Question

Round the weight to the nearest tenth. Order: Heparin drip at 18 units/kg/hr. Available: 25,000 units of heparin sodium in \(1,000 \mathrm{~mL}\) of \(\mathrm{D} 5 \mathrm{~W}\). The client weighs \(80 \mathrm{~kg}\). At what rate will you set the infusion pump?

Short answer

Set the infusion pump to 57.6 mL/hr.

Step-by-step solution

Calculate Total Units Needed Per Hour

First, we need to determine how many units of heparin are required per hour for the client. The order specifies 18 units per kilogram per hour. Given the client's weight is 80 kg, multiply 18 units by 80 kg: \[18 \text{ units/kg/hr} \times 80 \text{ kg} = 1440 \text{ units/hr}\] This means we need 1440 units of heparin per hour for this client.

Convert Units to Volume Based on Available Solution

Now that we know we need 1440 units per hour, we have to find out how much volume in milliliters corresponds to this number of units based on the available solution, which is 25,000 units of heparin in 1000 mL of D5W. First, find out how many units are in one milliliter: \[\text{Concentration} = \frac{25000 \text{ units}}{1000 \text{ mL}} = 25 \text{ units/mL}\] Next, calculate the volume of solution that contains 1440 units:\[\text{Volume (mL)} = \frac{1440 \text{ units}}{25 \text{ units/mL}} = 57.6 \text{ mL}\]Therefore, to administer 1440 units per hour, set the infusion pump to 57.6 mL/hr.

Rate Setting on Infusion Pump

Since the infusion pump needs to be set in milliliters per hour, we use the volume calculated in the previous step. Therefore, you will set the pump to deliver the solution at a rate of 57.6 mL per hour.

Key concepts

Infusion Rate Calculation

Calculating the infusion rate is an essential skill in medical dosing. It involves determining how quickly a medication should be administered to a patient. This task requires understanding both the dosage required per unit of time and the concentration of the solution available. For instance, consider the infusion of heparin as outlined in the original exercise. The doctor orders 18 units of heparin per kilogram of body weight per hour. For a patient who weighs 80 kg, this means they need \(18 imes 80 = 1440\) units every hour.
After calculating the necessary units per hour, the next step involves figuring out how much of the available solution corresponds to this dosage.By knowing there are 25,000 heparin units in 1000 mL of solution, you can derive that there are 25 units in each mL. To find the required volume for 1440 units, divide by the concentration (25 units/mL), resulting in a rate of 57.6 mL/hr. This calculation ensures the patient receives the correct dose safely within the prescribed time frame. Accurate infusion rate calculation is essential to avoid underdosing or overdosing, directly impacting patient safety and treatment effectiveness.

Rounding to the Nearest Tenth

Rounding figures appropriately is crucial in medication dosage calculations. This process simplifies numbers and makes them easier to work with, especially when setting an infusion pump. When you have a decimal number, such as 57.6, rounding to the nearest tenth means looking at the first decimal place. If the digit in the hundredth place—right after the tenths place—is 5 or above, you round up the tenths place by one. If it is less than 5, the tenths place remains the same. For example, 57.6 already ends in a tenth, so it remains as is. On the other hand, if you had 57.64, it would round up to 57.6, but if it were 57.65, it would round to 57.7. Rounding ensures that your calculations are consistent with how medical devices, like infusion pumps, interpret the numbers. It also prevents discrepancies that could arise from minor variations in measurements.

Unit Conversion

Unit conversion is a fundamental element in medication dosage calculations. It helps translate various measurement units into a format suitable for precise dosing. Without proper conversion, administering correct medication amounts would be challenging. In our example involving heparin dosage, the purpose is to convert the units per kilogram to units per hour, and finally to milliliters per hour. Starting with 18 units of heparin per kilogram of body weight, multiplying by the patient's weight (80 kg) gives the total number of units needed per hour. Once we've determined that 1440 units are required per hour, the task is to express these units in terms of the available liquid solution. Here, you convert 25,000 units in a 1000 mL solution to find the concentration — 25 units/mL. Then, calculate how many milliliters of liquid correspond to the needed 1440 units by dividing by the concentration. Converting between units ensures that medications are delivered safely and accurately.

Step-by-Step Problem Solving

A structured, step-by-step approach is invaluable when solving medication dosing problems. Organizing tasks methodically minimizes errors and increases precision. Each problem often includes multiple layers that need careful attention. Take the heparin infusion problem as an example. It starts with the determination of total units needed per hour. By multiplying the specified dosage (18 units/kg/hr) by the patient’s weight, you achieve the hourly unit requirement. Then, shift focus to converting these units into milliliters per hour. This involves first understanding the concentration of the medication solution, then figuring out the volume corresponding to the unit requirement. This logical sequencing of tasks not only aids in achieving the correct answer but also helps students recognize patterns and strategies applicable to other medication dosing problems. Assess each step thoroughly to ensure that no important detail is overlooked. Problem-solving is like piecing together a puzzle where each part matters, contributing to an accurate and safe medication plan.