Question

Calculate the units as indicated by the problem. Use labels where provided to calculate dosages. Order: Heparin 25,000 units in \(250 \mathrm{~mL}\) D5W to infuse at \(11 \mathrm{~mL} / \mathrm{hr}\). Calculate the hourly heparin dosage (units/hr).

Short answer

The hourly heparin dosage is 1100 units/hr.

Step-by-step solution

Identify Known Quantities

First, we identify the provided quantities: Heparin is available in 250 mL of D5W, and the total amount of Heparin is 25,000 units. The infusion rate is 11 mL/hr.

Set Up a Proportion

We use the known quantities to set up a proportion to find the number of Heparin units per hour. We need to find how many units are present in 11 mL of the solution. The proportion is: \( \frac{25000 \text{ units}}{250 \text{ mL}} = \frac{x \text{ units}}{11 \text{ mL}} \).

Solve the Proportion

Cross-multiply to find the number of units in 11 mL. This gives us: \( 25000 \times 11 = 250 \times x \). Simplify to find \( x \): \( 275000 = 250x \).

Calculate x

Solve for \( x \) by dividing both sides by 250: \( x = \frac{275000}{250} \). Calculating this gives us \( x = 1100 \) units.

Key concepts

Heparin Dosage

Heparin is a commonly used anticoagulant that helps prevent blood clots. In medical settings, calculating the correct dosage of heparin is crucial. The dosage depends on the patient's condition and the desired rate of infusion. Understanding how to calculate the heparin dosage helps ensure that patients receive the right amount of medication to treat their conditions effectively.

In this exercise, the heparin dosage is initially given in a solution of D5W (5% dextrose in water). The bag contains 25,000 units of heparin in 250 mL of solution. This sets up the basis for any dosage calculations we need to make. Using proper calculations helps healthcare professionals prevent underdosing or overdosing the patient.

Proportion Method

The proportion method is a powerful mathematical tool used to solve dosage calculations. It's useful for determining how much medication is administered in a specific volume of solution.

To apply the proportion method, we set up a simple equation that allows cross-multiplication.

• First, arrange the known values into a fraction. Here, we use the ratio of heparin units to the total solution volume: \( \frac{25000 \, \text{units}}{250 \, \text{mL}} \).
• Next, set this fraction equal to a new fraction with the unknown value \( x \) and the given infusion rate: \( \frac{x \, \text{units}}{11 \, \text{mL}} \).

This proportion can be solved by cross-multiplying and then dividing. The result is the amount of heparin delivered per hour.

Infusion Rate

The infusion rate refers to the speed at which the intravenous solution is administered to the patient. This is typically specified in milliliters per hour (mL/hr).

Correctly calculating the infusion rate is vital for ensuring that the medication is delivered at the right pace. In the exercise, the infusion rate is given as 11 mL/hr. This indicates that 11 milliliters of the solution are administered each hour.

• To find how much heparin is in those 11 mL, use the previously calculated value from the proportion.
• This rate allows healthcare providers to control the dosage based on the patient's needs.

Understanding and managing the infusion rate is key in continuous medication administration, especially with sensitive drugs like heparin.

Units per Hour

"Units per hour" is a term used to quantify how much of a drug is administered to a patient over the course of an hour. It is essential for maintaining consistent and appropriate medication levels in the bloodstream.

The exercise involves calculating the exact number of heparin units delivered per hour, based on a previous proportion calculation. Here, we calculated that 1,100 units of heparin are delivered every hour.

This unit rate is valuable, as it allows healthcare providers to make across-the-board adjustments if the prescribed treatment plan requires it. For example, if a patient's situation changes, a doctor may order a change to a higher or lower infusion rate, and this unit hourly calculation will need to be adjusted accordingly to maintain patient safety.