Question

Calculate the IV flow rate in \(\mathrm{gtt} / \mathrm{min}\) for the following IV administrations, unless another unit of measure is stated. Infuse ampicillin \(1 \mathrm{~g}\) that has been diluted in \(40 \mathrm{~mL} 0.9 \% \mathrm{NS}\) to infuse in 40 minutes. Drop factor: \(60 \mathrm{gtt} / \mathrm{mL}\) At what rate in \(\mathrm{gtt} / \mathrm{min}\) should the IV infuse?

Short answer

The IV should infuse at 60 gtt/min.

Step-by-step solution

Identify the Volume to be Infused

The total volume of IV fluid to be infused is given as \(40 \text{ mL}\). This includes the ampicillin and the diluent.

Note the Time for Infusion

The infusion is to be completed in \(40\) minutes as stated in the problem.

Write Down the Drop Factor

The drop factor provided is \(60 \text{ gtt/mL}\), which means for every \(1 \text{ mL}\) of IV fluid, there are \(60\) drops.

Calculate the Flow Rate in gtt/min

To find the infusion rate in \(\text{gtt/min}\), use the formula: \[\text{Flow Rate (gtt/min)} = \left(\frac{\text{Total Volume (mL)}}{\text{Time (min)}}\right) \times \text{Drop Factor (gtt/mL)}\]Substituting the given values:\[\text{Flow Rate (gtt/min)} = \left(\frac{40 \text{ mL}}{40 \text{ min}}\right) \times 60 \text{ gtt/mL}\]Calculate this to find the flow rate.

Compute the Final Answer

Calculate the expression from Step 4:\[\text{Flow Rate (gtt/min)} = 1 \text{ mL/min} \times 60 \text{ gtt/mL} = 60 \text{ gtt/min}\]So, the IV should be infused at \(60 \text{ gtt/min}\).

Key concepts

Nursing Mathematics

Nursing mathematics is an essential skill that involves using arithmetic and algebraic skills to ensure patient safety in areas such as medication administration. Calculating IV flow rates accurately is crucial because administering the wrong dosage can lead to patient harm. Nurses often use basic mathematical equations in combination with units of measurement such as milliliters (mL), grams (g), and minutes (min) to calculate various medication dosages and infusion rates. For IV flow rate calculations, it's necessary to identify the volume of the solution, the time it needs to be infused, and the drop factor, all of which are crucial elements in the process. Understanding nursing mathematics empowers nurses to provide safe and effective patient care.

Medication Administration

Medication administration is a key component of nursing practice, requiring careful attention to detail. It involves giving medications to patients in various forms, including oral, topical, or intravenous (IV). Each method of administration can have specific procedures and calculations. Intravenous medication administration is particularly sensitive because it involves delivering medication directly into the bloodstream. The IV flow rate must be correctly calculated to ensure the patient receives the proper dosage over the correct period. Nurses must double-check all calculations and follow the prescribed treatment plan to ensure patient safety and efficacy of the medication. Errors in medication administration can have serious consequences, making it paramount for healthcare professionals to understand and meticulously follow the correct procedures.

Drop Factor

The drop factor is a term often used in the context of calculating IV flow rates. It refers to the number of drops that make up a milliliter of fluid and is determined by the IV tubing. The drop factor is typically specified on the IV tubing package, and different types of IV tubing may have different drop factors, such as 10, 15, 20, or 60 gtt/mL (gtt stands for drops and mL stands for milliliters).In the given scenario, the drop factor is 60 gtt/mL, which means that each milliliter of fluid corresponds to 60 drops. This information is crucial for calculating the flow rate of an IV infusion, allowing healthcare providers to use the formula:\[\text{Flow Rate (gtt/min)} = \left(\frac{\text{Volume (mL)}}{\text{Time (min)}}\right) \times \text{Drop Factor (gtt/mL)}\]By understanding the drop factor, nurses ensure the proper delivery of the medication, which helps maintain patient safety and achieve the desired therapeutic outcomes.