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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 C₁x 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) =1mg/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.