Final answer:
To calculate the grams of mannitol the patient will receive, multiply their weight by the dosage. To calculate the volume to prepare, divide the total amount of mannitol by the concentration of the solution.
Step-by-step explanation:
To calculate the number of grams of mannitol the patient will receive, we need to multiply the patient's weight in kilograms by the recommended dosage in grams per kilogram. Since the patient weighs 165 lbs, we need to convert this weight to kilograms by dividing it by 2.2046. This gives us approximately 74.8 kg. Multiplying this weight by the recommended dosage of 0.5 g/kg, we find that the patient will receive approximately 37.4 grams of mannitol.
To calculate the volume of mannitol to prepare for the infusion, we need to divide the total amount of mannitol (37.4 grams) by the concentration of the mannitol solution. The 100-mL vial of 20% mannitol contains 20 grams of mannitol per 100 mL. Setting up a proportion, we find that the patient will need approximately 187 mL of mannitol solution for the infusion.