One of the most common equations used in dilution calculations is C1V1 = C2V2 where C1 and C2 are the original and new solution concentrations respectively and V1 and V2 are the original and new volumes respectively. Knowing 3 of the measurements allows for the 4th to be calculated. These equations can be used to:
- Determine the final concentration of a solution based on a known original volume and known original concentration with a given volume increase of the final solution. C1 x V1 = C2 x V2
- Determine the final volume of a solution based on a known original volume and known original concentration with a given concentration decrease of the final solution. C1 x V1 = C2 x V2
- Determine the original concentration of a solution with a known final volume and known final concentration with a known volume of the original solution. C1 x V1 = C2 x V2
- Determine the original volume of a solution with a known final volume and known final concentration with a known volume of the original solution. C1 x V1 = C2 x V2
Let's go through an example:
A patient serum sample has an original concentration of testosterone of 1500 ng/dL which is outside the range of the immunoassay and needs to be diluted. If 0.50 mL of that serum is available to use, what final volume of diluted material would be needed to create a diluted result of 150 ng/dL testosterone?
- Identify the concentrations and volumes that are known.
- C1 = 1500 ng/dL, V1 = 0.50 mL, and C2 = 150 ng/dL
- We do not know what the final volume (V2) is and will need to calculate it.
- Arrange your measured values using C1 x V1 = C2 x V2 as shown in step 1 of the image.
- Perform multiplication of the measured C1 and V1 while leaving both sets of units unchanged (see step 2).
- Note as long as the two known concentrations or two known volumes have the same units, they will cancel out and leave the final concentration or volume units.
- To isolate the final volume (V2), divide both sides of the equation by the final concentration (C2) (see step 3).
- Concentrations and their units cancel and what is left after the calculation is the unknown final volume equaling 5.0 mL (see step 4).
- To calculate the amount of diluent needed, subtract the total final volume by the original volume of serum to get 4.5 mL of diluent needed (see step 5).
Based on that calculated final volume and known original volume of material, what dilution would need to be implemented?
- Dividing the diluent needed by the original sample volume of the serum sample equals 9 which means 9 parts of diluent are needed for every 1 part of serum which is a 1 to 10 dilution (see step 6).
