3: Working out the dilution

When you’re thinking about dilution, it helps to simplify your actions into dilution factors. When we said the diluted coffee was

“1/10th as strong as the original”

We were explaining how much the coffee was diluted. We could also have said:

“The coffee was diluted 1/10”, or “The coffee was diluted 10-1”, or, less frequently, “The coffee was diluted 0.1”

Here are some more examples for you to try:

  1. 1 mL coffee + 4 mL water =
  2. 1 mL coffee + 9mL water =
  3. 1 mL + 99mL water =

As you’ve probably guessed, this works exactly the same whether you’re talking about caffeine or bacterial cells. Here’s what a dilution of 1/100, or 10-2, looks like on the lab bench:

1:100 dilution

Notice that it really doesn’t matter how much of the original stock you started with, as long as you had enough to put 1 mL into the new container. What matters is how much you transfer and how much water you add. The dilution is then defined as:

Volume transferred / total volume

Where the total volume is the volume transferred + volume of water added. Therefore,

1 / (1+99) = 1/100 = 10-2 = 0.01.

As shown above, the dilution can be expressed as a fraction (1/100), in scientific notation (10-2) or, less commonly, as a decimal (0.01). In this example, water is the diluent (a general term for the liquid used to dilute the sample). In the applet below, give the dilution factor as a decimal:

Make a solution with
a dilution factor of … 1/500

1 mL stock + ??? mL water