration of the diluted (target) solution.
• V₂ — final volume of the diluted solution.

Rearranging to solve for the stock volume:

V₁ = (C₂ × V₂) ÷ C₁

This works for any concentration unit as long as C₁ and C₂ use the same units, and any volume unit as long as V₁ and V₂ use the same units.

Worked Examples

Example 1: Dilute 1 M stock to 0.1 M

Prepare 500 mL of 0.1 M solution from a 1 M stock.

1. V₁ = (0.1 × 500) ÷ 1 = 50 mL.
2. Transfer 50 mL of stock into a 500 mL volumetric flask.
3. Dilute to the 500 mL mark with solvent.

Result: 50 mL of 1 M stock diluted to 500 mL gives 0.1 M.

Example 2: Dilute 10× buffer to 1×

Prepare 1 L of 1× buffer from a 10× stock.

1. V₁ = (1 × 1000) ÷ 10 = 100 mL.
2. Combine 100 mL of 10× stock with 900 mL of water.

Result: 100 mL of 10× stock + 900 mL water = 1 L of 1× buffer.

Example 3: Prepare a very dilute solution

Prepare 100 mL of 0.001 M solution from a 0.1 M stock.

1. V₁ = (0.001 × 100) ÷ 0.1 = 1 mL.
2. Add 1 mL of stock to a 100 mL volumetric flask.
3. Dilute to the 100 mL mark.

Result: 1 mL of stock diluted to 100 mL gives 0.001 M.

Example 4: Serial dilution

To go from 1 M to 10⁻⁶ M, you can do a series of 1:10 dilutions. Each step:

1. Take 1 mL of the previous solution, add 9 mL of solvent → 1:10 dilution.
2. Repeat 6 times to reach 10⁻⁶ M.

Serial dilution reduces error accumulation compared to a single large dilution, especially for high dilution factors.

The Dilution Factor

The dilution factor (DF) is the ratio of the final volume to the stock volume:

DF = V₂ / V₁ = C₁ / C₂

Common dilution factors:

Note: "1:N" ratio means 1 part of the original solution plus (N−1) parts of diluent, resulting in a total of N parts. This convention differs from the DF concept — the DF is the ratio of final volume to stock volume, which is N.

Practical Lab Technique

• Use a volumetric flask. For accurate results, measure the final volume with a volumetric flask, not a graduated cylinder. Volumetric flasks are calibrated to a specific volume at a specific temperature (usually 20 °C).
• Add solute first, then dilute. Add the stock solution to the flask, then add solvent up to the mark. Adding the stock to already-filled solvent can cause inaccurate volume if the solute changes volume (which happens with salts).
• Mix thoroughly. After filling to the mark, invert the flask several times to ensure complete mixing.
• Temperature matters. Volumetric flasks are calibrated at 20 °C. If your lab is significantly warmer or colder, either let the flask equilibrate or use a volumetric flask calibrated at your working temperature.
• Serial dilutions for large factors. To dilute by 10,000×, do two 1:100 dilutions rather than a single 1:10000 — the error accumulates much less.
• Record everything. Note the stock concentration, the volume taken, the final volume, and the dilution factor in your lab notebook.

Common Applications

• Preparing working solutions: Antibiotics, buffers, and reagents are often shipped concentrated and diluted before use.
• Standard curves: Preparing a series of known concentrations for calibration requires careful dilution.
• Sample preparation: Environmental, clinical, and food samples are often diluted to bring them into the analytical range of an instrument.
• Cell culture: Media components and drugs are diluted to working concentrations from stocks.
• Home use: Cleaning products, pool chemicals, and garden fertilizers often specify dilution ratios.

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