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

Where:
M1	=	Concentration 1
V1	=	Volume 1
M2	=	Concentration 2
V2	=	Volume 2

Therefore:

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

or:
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....

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Additional Resources

• 📗 - Maths and Chemistry Refresher for Life and Biomedical Scientists
• 📗 - Catchup Chemistry (affiliate link to the book)
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