Question

q8. a physician orders 2,500,000 u penicillin to be administered intramuscularly. in stock is a vial that contains 5,000,000 u penicillin. on the side of this vial is written that when: 18.2 ml diluent is added, the concentration will be 250,000 u/ml. 8.2 ml diluent is added, the concentration will be 500,000 u/ml. 3.2 ml diluent is added, the concentration will be 1,000,000 u/ml. which of the three sets of directions should be followed to fill this order?

Explanation:

Step1: Calculate volume for first dilution

Use the formula $V=\frac{D}{C}$, where $D$ is the dose and $C$ is the concentration. For the first case with $C = 250000$ U/mL and $D=2500000$ U. Then $V_1=\frac{2500000}{250000}=10$ mL.

Step2: Calculate volume for second dilution

For the second case with $C = 500000$ U/mL and $D = 2500000$ U. Then $V_2=\frac{2500000}{500000}=5$ mL.

Step3: Calculate volume for third dilution

For the third case with $C=1000000$ U/mL and $D = 2500000$ U. Then $V_3=\frac{2500000}{1000000}=2.5$ mL.
Since a vial is used and we want to use the least - amount of diluent and still be able to measure the required volume accurately, we choose the third option where the concentration is 1000000 U/mL after adding 3.2 mL of diluent.

Answer:

Add 3.2 mL diluent (concentration 1,000,000 U/mL)