Question

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

Answer 1

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

Explanation:

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`