C1V1 = C2V2 Calculators

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The dilution formula C1V1 = C2V2 is used to calculate the volume of a stock solution needed to prepare a diluted solution of a specific target concentration. C1 = initial (stock) concentration; V1 = volume of stock to use; C2 = final (desired) concentration; V2 = total final volume. This equation is derived from conservation of moles of solute: moles before dilution = moles after dilution. It applies to any unit of concentration (molarity, mass/volume %, ppm) as long as the same units are used consistently on both sides. It is one of the most frequently used calculations in laboratory science.

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C1V1 = C2V2 Formula

C1 × V1 = C2 × V2

Solve for any unknown: V1 = (C2 × V2) / C1. Example: prepare 500 mL of 0.1 M NaCl from a 5.0 M stock: V1 = (0.1 × 500) / 5.0 = 10 mL. Add 10 mL of 5.0 M stock to a volumetric flask; bring to 500 mL total volume with water.

Key Points

  • Units must be consistent: C must be in same units on both sides; V must be in same units on both sides (but C and V units can differ from each other)
  • Solutes are not created or destroyed — only diluted
  • V2 is the TOTAL final volume, not the volume of water added
  • Dilution factor = C1/C2 = V2/V1

Serial Dilutions

For serial dilutions: concentration at step n = C₀ × (dilution factor)^n. Example: 1:10 serial dilution from 1 M: Step 1: 0.1 M; Step 2: 0.01 M; Step n: 10^(−n) M.

Practice Examples

Example 2: prepare 200 mL of 3% H₂O₂ from 30% stock: V1 = (3 × 200) / 30 = 20 mL of 30% stock → add water to 200 mL. Example 3: dilute 50 mL of 2 M HCl with 150 mL water: C2 = (2 × 50) / (50+150) = 0.5 M.

Glossary

C1V1 = C2V2
The dilution equation: initial concentration × initial volume = final concentration × final volume; based on conservation of moles; solve for V1 = (C2×V2)/C1 to find stock volume needed.
Dilution Factor
C1/C2 = V2/V1; the factor by which concentration is reduced; 10-fold dilution = dilution factor of 10; applied repeatedly in serial dilutions: Cn = C₀ × (dilution factor)^(−n).
Stock Solution
A concentrated solution from which working solutions are prepared by dilution; characterized by C1 in C1V1 = C2V2; prepared accurately once and stored; diluted as needed to working concentrations.

Frequently Asked Questions

C1V1 = C2V2 calculates how to dilute a concentrated stock solution to a desired lower concentration. C1 = starting (stock) concentration; V1 = volume of stock solution to take; C2 = desired final concentration; V2 = desired total final volume. The formula is based on conservation of solute moles: n = C × V = constant during dilution. Used whenever: preparing a working solution from a stock; calculating the resulting concentration from mixing; designing serial dilution experiments; converting between concentration units after adding diluent.

Step 1: Identify the known values (usually C1, C2, V2). Step 2: Solve for V1 = (C2 × V2) / C1. Step 3: Measure V1 of the stock solution. Step 4: Transfer to a volumetric flask. Step 5: Add diluent to reach V2 total volume. Example: 100 mL of 0.25 M glucose from a 2.0 M stock: V1 = (0.25 × 100) / 2.0 = 12.5 mL. Pipette 12.5 mL of 2.0 M glucose into a 100 mL volumetric flask; add water to the 100 mL mark. Critical: V2 is the total final volume, not the volume of water added separately (V_water = V2 − V1).

In serial dilutions, each step applies C1V1 = C2V2 where V2 is the new tube volume and the dilution factor = V₁/V₂ = volume transferred / total volume. Example: 1:10 serial dilution — transfer 1 mL into 9 mL diluent → dilution factor 10⁻¹ each step. Starting from 10⁶ CFU/mL: After step 1: 10⁵ CFU/mL. After step 2: 10⁴. After step n: 10^(6−n) CFU/mL. Concentration at step n = C₀ × (dilution factor)^n. This applies to: microbiology (CFU counting), pharmacology (dose-response curves), chemistry (standard curve preparation).

Mistake 1: Confusing V2 (total final volume) with volume of water added. V2 = total; water to add = V2 − V1. Example: to make 100 mL at 0.1 M from 1.0 M stock: V1 = 10 mL of stock; add 90 mL water (not 100 mL). Mistake 2: Using inconsistent units. C1 must be in the same units as C2; V1 in the same units as V2 — but C units and V units don't need to match each other. Mistake 3: Applying C1V1 = C2V2 when mixing two different solutions with different solutes — the formula applies only when the same solute is being diluted. Mistake 4: Not accounting for density changes in very concentrated solutions — significant when mixing highly concentrated acids or bases.