Question

Calculate the units as indicated by the problem. Use labels where provided to calculate dosages. Order: Heparin 40,000 units in \(500 \mathrm{~mL}\) D5W to infuse at \(30 \mathrm{~mL} / \mathrm{hr}\). Calculate the hourly heparin dosage (units/hr).

Short answer

2400 units/hr

Step-by-step solution

Identify Total Heparin Dose

The total amount of heparin is 40,000 units in a 500 mL solution of D5W. This is given in the problem.

Determine the Infusion Rate

The infusion rate is given as 30 mL/hr.

Calculate Units per mL

First, we find how many units of heparin are in each milliliter of the solution. Divide the total units (40,000 units) by the total volume (500 mL). \[\frac{40,000 \text{ units}}{500 \text{ mL}} = 80 \text{ units/mL}\]

Calculate Hourly Dosage

Next, multiply the units per mL by the infusion rate (in mL/hr) to find out the units per hour.\[80 \text{ units/mL} \times 30 \text{ mL/hr} = 2400 \text{ units/hr}\]

Key concepts

Heparin Dosage

Heparin is a medication used to prevent blood clots, often given in hospital settings. The dosage calculation is crucial in ensuring patient safety. In this context, heparin is measured in units, a standardized quantity, as opposed to milligrams like many other medications.
To calculate a heparin dosage, it is important to first know the total number of units ordered by a healthcare provider. In this problem, the order was for 40,000 units of heparin mixed in a 500 mL intravenous (IV) solution. This is the starting point for any dosage calculation. Without this key information, it would be impossible to safely determine how much of the medication a patient would receive.

Infusion Rate

The infusion rate is the speed at which the IV solution is administered to the patient. It is typically measured in milliliters per hour (mL/hr).
In our scenario, the infusion rate is 30 mL/hr. This means every hour, 30 mL of the 500 mL solution are administered to the patient. Knowing this rate is crucial because it lets us synchronize the medication delivery with the patient’s therapeutic needs. The faster the rate, the quicker the medication is introduced into the bloodstream, impacting how quickly the patient responds to treatment. Ensuring the correct infusion rate prevents potential risks like overdosing or underdosing.

Units per Milliliter

The concept of units per milliliter (units/mL) is central to understanding how heparin is dosed. It tells us the concentration of the medication within the solution. Calculating this is straightforward: simply divide the total units of medication by the total volume of the solution.
For this problem, divide 40,000 units by 500 mL to find that there are 80 units of heparin in every milliliter of solution \[\frac{40,000 \text{ units}}{500 \text{ mL}} = 80 \text{ units/mL}\]
This calculation is foundational because it relates the amount of active drug delivered to the patient with the volume of the solution being infused. Knowing the concentration allows healthcare providers to adjust infusion volumes to achieve the desired dosage.