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Lessons · Pharmacy · C1V1 = C2V2

C1V1 = C2V2: the drug does not change

Diluting adds liquid and adds no drug, so the strength times the volume before equals the strength times the volume after.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

Half of compounding is making a weaker thing out of a stronger thing that is already on the shelf. This one line is the whole method, and it works with percents, with milligrams per millilitre, with anything, as long as both strengths are in the same unit.

How to think about it

Write the four slots and fill in the three you know. Both C values in the same unit, both V values in the same unit. Then rearrange for the empty slot. The stock volume is always the smaller of the two volumes, which is the check.

Worked example

C1 x V1 = C2 x V2
Strength times volume, before and after.
10% x V1 = 2% x 400 mL
Making 400 mL of a 2% from a 10% stock.
V1 = (2 x 400) / 10 = 80 mL
Eighty millilitres of the stock.
Diluent = 400 - 80 = 320 mL
The rest is what gets added. The stock volume came out smaller, as it must.

Your turn

Make 200 mL of a 5% solution from a 20% stock. Write the volume of stock needed.

(5 x 200) / 20 =  mL

The trap

Answering with the diluent when the stock was asked for, or the other way round. They are different numbers and they add up to the final volume; read the question again before writing either one down.

Practise C1V1 = C2V2 on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.