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Monday, May 2, 2011

Calculating Dilutions


Dilutions can be divided into five categories:
1. To dilute a solution to an unspecified final volume in just one step.
2. To dilute a solution to a specified final volume in just one step.
3. To dilute a solution to an unspecified final volume in several steps.
4. To dilute a solution to a specified final volume in several steps.
5. Serial dilutions.

Diluting a Solution to an Unspecified Volume in Just One Step

One must first calculate how many times to dilute (this is called the dilution factor) the initial material  (stock solution) to obtain the final concentration. To accomplish this type of dilution, use the following formula:

Initial Concentration (IC) / Final Concentration (FC) = Dilution Factor (DF)

For example, if you want to dilute a solution with an initial
concentration of solute of 5% down to 1%, using the above
formula gives
IC /FC  = DF 5% /  1% = 5

Thus, in order to obtain a 1% solution from a 5% solution, the latter must be diluted 5 times. This can be accomplished by taking one volume (e.g., cc, ml, liter, gallon) of the initial concentration (5%) and adding 4 volumes (e.g., cc, ml, liter, gallon) of solvent for a total of five volumes. Stated another way, 1 ml of a 5% solution + 4 ml of diluent will give a total of 5 ml, and each ml contains 1% instead of 5%.

Diluting a Solution to a Specified Volume in Just One Step

First, calculate the number of times the initial concentration must be diluted by dividing the final concentration (FC) into the initial concentration (IC)

Second, divide the number of times the initial concentration must be diluted (bottom left paragraph) into the final volume specified to determine the aliquot (or portion) of the initial concentration to be diluted.Third, dilute the aliquot of the initial concentration calculated in step 2 by the volume specified.
For example, you have a 10% solution and want a 2%solution. However, you need 100 ml of this 2% solution.

IC/FC = DF 10%/2% = 5

Divide the number of times the 10% solution must be diluted (DF) into the final volume specified:

100ml / 5 = 20ml

Dilute the portion of 10 to the volume specified:

20 ml of a 10% solution + 80 ml of diluent = 100 ml (each milliliter = 2%)

Another method for performing this type of dilution is to use the following formula:

C1/C2 = V1/V2 or C1V1 = C2V2

C1 = standard concentration available
C2 = standard concentration desired
V2 = final volume of new concentration
V1 = volume of C1 required to make the new concentration

For example, if you want to prepare 100 ml of 10% ethyl alcohol from 95% ethyl alcohol, then

C1 = 95%, C2 = 10%,
V2 = 100 ml,
V1 = x and

95/10 = 100/x

x = 1,000/95; so x = 10.5 ml

Thus, 10.5 ml of 95% ethyl alcohol + 89.5 ml of H2O = 100ml of a 10% ethyl alcohol solution.

Diluting a Solution to an Unspecified Volume in Several Steps

Frequently in the microbiology laboratory, large dilutions must be employed. They cannot be done in one step because they are too large. As a result, they must be done in several steps to conserve not only amounts of diluent to be used but also space. For example, a 0.5 g/ml solution diluted to 1 µg/ml is a 500,000-fold dilution.

0.5 g = 0.5 g × 106 µg/g
        = 500,000 µg

To obtain a solution containing 500,000 µg/ml in one step would require taking 1 ml of 0.5 gm/ml stock solution and adding 499,999 ml of diluent. As you can see, it would be almost impossible to work with such a large fluid volume.

A 500,000 times dilution can be easily performed in two steps by first taking 1 ml of the initial concentration and diluting it to 500 ml and second, by diluting 1 ml of the first dilution to 1,000 ml.
1 ml of 500,000 µg/ml + 499 ml of diluent = 1,000 µg/ml
1 ml of 1,000 µg/ml + 999 ml of diluent = 1 µg/ml
Thus, by this two-step procedure, we have cut down the volume of diluent used from 499,999 to 1,498 (499 ml + 999 ml).

Diluting a Solution to a Specified Volume in Several Steps

This type of dilution is identical to all previous dilutions with the exception that the specified final volume must be one factor of the total dilution ratio.
For example, you want a 1/10,000 dilution of whole serum (undiluted) and you need 50 ml.
Divide dilution needed by the volume:

10,000 / 50 = 200


200 (1/200 dilution) = the first step in the dilution factor;
the second is 1/50, obtained as follows:
1 ml of serum + 199 ml of diluent = 1/200 dilution.
1 ml of 1/200 dilution + 49 ml of diluent = 1/50.
To check: 50 × 200 = 10,000.


Serial Dilution : Making 10 fold Dilution

The first step in making a serial dilution is to take a known volume (usually 1ml) of stock and place it into a known volume of distilled water (usually 9ml). This produces 10ml of the dilute solution. This dilute solution has 1ml of extract /10ml, producing a 10-fold dilution. (i.e. the amount of stock in each ml of the diluted solution is 0.1ml.)
This process can be repeated to make successive dilutions.


References

Laboratory Exercises in Microbiology - Harley, Presscott
http://www.ruf.rice.edu/~bioslabs/methods/solutions/dilutions.html
http://biology.kenyon.edu/courses/biol09/tetrahymena/serialdilution2.htm