A hospital pharmacist prepared thirty 100-mL epidural bags containing 0.125% of bupivacaine hydrochloride and 1 mg/mL of fentanyl citrate in 0.9% sodium chloride injection. How many (a) 30-mL vials of 0.5% bupivacaine hydrochloride, (b) 20-mL vials of 50 mg/mL of fentanyl citrate, and (c) 1-L bags of 0.9% sodium chloride were required?

a) 25 vials

b) 3 vials

c) 3 bags

Explanation:

When a concentrated solution is diluted to form another solution, the new concentration can be calculated by:

C1V1 = C2V2

Where C is the concentration, V is the volume, 1 represents the initial solution, and 2 the final solution. The multiplication CV is constant because it represents the amount of matter in the solution which will not be changed.

a) Let's identify the volume (V1) needed when the concentrated solution has C1 = 0.5%, and the final solution has C2 = 0.125% and V2 = 100 mL

0.5*V1 = 0.125*100

0.5V1 = 12.5

V1 = 25 mL

Thus, this is the volume for 1 bag, for 30 bags, V = 30*25 = 750 mL. The vials needed is the volume divided by the volume of one vial:

750/30 = 25 vials.

b) Doing the same thing, now with C1 = 50 mg/mL, C2 = 1 mg/mL, and V2 = 100 mL:

50*V1 = 1*100

V1 = 2 mL

The volume for 30 bags is then 30*2 = 60 mL. The number of vials is:

60/20 = 3 vials.

c) In this case, the concentration of sodium chloride is the same in both solutions. Thus, the volume of it is the total volume of the bag (100 mL) less the volume of the other substances:

100 - 25 - 2 = 73 mL

The volume for 30 bags is 30*73 = 2190 mL. Thus, if the concentrated bag has 1 L = 1000 mL, the bags needed are:

2190/1000 = 2.19

Thus, 3 bags are needed (the 3rd bag will not be totally used!).