Dilution: One Equation, and Knowing When to Do It in Steps

Diluting does not change how much solute you have — only how much solvent it is spread through. That single fact is the whole of dilution arithmetic, and it is why C1V1 = C2V2 works: both sides are the same number of moles. The practical question is not the arithmetic but whether to do it in ONE step or several. A hundredfold dilution in one step means measuring 1 mL accurately and making it up to 100 mL, and 1 mL is right at the limit of what most glassware measures well. Two steps of ten give the same result while measuring 10 mL twice — a volume that is measured far more accurately. That is the entire reason serial dilution exists, and the arithmetic below shows exactly how much it buys.

初学者

2 hours

说明

C1V1 = C2V2, and what each letter is

C1 is the concentration you are starting from and V1 the volume of it you will take. C2 is the concentration you want and V2 the final volume you will make it up to. Rearranged, V1 = C2 x V2 / C1. V2 is the FINAL volume, not the amount of solvent added. Making 100 mL of diluted solution from 10 mL of stock means adding about 90 mL of solvent, not 100 — and treating V2 as the solvent added is the commonest error here. It works in any units as long as both concentrations match and both volumes match. Percent, mol/L, g/L, parts per million — the equation does not care, because it is only saying that the amount of solute is unchanged.

此步骤所需材料：

蒸馏水1 升

所需工具：

计算器

容量瓶

Take the aliquot with a pipette, make up in a flask

Measure V1 with a pipette or burette — volumetric glassware — and make up to V2 in a volumetric flask. Both numbers appear directly in the result, so both need to be measured rather than estimated. Rinse the pipette with the stock solution before use, not with water. A pipette wet with water dilutes the very aliquot it is about to measure, and the error is invisible. Deliver by touching the pipette tip to the inside wall of the flask and letting it drain, then touch off. Do not blow out the last drop of a bulb pipette: it is calibrated to deliver with that drop still in it.

此步骤所需材料：

蒸馏水1 升

所需工具：

带刻度移液管（莫尔式）

容量瓶

滴定管（玻璃）

实验室夹（滴定管/烧瓶）

One big step or several small ones

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此步骤所需材料：

蒸馏水1 升

所需工具：

带刻度移液管（莫尔式）

容量瓶

台式电脑

计算器

Label every intermediate, and keep the stock

Each step in a serial dilution is a solution in its own right and needs its own label. A bench with four unlabelled beakers of clear liquid differing thousandfold in concentration is a problem waiting to happen. Write the dilution factor as well as the concentration: "0.001 M NaCl, 1:1000 from 1 M stock, 3 x 10-fold". That records how it was made, so a suspect result can be traced to a step rather than re-done from scratch. Keep the stock solution and the intermediates until the work is finished and checked. Throwing them away the moment the final dilution exists means a disagreement can only be resolved by starting again.

此步骤所需材料：