Final answer:
To administer a 0.5 g dose from a vial labeled 750 mg, you will calculate the required milliliters by setting up a proportion. It turns out you need to administer 2.4 mL of the solution after reconstitution with sterile water.
Step-by-step explanation:
To calculate the number of milliliters you need to administer a 0.5 g dose of a drug from a vial labeled with 750 mg, first you need to convert the required dose to the same units as the vial. Since 1 g = 1000 mg, 0.5 g is equivalent to 500 mg. Now, using the information that adding 3.4 mL of sterile water provides an approximate volume of 3.6 mL, we can set up a proportion.
Since the full strength of the vial (750 mg) will be in 3.6 mL of the solution, we can find out how many mL will contain the required dose of 500 mg using the following proportion:
750 mg : 3.6 mL = 500 mg : x mL
Solving for x:
x = (500 mg * 3.6 mL) / 750 mg
x = 1800 mg·mL / 750 mg
x = 2.4 mL
Therefore, you will administer 2.4 mL of the solution to deliver a dose of 0.5 g of the drug.