Sunday 4 October 2009

Calculating Dilutions

I have received a number of emails about dilution calculations.

The type of question is:

You have been asked to dilute a 10 mg/ml solution to give 5 ml of a 1.5 mg/ml solution.

How many ml of water would you use?

How many ml of the stock protein solution would you use?

The way I would work this out is by saying that 5 ml of 1.5 mg/ml contains 5 x 1.5 mg = 7.5 mg.

If the stock is 10 mg/ml then I need to take a volume that would give 7.5 mg. So, the number of ml of the stock I need is 7.5 / 10 = 0.75 ml (that is, 0.75 ml of a 10 mg/ml solution contains 7.5 mg).

Therefore, I have 0.75 ml of the stock, and the final volume is 5 ml, so we need to add 5 - 0.75 = 4.25 ml of water.

The answer:

How many ml of water would you use? 4.25 ml

How many ml of the stock protein solution would you use? 0.75 ml

Although I prefer to work it out as above you can use a formula:

M1V1 = M2V2

M1 = Concentration 1
V1 = Volume 1
M2 = Concentration 2
V2 = Volume 2
M1 = Concentration 1 = 10 mg/ml
V1 = Volume 1 = Unknown X
M2 = Concentration 2 = 1.5 mg/ml
V2 = Volume 2 = 5 ml

M1V1 = M2V2 10 mg/ml x Unknown X = 1.5 mg/ml x 5 ml

Rearranging to solve for Unknown X:

Unknown X = (1.5 mg/ml x 5 ml) / 10 mg/ml Therefore, Unknown X = 0.75 ml

Using the formula is the same as the first solution, but in the first solution, I don't have to remember the formula....

If you struggle with 'Science Maths' then you may like to look at Maths4Biosciences.

If you would like to support my blogging efforts, then please feel free to buy me a coffee at

No comments:

Post a Comment