Getting Started in HPLC

Section 4C. Volumetric Dilution

In precise quantitative analysis, we dilute samples by pipetting some volume of sample into a volumetric flask, then filling the flask to the mark with the dilution solvent. Often the dilution solvent will be the mobile phase used in the LC analysis. Dilution can be regarded as taking some quantity of initial sample solution and expanding its volume. Because concentration is defined as (quantity of compound)/(volume of sample solution), expanding the volume of the sample solution will decrease the concentration of all compounds in the original sample. This is another way of describing dilution.

Let's consider an example. Suppose we have an initial sample solution that contains 50 mg/mL of compound "A". Let's dilute the sample 1 to 50, by pipetting 1 mL of sample into a 50 mL volumetric flask and filling to the mark. What is the final concentration?

We have: 1 mL of 50 mg/mL

We want: dilution to 50 mL

Now the question is: what is the final concentration of compound A in the diluted sample? The key to dilution problems is the fact that the total amount of compound A that is diluted - measured in grams or other units of weight - does not change. For example in the above example, we start out with 1 mL of sample that contains 50 mg/mL of compound A. This means we begin with 50 mg of A in the 1 mL of initial sample solution. We can generalize this by proceeding as follows:

concentration of A = (quantity of A) / (volume of solution)

quantity of A = (concentration of A) x (volume of solution)

= (50 mg/mL) x (1 mL)

= 50 mg of A

We can also write for cases of this type:

(initial quantity) = (final quantity) or

C1 x V1 = C2 x V2

Here C1 is the concentration of A in the initial solution and V1 is the volume of that solution (volume of the pipette); C2 is the concentration of A in the final solution (after dilution) and V2 is the volume of final solution (volume of the flask).

Now we have 50 mg of A in the initial 1 mL of sample solution that is pipetted, and the final volume of solution after dilution is 50 mL. So the concentration of A in the final sample solution is:

(quantity of A) / (volume of solution) = (50 mg)/(50 mL)


In solving dilution problems we can proceed in various ways. We can simply calculate a DILUTION FACTOR (DF) as the ratio of the flask volume (V2) to the pipette volume (V1):

DF = V2 / V1

Then from we can write:

C2 = C1 x V1 / V2 = C1 / DF

That is, our final sample concentration C2 is equal to the initial concentration C1 divided by the dilution factor DF. Or we can rearrange into

C2 = C1 x V1 / V2

and solve for the new concentration C2 in terms of the initial concentration (before dilution) C1, the pipette volume V1, and the flask volume V2. You should use whichever of these dilution calculations you feel comfortable with. Most people use the dilution factor approach.



2000, LC Resources Inc. All rights reserved.
Last revised: April 06, 2001.