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 the volume for each concentration

For the first case ($C_1 = 250000\ U/mL$):
Use the formula $V=\frac{D}{C}$, where $D = 2500000\ U$ (dose) and $C$ is the concentration.
$V_1=\frac{2500000}{250000}=10\ mL$
For the second case ($C_2 = 500000\ U/mL$):
$V_2=\frac{2500000}{500000}=5\ mL$
For the third case ($C_3 = 1000000\ U/mL$):
$V_3=\frac{2500000}{1000000}=2.5\ mL$

Step2: Check if the volume is a reasonable amount for intramuscular injection

Intramuscular injection volumes are typically in the range of $1 - 5\ mL$. A volume of $10\ mL$ (from the first concentration) is too large for a single - intramuscular injection. A volume of $2.5\ mL$ (from the third concentration) is at the lower end but still acceptable, and a volume of $5\ mL$ (from the second concentration) is also acceptable. However, when we consider the practicality of measuring and administering, a $5\ mL$ dose (from the $500000\ U/mL$ concentration) is more straightforward to measure accurately than a $2.5\ mL$ dose (since measuring $2.5\ mL$ may have more measurement error in a clinical setting).

Answer:

The directions for adding $8.2\ mL$ diluent (resulting in a concentration of $500000\ U/mL$) should be followed.