Dilutions
Overview
If we have a solution of one concentration, and we wish to make a less concentrated solution, it
is often more convenient to dilute the original solution with additional solvent than it is to
prepare the less concentrated solution entirely from scratch.
Suppose, for example, that have a 5% NaCl solution, and we wish to prepare a solution
containing 0.5% NaCl. This is more easily done simply by diluting 1.0 ml of the 5% solution
with 9.0 ml of solvent (water). The resulting solution is 0.5% in NaCl, since the original 5%
solution has been diluted tenfold.
NOTICE THAT IT IS THE FINAL VOLUME OF SOLUTION THAT IS IMPORTANT IN
DETERMINING THE TOTAL AMOUNT BY WHICH WE DILUTED THE ORIGINAL
SOLUTION.
Hence the total dilution is equal to:
The concentration of the new solution is: therefore,
To prove that we have made the proper dilution, we can check our calculations
5% NaCl = 5g NaCl/100 ml of solution
Therefore, 1 ml of 5% NaCl (the amount we diluted above) contains 0.05 g of NaCl.
Hence:
Now let us look at a more complicated example.
Suppose we wish to make a 0.2 M solution from a 7.4 M solution. First we must calculate the
DILUTION FACTOR, or the total amount by which we must dilute the original solution to
obtain the desired solution.
1 and, by substituting in the equation above:
Thus we must dilute our original solution 37-fold in order to obtain a solution of 0.2 M. An easy
way of doing this is to add 1.0 ml of 7.4 M solution to 36.0 ml of water. This will give us a total
dilution of 37 because
If 37 ml of solution is much more than we have use for, we could make the same dilution by
adding 0.1 ml of 7.4 M solution to 3.6 ml of water, and the total dilution would be the same:
Alternatively, if we need more than 37 ml of solution we could add 10 ml of 7.4 M solution to
360 ml of water.
Serial Dilutions
In practice, it is not always possible to make a very dilute solution from a concentrated one in a
single step. In this case it is usually necessary to make a series of dilutions.
Let us suppose that we have a 1 M NaCl solution, and we need a few milliliters of 1X10-5 M
NaCl. In this case the dilution factor would be:
Theoretically, we could make this dilution by adding 0.001 ml of the 1 M solution to 99.999 ml
of water, but in practice it is difficult to measure the smaller volume accurately. Alternately, we
2 might add 0.1 ml (a reasonable amount to measure accurately) of 1 M NaCl to 9999.9 ml of
water, but we would need very large vessels, and would end up with 10 liters of solution - much
more than we need.
Rather than try to dilute the solution in one step, we could use a series of dilutions. For example,
we could dilute 0.1 ml of the 1 M solution with 9.9 ml of water (this is a 100-fold dilution). Then
we could remove 0.1 ml of the resulting solution and dilute it, in turn, with 9.9 ml of water (this
is another 100-fold dilution). Finally, we could dilute 1.0 ml of this last solution with 9.0 ml of
water (a 10-fold dilution); see Figure 1. The last solution in the series would have a
concentration of 1X10-5 M.
NOTICE THAT THE TOTAL DILUTION OF THE ORIGINAL SOLUTION IS THE
PRODUCT OF THE INDIVIDUAL DILUTIONS: (100 X 100 X 10 = 100,000)
FIGURE 1. A 100,000-fold dilution of a 1 M solution may be performed as shown in this
illustration. 0.1 ml of the 1 M solution is added to 9.9 ml of solvent (in Tube 1). After thorough
mixing, 0.1 ml of the solution in Tube 1 is added to 9.9 ml of solvent in Tube 2. Again, after
mixing thoroughly, 1.0 ml of the solution in Tube 2 is added to 9.0 ml of solvent in Tube 3. The
concentration of the solution in Tube 3 is 1/100,000 of that of the original solution.
In some of the experiments you will perform, it will be necessary to calculate the concentration
of an original solution by determining the concentration of a diluted aliquot (portion) of the
original solution. This is done by multiplying the concentration of the diluted solution by the
dilution factor.
3 Consider the following example. You have diluted a solution 1000-fold and have determined the
concentration of the diluted solution to be 0.25 mg/ml. Therefore, the concentration of the
original solution is:
0.25 mg/ml X 1000 = 250 mg/ml
The principle of dilutions is used in many of the experiments in this course. It is absolutely
essential that you thoroughly understand how to calculate dilution factors, how to make
dilutions, and how to calculate concentrations of diluted solutions.
From DeWitt, W. and E.R. Brown. 1977. Biology of the Cell Laboratory Explorations. W.B.
Saunders Co. Philadelphia. pgs. 183-185.
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