A client is receiving an intravenous infusion of 1.5 L of saline solution at a rate of 75 mL/hr.
How many hours will it take to finish the infusion at the current rate?

To answer this question, we need to calculate the infusion rate in mL per hour by using the following formula²:

Infusion rate (mL/h) = Dose (mcg/kg/min) × Weight (kg) × 60 min/h × Volume (mL) / Concentration (mcg/mL)

In this case, the infusion rate is:

Infusion rate (mL/h) = 3 mcg/kg/min × 70 kg × 60 min/h × 250 mL / 2500 mg

We need to convert lb to kg by dividing by 2.2

Infusion rate (mL/h) = 3 mcg/kg/min × (154 lb / 2.2 kg/lb) × 60 min/h × 250 mL / 2500 mg

We need to convert mg to mcg by multiplying by 1000:

Infusion rte (mL/h) = 3 mcg/kg/min × (154 lb / 2.2 kg/lb) × 60 min/h × 250 mL / (2500 mg × 1000 mcg/mg)

We can simplify the equation by canceling out some units and numbers:

Infusion rate (mL/h) = 3 × 154 × 250 / (2.2 × 2500 × 1000)

We can use a calculator to get the final answer:

Infusion rate (mL/h) = 12.6363636363636 mL/h

To find the amount of solution to draw for one dose, you need to calculate the following:

- The body surface area (BSA) of the client in square meters (m²) using the formula: BSA (m²) = √(Height (cm) x Weight (kg) / 3600)
- The dose of allopurinol in milligrams (mg) using the formula: Dose (mg) = BSA (m²) x Prescribed dose
(mg/m²)
- The volume of solution in milliliters (mL) using the formula: Volume (mL) = Dose (mg) / Concentration (mg/mL)

First, use the formula for BSA to find the client's body surface area in square meters:

BSA (m²) = √(Height (cm) x Weight (kg) / 3600)

Since the client's height is 148 cm and weight is 55 kg, plug in these values into the formula:

BSA (m²) = √(148 cm x 55 kg / 3600)

Simplify and solve for the BSA:

BSA (m²) = 1.41 m²

Next, use the formula for dose to find the amount of allopurinol in milligrams:

Dose (mg) = BSA (m²) x Prescribed dose (mg/m²)

Since the client's BSA is 1.41 m² and the prescribed dose is 115 mg/m², plug in these values into the formula:

Dose (mg) = 1.41 m² x 115 mg/m²

Simplify and solve for the dose:

Dose (mg) = 162.15 mg

Then, use the formula for volume to find the amount of solution in milliliters:

Volume (mL) = Dose (mg) / Concentration (mg/mL)

Since the dose is 162.15 mg and the concentration is 25 mg/mL, plug in these values into the formula:

Volume (mL) = 162.15 mg / 25 mg/mL

Simplify and solve for the volume:

Volume (mL) = 6.486 mL

Therefore, the nurse should draw **6.486 mL** of solution for one dose of allopurinol.