How do we dilute a bacterial culture 50-fold, 100-fold, and 200-fold?

Question

Serenity Allen · Accepted Answer

You could do the dilutions in one step, or you might have to do serial dilutions.

There is a limit to how much you can dilute a sample in one step. You probably wouldn't want to dilute by more than a factor of 100 in a single step, because that would give you a large volume of dilute solution. Rather, you would use the serial dilution technique. Remember the formula for dilution factor (#"DF"#): #"DF" = V_f/V_i#, where #V_i = "aliquot volume"# and #V_f = "final volume" = "aliquot volume + diluent volume"# (a) #"DF" = 50# Here we can do a single dilution. We can add 0.2 mL of sample to 9.8 mL of diluent (normal saline? cells will burst in distilled water because of osmotic pressure). #V_f = "0.2 mL + 9.8 mL" = "10.0 mL"# #"DF" = V_f/V_i = (10.0 cancel("mL"))/(0.2 cancel("mL")) = 50# (b) #"DF" = 100# Here, too, we can do a single dilution. This time we add 0.1 mL of sample to 9.9 mL of saline. #V_f = "0.1 mL + 9.9 mL" = "10.0 mL"# #"DF" = V_f/V_i = (10.0 cancel("mL"))/(0.1 cancel("mL")) = 100# (c) #"DF" = 200# Here you might want to do a serial dilution. The formula for serial dilutions is #"DF" = "DF"_1 × "DF"_2 × "DF"_3 ×…# How about a 1:100 dilution followed by a 1:2 dilution? (1) Add 0.1 mL of sample to 9.9 mL of diluent. #"DF"_1 = 100#. Call this "Solution 1". (2) Add 5 mL of Solution 1 to 5 mL of saline. Call this "Solution 2". #V_i = "5 mL"# #V_f = "5 mL + 5 mL" = "10 mL"# #"DF"_2 = V_f/V_i = (10 cancel("mL"))/(5 cancel("mL")) = 2# #"DF" = "DF"_1 × "DF"_2 = 100 × 2 = 200#

Noah Aldrich · Answer

undefined For a 50-fold dilution: Add 1 mL of the bacterial culture to 49 mL of diluent.
For a 100-fold dilution: Add 1 mL of the bacterial culture to 99 mL of diluent.
For a 200-fold dilution: Add 1 mL of the bacterial culture to 199 mL of diluent.