Final answer:
To administer 75 mg of meperidine intramuscularly, the nurse should administer 1.5 mL of the medication.
Step-by-step explanation:
To calculate the number of milliliters that the nurse should administer to the client, we need to use the formula C₁V₁ = C₂V₂. In this case, C₁ is the concentration of the medication in the ampule (50 mg/mL), V₁ is the number of milliliters to be administered, C₂ is the desired dosage (75 mg), and V₂ is the volume of the medication (unknown).
Rearranging the formula, we have V₁ = (C₂ * V₂) / C₁. Plugging in the values, we get V₁ = (75 mg * V₂) / 50 mg/mL.
Since we want to find the volume in milliliters, we can cancel out the mg units and solve the equation: V₁ = (75 * V₂) / 50 = 1.5 * V₂. Thus, the number of milliliters that the nurse should administer to the client is 1.5 mL.