Dilution Calculator

Adjust parameters and observe how the result changes in real time · C₁·V₁ = C₂·V₂

Unknown

Parameters

Initial concentration

Concentration of the concentrated stock solution

0.0120

Initial volume

Volume to take from the stock solution

12000

Final concentration

Target concentration after dilution

0.0120

FD = \frac{C_1}{C_2} = 1:2.50

≈ 1 part stock + 1.5 parts solvent

Results

Final volume (V₂)

250

Solvent to add

150

Unit of V₂:

Volume comparison

Stock Sol.

Diluted Sol.

Fundamentals & Explanation

Dilution Law

C_1 \cdot V_1 = C_2 \cdot V_2

$C_1, V_1$ — concentration and volume of the stock solution.
$C_2, V_2$ — concentration and volume of the final diluted solution.

Solving for the unknown

V_2 = \frac{C_1 \cdot V_1}{C_2}

Algebraic rearrangement of the dilution law to isolate the variable you are solving for ( $V₂$ ).

Dilution Factor (DF)

DF = \frac{C_1}{C_2} = \frac{V_2}{V_1}

Dimensionless ratio telling you how many times the original concentration has been diluted. It also reads as a 1 : (DF − 1) ratio — 1 part stock per (DF − 1) parts solvent —, as shown under the result. It is the basis for planning serial dilutions in microbiology and biochemistry.

1. Why it works: mass is conserved

Diluting means adding solvent without touching the solute: the amount of solute (moles or mass) stays constant ( $n_1 = n_2$ ). Since that amount is concentration times volume ( $n = C \cdot V$ ), equating «before» and «after» gives $\;C_1 V_1 = C_2 V_2$ directly. The whole calculator is, at heart, this single mass balance.

2. The additive-volumes trap

On paper, the solvent to add is $V_2 - V_1$ . But at the bench volumes of real mixtures are rarely additive, because of intermolecular interactions (hydrogen bonding, for instance). Mixing 50 mL of ethanol with 50 mL of water yields ~96 mL, not 100 mL, due to the contraction of partial molar volumes.

Correct technique: never measure the solvent to add. Take

V_1

and add solvent until you make up to volume (reach the calibration mark) of the final volume

V_2

in a volumetric flask.

3. Heat of dilution ( $\Delta H_{\text{mix}}$ ) and safety

Diluting highly concentrated solutions —especially strong acids and bases— is not thermally neutral: ion hydration releases a large amount of heat. To prevent splashing from localized boiling, the golden rule is to always add the concentrated reagent slowly to the solvent, never the reverse («acid to water»).

4. Where the model ends: diluting vs. concentrating

$C_1 V_1 = C_2 V_2$ only describes adding solvent: concentration drops, volume rises. If the inputs imply $C_2 \geq C_1$ or $V_2 \leq V_1$ , the process is no longer a dilution but a concentration, which requires evaporating solvent, adding pure solute, or precipitation — and obeys a different mass balance. The calculator flags this with a warning when the values cross that boundary. To prepare a solution from a concentrated commercial reagent, use the Commercial Solutions & Reagents calculator.

References

[1] IUPAC. Compendium of Chemical Terminology (Gold Book), entries amount concentration and dilution.
[2] Skoog, D. A., West, D. M., Holler, F. J. & Crouch, S. R. (2014). Fundamentals of Analytical Chemistry (9th ed.), Ch. 4. Cengage Learning.
[3] Atkins, P. & de Paula, J. (2014). Physical Chemistry (10th ed.) — partial molar volumes. Oxford University Press.

Dilution Calculator

Parameters

Results

Volume comparison

Fundamentals & Explanation

1. Why it works: mass is conserved

2. The additive-volumes trap

3. Heat of dilution (ΔHmix\Delta H_{\text{mix}}ΔHmix​) and safety

4. Where the model ends: diluting vs. concentrating

References

You may also like:

1. Why it works: mass is conserved

2. The additive-volumes trap

3. Heat of dilution (ΔHmix\Delta H_{\text{mix}}ΔHmix​) and safety

4. Where the model ends: diluting vs. concentrating

References

3. Heat of dilution ( $\Delta H_{\text{mix}}$ ) and safety

3. Heat of dilution ( $\Delta H_{\text{mix}}$ ) and safety