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How to dilute a stock solution correctly

How to prepare a diluted solution from a concentrated stock, work out the volume to pipette, and avoid the common C1V1 = C2V2 mistakes.

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Why the C1V1 = C2V2 rule works

A dilution adds solvent without adding or removing solute, so the total amount of dissolved material is conserved. Concentration times volume equals that amount, which is why C1 x V1 must equal C2 x V2 before and after you add water or buffer. The concentration falls only because the same solute now occupies a larger volume. Once you see the equation as a statement of conservation, rearranging it for any one of the four terms feels natural rather than memorised.

Working out the volume to pipette

The most common question in the lab is how much stock to draw up. Rearrange the rule to V1 = C2 x V2 / C1, plug in your target concentration and volume, and read the stock volume. Pipette that amount into your vessel first, then bring the level up to the final volume V2 with solvent, rather than adding solvent and then stock. Adding stock to a partly filled vessel and topping up last keeps the final volume exact and avoids overshooting.

Keeping units consistent

The equation does not care whether you work in molar, milligrams per millilitre, percent, or fold concentrations such as 5x buffer. It only requires that C1 and C2 use the same concentration unit and that V1 and V2 use the same volume unit. Mixing millilitres with microlitres, or molar with millimolar, is the single most frequent source of a wrong answer. Convert everything to one scale before you calculate, and the numbers take care of themselves.

Serial dilutions step by step

When one dilution cannot reach a very low concentration accurately, chain several smaller ones. Prepare the first dilution, then treat its final concentration as the stock for the next tube, and repeat. A tenfold serial dilution, for instance, carries a fixed volume into fresh solvent at each step, dropping the concentration by ten each time. Applying the single-step calculation down the row lets you plan every tube and predict the concentration at any point in the series.

Frequently asked questions

Should I add solvent to stock, or stock to solvent?

For most aqueous dilutions, add the stock to the vessel and then bring it up to the final volume with solvent. This makes the final volume precise. The exception is concentrated acids, where you always add acid to water to control the heat released.

How do I make a percentage dilution?

Treat the percentage as the concentration. A 10 percent stock diluted to 2 percent in 50 mL needs V1 = 2 x 50 / 10 = 10 mL of stock, topped up to 50 mL. The same C1V1 = C2V2 rule applies to any concentration unit.