Question

Calculate the units as indicated by the problem. Use labels where provided to calculate dosages. Order: Heparin 2,000 units/hr IV. Available: 25,000 units of heparin in \(1,000 \mathrm{~mL}\) of \(0.9 \% \mathrm{NS}\) What rate in \(\mathrm{mL} / \mathrm{hr}\) will deliver 2,000 units/hr?

Short answer

80 mL/hr

Step-by-step solution

Identify the Unit Ratio

First, find the concentration of Heparin in the IV solution. We have 25,000 units of Heparin in 1,000 mL. This means that the concentration of Heparin is \( \frac{25,000 \text{ units}}{1,000 \text{ mL}} \).

Calculate the Unit Conversion Rate

Convert the concentration into its simplest form. \( \frac{25,000 \text{ units}}{1,000 \text{ mL}} = 25 \text{ units/mL} \).

Determine the Required Flow Rate

We need to deliver 2,000 units per hour. To find out how many mL this corresponds to, set up the equation: \( \frac{2,000 \text{ units}}{x \text{ mL}} = 25 \text{ units/mL} \).

Solve for the Flow Rate

Solving the equation \( \frac{2,000}{x} = 25 \), we multiply both sides by \( x \) to get \( 2,000 = 25x \). Now, divide both sides by 25 to find \( x \). Thus, \( x = \frac{2,000}{25} = 80 \).

Confirm the Flow Rate

The solution tells us that by setting the infusion pump to 80 mL/hr, you will deliver 2,000 units of heparin each hour, which confirms our calculation.

Key concepts

Unit Conversion

Understanding unit conversion is crucial when calculating medication doses, as it ensures accuracy and patient safety. When given a concentration of a drug in a solution, like heparin in saline, it's important to know how many active units exist per volume of liquid. This involves changing the units from one form to another.For instance, in this exercise, we start with a known concentration: 25,000 units of heparin in 1,000 mL of solution. To work with this data, simplify the concentration to its most manageable form. Divide the total units by the total volume to convert this ratio into units per milliliter. So, you calculate:\[ \frac{25,000 \text{ units}}{1,000 \text{ mL}} = 25 \text{ units/mL} \]This conversion makes it easier to determine how much solution to administer per hour to achieve a specific dosage.

Flow Rate Determination

Determining the flow rate in mL/hr is vital to ensure the correct amount of medication is delivered to the patient. Once you know the concentration of the solution, you can calculate the flow rate needed to deliver the prescribed dose.In this scenario, the physician has ordered a dose of 2,000 units per hour. To find out how many mL per hour will deliver this dose, set up a relationship using the concentrations you've calculated. You know the solution contains 25 units per mL, so:\[ \frac{2,000 \text{ units}}{x \text{ mL}} = 25 \text{ units/mL} \]Here, \(x\) represents the volume of mL per hour we need. Solve for \(x\) by rearranging the equation:Multiply both sides by \(x\):\[ 2,000 = 25x \]Then divide both sides by 25 to isolate \(x\):\[ x = \frac{2,000}{25} = 80 \]This confirms that you need to set the infusion to 80 mL/hr.

Intravenous Infusion Rate

The intravenous infusion rate, a critical component of dosage calculations, determines how quickly fluid is administered through an IV line. Incorrect calculations can lead to underdosing or overdosing, both potentially hazardous. In our calculation, the process involved converting the prescribed units per hour into the corresponding mL/hr, simplified through the use of the concentration value: - **Concentration:** 25 units/mL determined from the unit conversion. - **Dose Order:** 2,000 units/hr needed. - **Target Volume:** 80 mL/hr determined using flow rate calculations. The infusion rate of 80 mL/hr successfully administers 2,000 units per hour. Such calculations are routine in medical settings, and practicing these ensures efficiency and safety in patient care. Adjusting the infusion equipment to this rate ensures the patient receives the correct dosage consistently.