DILUTIONS: Principles and ApplicationsProfessor of Biology and Chemistry University of Cincinnati Clermont College, Batavia OH 45103 

rvsd 2 July 1993, rvsd 29 June 1994, 1 July 1996, 12 Feb '97, 3 Feb 98, 29 June 00, 28 June 01, 18July04 

Because solutions in science are often much more concentrated
than are
desired or can be managed for a given protocol, it is frequently
necessary
to dilute these solutions to a desired level. This requires a
working
knowledge
of the principles of diluting, dilution factors, concentration
factors
and the calculations involved. High dilutions are usually
expressed
exponentially
(i.e: a solution which has been diluted a million fold is
termed
a 10^{6} dilution, or is 10^{6} concentration).
DEFINITIONS:
Aliquot: a measured subvolume of original sample.
Diluent: material with which the sample is diluted
Dilution factor (DF): ratio of final volume/aliquot volume (final volume = aliquot + diluent)
Concentration factor (CF):
ratio of aliquot volume divided by the final volume (inverse
of the
dilution factor)
To calculate a dilution factor:
Remember that the dilution factor is the final volume/aliquot volume.
EXAMPLE: What is the dilution factor if you add 0.1 mL aliquot of a specimen to 9.9 mL of diluent?
To prepare a desired volume of solution of a given dilution:
1. Calculate the volume of the aliquot: it is equal either to
2. Calculate the volume of the
diluent:
which is equal to (the final volume  aliquot volume)
3. Measure out the correct volume of diluent, add the correct volume of aliquot to it, mix.
EXAMPLE: How would you prepare 20 mL of a 1:50 dilution?
1. How much sample (what sized aliquot) is required to prepare 10 mL of a 1 to 10 dilution, and how much diluent would you need?
2. What is the dilution factor when 0.2 mL is added to 3.8 mL diluent? What is the concentration factor?
3. You are to prepare 5 mL of a 10^{2} dilution. What should the aliquot and diluent volumes be?
4. How would you prepare 20 mL of a 1:400 dilution?
5. What is the dilution factor when you add 2 mL sample to 8 mL diluent?
6. You add a pint of STP gas treatment to a 12 gallon fuel tank, and fill it up with gas. What is the dilution factor? (8 pints/gallon)
7. You want 1 liter of 0.1 M NaCl, and you have 4 M stock solution. How much of the 4 M solution and how much dH_{2}O will you measure out for this dilution?
For problems like the following, you need to know the ratio of the diluent to the aliquot. For instance, if you are making a 1:20 dilution, the ratio of diluent to aliquot will be1 less than the dilution factor, or 19 parts diluent, 1 part aliquot:
8. You have 0.6 mL of sample, and want to dilute it all to a fiftieth of its present concentration. How much diluent will you add, and what will the final volume be?
9. You diluted a bacterial culture 10^{6}, plated out 0.2 mL and got 45 colonies on the plate. How many bacteria/mL were in the original undiluted culture?
A harder one which requires a little algebra:
10. You have 100.00 mL of dH_{2}O.
How
much glycerine would you have to add in order to make a 2.000 %
v/v
dilution?
(Hint, let the volume of glycerine = X, set up the standard
equation
for a dilution factor using X, and solve for X.
ANSWERS:
1) 1 mL sample + 9.0 mL diluent
2) DF = 20, CF = 0.05
3) aliquot = 0.05 mL, diluent = 4.95 mL
4) 0.05 mL sample, 19.95 mL diluent
5) DF = 5
6) F.V. = 12 gallons x 8 pints/gallon = 96 pints. Therefore 96pints/1 pint = D.F. =96
7) 25 mL 4.0 M stock solution + 975 mL dH2O
8) 29.4 mL diluent, final volume = 30 mL
9) 2.25 x 10^8
10) ans: 2.04 mL glycerine [ To solve: a) X/(100+X) = 0.02; b) X = 0.02 (100 +X); c) X = 2 + 0.02X ; d) X  0.02X =2; e) 0.98X =2; f) X = 2.04 ]