# Serial dilutions

Serial dilutions are useful when we want to obtain a very diluted solution from very concentrated stock solutions. For example, if we want to obtain 10 ml of 1 mM solution from a 1M stock solution

## By direct dilution:

M1V1 = M2V2

V1 = M2V2 / M1

V1 = (10 ml * 1/1000 M)/1 M

V1 = 0.01 ml m one times v one equals m two times v two, which means that v one equals m two times v two divided by m one. Then, v one is equal to 10 milliliters times 1 divided by 1000 molar divided by one molar

Water to add: 10 ml - 0.01 ml = 9.99 ml

In these cases, direct dilution is not very helpful because it would be difficult to pipette exactly 9.99 ml.

## By serial dilution

Whereas if it was done by serial dilution, we first look at the final volume and concentrations needed, then determine the dilution factor.

So if we need 10 ml of a 1 mM solution, our dilution factor is:

Dilution factor = 1 / (final concentration / initial concentration) = 1 / (0.001M / 1M) = 1000X dilution factor equals one divided by the final concentration divided by the initial concentration, which equals one divided by 0.001 molar divided by 1 molar, which equals 1000

We can split up 1000X into multiple factors: 10 X 10 X 10. This means we can set up 3 tubes to perform the serial dilution. When it is a 10X dilution, it means that it is 1 part of the solution, 9 parts of the diluent (usually it is water). Similarly, for a 15X dilution, a thousand times dilution into multiple factors: 3 times a 10-fold dilution. This means we can set up 3 tubes to perform the serial dilution. When it is a 10-fold dilution, it means that it is 1 part of the solution, 9 parts of the diluent (usually it is water). Similarly, for a 15-fold dilution, it will be 1 part of the solution, 14 parts of the diluent.

Figure 1: Serial dilution. 1 mL of stock is transferred to the second tube that contains 9 mL of diluent (e.g water). Then 1 mL (aliquot) of the second tube is taken and transferred to the third tube. The process of transferring aliquot is repeated until the desired dilution concentration is achieved.

Although serial dilution requires more preparation, it will give more accurate dilutions, provided that your technique is precise.