q8. a physician orders 2,500,000 u penicillin to be administered intramuscularly. in stock is a vial that…
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?
Answer
Explanation:
Step1: Calculate concentration for 18.2 mL diluent
We know the initial amount of penicillin is $n = 5000000$ U. When $V_1=18.2$ mL of diluent is added, the concentration $C_1$ is calculated using the formula $C=\frac{n}{V + V_1}$, where the initial volume $V$ of the solution in the vial is assumed to be 0 (since we are mainly interested in the final - volume after dilution). So $C_1=\frac{5000000}{18.2}\approx274725.27$ U/mL.
Step2: Calculate concentration for 8.2 mL diluent
When $V_2 = 8.2$ mL of diluent is added, $C_2=\frac{5000000}{8.2}\approx609756.10$ U/mL.
Step3: Calculate concentration for 3.2 mL diluent
When $V_3=3.2$ mL of diluent is added, $C_3=\frac{5000000}{3.2}=1562500$ U/mL.
Step4: Compare with required concentration
The physician orders a concentration of 1000000 U/mL. The closest concentration to 1000000 U/mL is when 3.2 mL of diluent is added.
Answer:
The set of directions with 3.2 mL diluent should be followed.