DILUTIONS AND STANDARDS
Many of the laboratory procedures involve the use of dilutions. It is important to
understand the concept of dilutions, since they are a hand tool used throughout all areas of
the clinical laboratory. These dilutions have to be considered as they make a quantitative
difference in what is going on. First, there are several terms used in expressing dilution:
1. "Dilution: - Dilutions are expressed as the ratio of the quantity of a desired solute (serum,
urine, chemical solution, etc.) contained in a solvent (diluent). A 1:10 dilution of serum was
made by adding one part serum to nine parts diluent to make a total of ten parts. If 1.0
milliliter of serum is added to 9.0 milliliters of H20, a total volume of 10.0 milliliters is obtained.
Therefore, the dilution is expressed according to the following equation.
volume of serum/volume of solution = [1.0 mL serum ]/[1.0 ml serum + 9.0 mL H 20]
1.0 mL serum/10 mL solution = 1:10 total
This means that each milliliter of solution contains 1/10 as much serum as each milliliter of
the original serum. Another way to say this a serum sample was diluted 1:10 with H 20.
One precaution: Some people write ratio meaning the amount of solute in proportion to the
amount of solute. If you are unsure of someone's intent, ask to clarify.
2. "Diluted to" - This is essentially the same as "dilution." If 1 milliliter is diluted to 10 milliliters,
enough diluent is added to the original volume to yield a final, total volume of 10 milliliters.
For example, if a 1 milliliter of serum is diluted to 10 milliliters of solution, 9 milliliters of H 20 is
added to the original serum sample. Using this information, one can see why "diluted to" is
the same as "dilution" using the following equation:
volume of serum/total volume of solution = 1 mL/10mL = 1:10
One milliliter of serum was diluted to 10 milliliters.
3. "Added to" - This expression is usually a hang-up since it is not the same as "diluted to."
"Added to" refers to the volume of the solute added to a specified volume of solvent.
For example, if 1 milliliter of serum is added to 10 milliliters of H20, this means 1 mL + 10 mL
yields a total volume of 11 mL. If you expressed this using one of the above terms you must
say 1 mL was added to 10 mL or 1 mL was diluted to 11 mL. This means a 1/11 dilution was
made since:
volume of serum/total volume of solution = 1 mL serum/[1 mL serum +10 mL H 20] =
1:11
4. "Serial dilution" - This term is frequently used and refers to a "multiple" dilution problem. In
other words, an initial dilution is made and then this dilution is used to make a second
dilution, and so on.
For example, a 1:2 serial dilution is made using a 1 mL volume of serum. This expression
indicates that 1 mL of serum is added to 1 mL of H20 and then mixed. This initial dilution is
1:2. Then, 1 mL of this dilution is added to 1 mL of H20 further diluting the sample. This same
process is continued.
Dilutions must be used carefully and the calculation of dilution factors must be done
accurately, since an error may seriously affect a test result. Read the following material
closely in order to understand the variety of ways dilutions are used.
Preparation of Dilutions
The first rule in performing dilutions is careful reading of procedural instructions. For
example:
"A 1 mL serum specimen diluted to 50 mL is not the same as: "A 1 mL serum specimen
added to 50 mL."
If several dilutions are made in succession of one another, the final dilution can be calculated
by simply multiplying each dilution factor involved. To illustrate, consider the following
situations:
A serum specimen was diluted 1:20 and then 2 mL of that was diluted to 10mL, and 1 mL of
that was added to 4 mL using H20. Exactly 2 mL of this last dilution was discarded, and the
remainder was diluted to 30 mL.
What was the final dilution of the serum specimen? Read each portion carefully.
1/20 x 2/10 x 1/5 x 3/30 = 6/30,000 = 1/5,000 or 1:5000
Always reduce the final answer to a fraction with the lowest possible denominator.
In the Immunology or Serology area serial dilutions, sometimes referred to as serological
dilutions, are extensively used in the test procedures. Serial dilutions usually refer to dilutions
of the same proportion made repeatedly from the previous dilution. The directions for
preparing these serial dilutions may be written several ways. To illustrate, consider the
following two examples:
Example 1:
Eight test tubes are placed in a rack. To the first tube add 3 mL of saline. To each of the
remaining seven tubes add 2 mL of saline. To the first tube add 1 mL of serum and mix well.
Transfer 2 mL of tube # 1 to tube # 2 and mix well. 2 mL of the contents of tube # 2 is then
transferred to tube # 3, and the procedure is repeated for the remaining tubes, finally
discarding 2 mL from the last tube. What is the dilution of serum in tube # 8?
Dilution 1/4 x 2/4 x 2/4 x 2/4 x 2/4 x 2/4 x 2/4 x 2/4 = 1/512
Example 2:
One mL of serum is added to 3 mL of saline in the first tube of a series of eight. A 1:2 serial
dilution is then made. What is the dilution of serum in the 8th tube?
1/4 x 2/4 x 2/4 x 2/4 x 2/4 x 2/4 x 2/4 x 2/4 = 1/512
Both example 1 and example 2 illustrate how the same serial dilution problem may be
expressed in two different ways. In the first example a step-by-step procedural outline is
provided. Go back and look at example 1. In the first tube 1 mL of serum was added to 3 mL
of saline. To calculate the dilution contained in this tube, apply the following.
volume serum/total volume of solution = 1mL/l mL serum + 3 mL saline = 1/4
In the second tube 2 mL of the first dilution was added to 2 mL of saline:
1/4 x 2/4 or 1/4 x 1/2 = 1/8 in 2nd tube
By transferring 2 mL of dilution from one tube to a second tube containing 2 mL of saline, and
continuing to do so, this is actually making a 1:2 serial dilution.
PROBLEMS:
1. You made a 1:2 dilution of serum. Then you added 2 mL of that to 4 mL of water. Then 1
mL of that was diluted to 8 mL. What was the final dilution of serum?
2. You took 4 mL of a glucose solution and diluted it to 10 mL. Then a 1:10 dilution was made
of that. What was the final dilution?
3. In performing a serological procedure, you add 1 mL of serum to 5 mL of saline. A 1:2
serial dilution is then made. What is the dilution of serum contained in tube 6?
4. Six tubes are placed in a rack. To all six tubes you add 2 mL of water. Then 1 mL of serum
is added to the first tube and mixed well. You then transfer 1 mL of that to the second tube
and again mix well. You continue the transfer of 1 mL of mixture from one tube to each
subsequent tube, finally discarding 1 mL from tube 6. What is the dilution of serum contained
in tube 6?
5. How would you set up a series of tubes with a 1:4 dilution such that you end up with 3 mL
of solution in each tube at the end of the procedure?
6. How would you set up a series of tubes for a 1:2 dilution so that you end up with 0.5 mL of
solution in each tube at the end of the procedure?
Determining Concentrations of Dilutions
If you want to determine the concentration of a substance in a particular dilution, you multiply
the original concentration times the dilution. To illustrate consider the following:
Example 1:
You had a solution with 4 g of glucose per mL. You dilute this original solution by adding 1
mL of it to 9 mL of water. What is the dilution you prepared?
By adding 1 mL of solution to 9 mL of water, you have prepared a 1:10 dilution. Therefore:
4 g/mL x 1/10 = 4 g/mL/10 = 0.4 g/mL
Example 2:
If you had a 100 mg/dL solution of glucose and made a 1:5 dilution, what concentration of
glucose is contained in the dilution?
100 mg/dL x 1/5 = 100 mg/dL/5 = 20 mg/dL
Problems:
7. What is the final concentration of your solution when you took 1 mL of a 100 mg/dL
solution and added 9 mL of water?
8. You had a 1,000 mg/dL solution of glucose. You took 1 mL of that and diluted it to 5 mL.
Then you took 4 mL of that and added it to 12 mL of water. What is the final concentration of
your glucose solution?
Preparation of Standards
Another common way we use dilution problems is in making standards for out tests. We
dilute "stock" standards to make "working" standards. These working standards are then
used in testing and calculating unknown concentrations. For example, we may have a stock
glucose standard of 10 mg/mL. When we run glucose levels on patients we need to also run
a standard to calculate the results. The working standard should be within the ball park of the
normal values. The normal individual may have a glucose of between 60-90 mg/dL, so a
good glucose working standard would be about 100 mg/dL. We are now faced with preparing
such a working standard.
1. Since the stock standard is expressed in mg/mL and the working standard is expressed in
mg/dL, we must first convert the concentration of them both to the same units.
Stock standard = 10 mg/mL x 100 mL/1dL = 1,000 mg/dL
2. To determine the dilution that must be made to yield a working standard of the desired
concentration, we use the following equation:
desired concentration of working std./concentration of stock std. = dilution required
Using the information from our example, we now see:
100 mg/dL = 1/10
1000 mg/dL
Therefore, a 1:10 dilution needs to be made of the stock standard to obtain a working
standard of the desired 100 mg/dL concentration, i.e., one part (mL or whatever) of stock qs
10 parts total solution (qs = quantity sufficient to make).
3. To determine the actual amounts of stock standard and diluent needed to prepare the
working standard, use the following equations.
Vol wanted x desired conc/stock conc.. = vol of stock std needed
[total vol working std needed] - [vol of stock std to use] = vol of diluent needed
Suppose we wanted to prepare 50 mL of a 100 mg/dL working standard of glucose from the
original stock standard of 10 mg/mL.
50 mL needed x 1/10 = 5 mL stock standard
50 mL needed - 5 mL stock std = 45 mL diluent
Therefore, to prepare 50 mL of working standard, 5 mL of stock standard is added to 45 mL
diluent (such as water).
Problems:
9. How would you make 50 mg/dL working glucose solution from a 2.0 g/dL stock glucose
solution?
10. How would you make a 4 mg/dL uric acid working standard from a 200 mg/dL stock uric
acid standard?
11. You have a serum with 7 g/dL of protein. What is the concentration in mg/dL of protein in
the 6th tube of a 1:2 serial dilution of the serum?
12. 5 mL of a stock urea nitrogen standard contains 1mg Nitrogen. 5 mL is diluted to 10 mLs.
1 mL of this is rediluted to 10mL. 2.5 mL of this is rediluted to 25 mL. What is the
concentration of nitrogen per mL of the final dilution.
13. If you use 5 mL of stock glucose containing 10 mg/mL and dilute to 100 mL, what is the
concentration of glucose per mL in the dilution?
14. How would you dilute a 1 mg/mL urea stock standard to be equivalent to a 5 mg/dL
working standard?
15. How would you dilute a 2 mg/mL glucose stock standard to make 100 mL of a 50 mg/dL
standard?