Question

Calculate the units as indicated by the problem. Use labels where provided to calculate dosages. Order: Heparin 1,800 units/hr IV. Available: 25,000 units heparin in \(250 \mathrm{~mL}\) D5W. What rate in \(\mathrm{mL}\) per hr will deliver 1,800 units/hr?

Short answer

The rate is 18 mL/hr.

Step-by-step solution

Understand the Problem

The problem requires us to determine the rate in milliliters per hour (mL/hr) for administering heparin at a dosage of 1,800 units per hour. We have a solution of 25,000 units of heparin diluted in 250 mL of D5W. We need to calculate how many mL correspond to the required 1,800 units.

Calculate the Concentration of Heparin

First, find the concentration of heparin per mL in the provided solution. Since there are 25,000 units in 250 mL, divide to get the units per mL:\[ \text{Concentration} = \frac{25,000 \text{ units}}{250 \text{ mL}} = 100 \text{ units/mL} \]

Determine the Volume to Deliver 1,800 Units

Next, calculate how many mL/hr will provide 1,800 units/hr using the concentration we determined:\[ \text{Required rate (mL/hr)} = \frac{1,800 \text{ units/hr}}{100 \text{ units/mL}} = 18 \text{ mL/hr} \]

Verify the Calculation

Double-check the calculation by ensuring the rate aligns with the concentration:If the infusion is set at 18 mL/hr and each mL contains 100 units, then: \[ 18 \text{ mL/hr} \times 100 \text{ units/mL} = 1,800 \text{ units/hr} \] This verification confirms the calculation is correct.

Key concepts

Understanding Heparin Dosage

Heparin is a medication used to prevent and treat blood clots, making it an essential drug in various medical situations. When calculating the heparin dosage, it’s crucial to ensure accuracy, as too much or too little can have significant health implications. The exercise demonstrates how to achieve the desired heparin dosage rate safely for intravenous administration. Here, the doctor ordered 1,800 units per hour. We have a supply solution where 25,000 units of heparin are dissolved in 250 ml of D5W.

To find out how to administer this precisely, understanding the concentration of the heparin solution is important. In this case, we calculated that each milliliter of the solution contains 100 units of heparin. This accurate dosage calculation guarantees the patient receives the correct therapeutic level of medication.

Calculating Intravenous Infusion Rates

Intravenous (IV) infusion rates are critical for ensuring medications are administered at the proper therapeutic speed. This involves determining the volume of solution that must be delivered over a certain period. In this scenario, our task is to establish how many mL per hour should be delivered to meet the doctor's order of 1,800 units/hr of heparin.

Given that the concentration is 100 units of heparin per ml, we need to calculate how much of this solution provides the exact units required. The formula used in this calculation is straightforward: divide the ordered units per hour by the concentration per ml:

• Required rate (mL/hr) = Ordered units (units/hr) / Concentration (units/mL)
• Substitute the values into the equation: \[ \frac{1,800 \text{ units/hr}}{100 \text{ units/mL}} = 18 \text{ mL/hr} \]

Thus, setting the infusion pump to 18 mL per hour ensures the patient receives the required dosage.

Converting Medication Concentrations

Medication concentration conversion is a key skill in nursing and pharmacology. It involves understanding how to transition between various units to apply a prescribed order accurately. For any drug like heparin, it's about making sure that the formula is applied correctly without compromising the dosage instructions.

In this example, we began by finding the concentration of heparin in the IV solution, which was determined to be 100 units per mL through a simple division of total units by total milliliters available. This concentration allows the calculation needed to convert units into a deliverable volume, ensuring precise dosing.

Getting familiar with how concentrations translate across different measurement systems provides a foundation for managing similar dosage calculations. Remember to always verify calculations by substituting back into the original setup to ensure that the units per hour align with the infusion rate. This verification step safeguards the process and confirms the correct medication dosage is being delivered.