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# How do you calculate dilution factor?

You divide the final volume by the initial volume.

##"DF" = V_f/V_i##

EXAMPLE 1:

What is the dilution factor if you add a 0.1 mL aliquot of a specimen to 9.9 mL of diluent?

Solution:

##V_f = "aliquot volume + diluent volume" = "(0.1 + 9.9) mL" = "10.0 mL"##

##"DF" = V_f/V_i = (10.0 cancel("mL"))/(0.1cancel("mL")) = 100##

You have diluted the sample by a factor of 100.

The dilution factor is often used as the denominator of a fraction.

For example, a ##"DF"## of 100 means a 1:100 dilution.

EXAMPLE 2:

How would you make 500 mL of a 1:250 dilution?

Solution:

##"DF" = V_f/V_i##

##V_i = V_f/("DF") ="500 mL"/250 = "2.00 mL"##

Pipet 2.00 mL of your stock solution into a 500 mL volumetric flask.

Add diluent to the mark on the flask (you will have added about 498 mL of water).

You now have a 1:250 dilution of your original solution.