Lessons · Nursing · diluting a solution: C1V1 = C2V2
Diluting a solution: C1V1 = C2V2
The amount of drug does not change when you add liquid, so the strength you start with times the volume you take equals the strength you want times the volume you end with: C1 × V1 = C2 × V2.
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
The stock bottle is stronger than the order, and the rest of the volume is diluent. Getting the stock volume right decides the strength that reaches the patient, and the amount of diluent is a subtraction afterwards, not a number of its own.
How to think about it
Write the four letters and fill in the three you know: the stock strength C1, the strength you want C2, and the final volume V2. Rearrange for V1 = C2 × V2 / C1. Then the diluent is V2 minus V1. Check that V1 is smaller than V2 whenever the stock is stronger.
Worked example
C1 = 10 percent, C2 = 2 percent, V2 = 500 mLThree known, one unknown.
V1 = C2 × V2 / C1 = 2 × 500 / 10 = 100 mLThe volume of stock to take.
Diluent = 500 - 100 = 400 mLWhat is added to it, so the final volume comes to 500 mL.
Check: 10 × 100 = 1000 and 2 × 500 = 1000Both sides equal, so the amount of drug did not change.
Your turn
Stock 25 percent, want 200 mL at 5 percent. Write the line for the stock volume.
V1 = 5 × 200 / = 40 mL
Solve one, graded on the server
The trap
Adding the diluent on top of the stock instead of up to the final volume. If the stock volume is 100 mL and the order says a final 500 mL, you add 400 mL, not 500; adding 500 gives 600 mL and a weaker solution than the order.