Question

Calculate the hourly dosage of heparin (units/hr). Order: 20,000 units of heparin in \(1 \mathrm{~L}\) of D5W to infuse at \(40 \mathrm{~mL} / \mathrm{hr}\).

Short answer

The hourly dosage is 800 units/hr.

Step-by-step solution

Identify the Total Units of Heparin

The problem states that there is a total of 20,000 units of heparin mixed in a 1-liter bag of D5W. This means that the entire solution contains 20,000 units of heparin.

Identify the Infusion Rate

It is given that the infusion rate is 40 mL per hour. This is the rate at which the heparin solution is administered to the patient.

Calculate the Concentration of Heparin in the Solution

Since there are 20,000 units of heparin in 1 liter (which is equivalent to 1,000 mL), we need to compute the concentration of heparin per mL. The concentration is:\[\text{Concentration} = \frac{20,000 \text{ units}}{1,000 \text{ mL}} = 20 \text{ units/mL}\]

Calculate the Hourly Dosage

Using the concentration from Step 3, the hourly dosage of heparin can be found by multiplying the concentration by the infusion rate:\[\text{Hourly Dosage} = 20 \text{ units/mL} \times 40 \text{ mL/hr} = 800 \text{ units/hr}\]

Conclusion

The hourly dosage of heparin that the patient receives is calculated to be 800 units per hour.

Key concepts

Understanding Heparin Dosage

When calculating heparin dosage, it is crucial to understand the total amount of heparin in the solution, as it determines how much of the medication a patient receives. In the given problem, you have 20,000 units of heparin mixed in a solution of D5W. This total dosage needs to be correctly dispensed over the course of treatment to ensure efficacy and safety. Heparin is an anticoagulant, meaning it helps to prevent blood clots from forming in the blood vessels. It is a sensitive medication, so proper dosage calculation is critical to avoid under- or over-dosing, which can result in severe complications. By calculating the exact hourly dosage, healthcare providers can maintain optimal therapeutic levels in the patient’s bloodstream.

Infusion Rate Calculation

The infusion rate is a pivotal part of accurately delivering medication like heparin. In this scenario, the infusion rate is specified as 40 mL per hour. This tells us how fast the solution should be administered to the patient. To link the infusion rate with the drug dosage, it is necessary to determine how this rate affects the total drug delivered.

• The infusion rate is the volume of fluid administered over a specific time period, usually measured in mL/hr.
• It helps determine how much medication reaches the patient each hour based on the known concentration of the drug in the solution.

Understanding and managing infusion rates ensures that patients receive the correct amount of medication steadily, maintaining the desired therapeutic effect.

Concentration Calculation

Concentration calculation helps determine the amount of medication, in this case, heparin, in each milliliter of solution. For the exercise given, we know that 20,000 units of heparin are dissolved in 1 liter (or 1,000 mL) of solution. To calculate concentration, you use the formula: \[\text{Concentration} = \frac{\text{Total Units of Heparin}}{\text{Total Volume in mL}}\] In this example:\[\text{Concentration} = \frac{20,000 \text{ units}}{1,000 \text{ mL}} = 20 \text{ units/mL}\] This concentration value is then critical for determining the actual dosage the patient will receive, as it directly relates to the infusion rate. Calculating concentration accurately is essential to ensure that each dose administered is consistent with the prescribed treatment plan.