 #### Lesson Goals

• To practice calculating a dilution to a specific concentration.

• Milli- (m)
• Micro- (μ)
• Nano- (n)

#### Script

Hi everybody! Welcome back to Synthetic Biology One. Today we are going to talk about a very practical skill that you will use every day in the lab: calculating dilutions.

What volume of a given 10 mM stock solution is required to make 20 ml of a 50 μM solution? Are you bored yet?

Me too. But when you are working in the lab, this kind of problem comes up every day. Somehow nothing is ever at the concentration that you need.

Before we begin, let’s remember our metric prefixes. In Biology, there are 3 that we use all the time.

• Milli (m) indicates division by one thousand, or 103.
• Micro (μ) indicates division by one million, or 106. (That Greek letter is called mu).
• Nano (n) indicates division by one billion, or 109.

Once you use these enough, they will become second nature. Now, let’s do some math and figure this one out.

The official method for doing this calculation makes use of the conservation of mass. We are starting with a small amount of solution at a high concentration, and we end up with a large amount of solution at a low concentration. But the total amount of dissolved stuff stays equal. That fact allows us to write this equation.

Concentration(Start) • Volume(Start) = Concentration(Final) • Volume(Final)

So, to calculate the starting volume, we divide both sides by the starting concentration. We need 0.1 mL, or 100 μL, in a total volume of 20 mL.

Another way to think about this calculation is to focus on the dilution factor. I start with 10 mM and I want to go to 50 μM. So that means I want a 1:200 dilution. The final volume I want is 20 mL. So 20 divided by 200 is 0.1 mL. For some people, breaking the calculation into two steps like this just makes the arithmetic easier.

When you start out in the lab, you should probably do these calculations on paper. Even if you are a super cool math dude like me, it’s easy to make a mistake and screw up your experiment.

After I finished this calculation, I would measure out 20 my mL of water and add 0.1 mL of concentrated solution. But remember that this is wrong. Bad bad bad. In this problem, we wanted the total volume to be 20 mL. And if we do it my way, we end up with a volume of 20.1 mL. But I’m lazy, and usually it is just easier to measure the added volume, rather than the total volume. Besides, the total error in the volume in this case is less than 1%. Biology is not rocket science. There are very few experiments that will be hurt by 1% error. So, I won’t tell if you won’t.

Until next time, happy diluting.