Question

The nurse is scheduled to administer \(500 \mathrm{mg}\) of ampicillin IV by secondary line. The drug is to be infused over 20 minutes. The ampicillin is in a \(50 \mathrm{ml}\) baggie of D5W. The IV drop factor for this IV is 15 . How many drops per minute should the nurse regulate the IV to infuse at over the required 20 minutes? A. \(20 \mathrm{gtts} / \mathrm{min}\) B. \(30 \mathrm{gtts} / \mathrm{min}\) C. \(40 \mathrm{gtts} / \mathrm{min}\) D. \(60 \mathrm{gtts} / \mathrm{min}\)

Short answer

C: 40 gtts/min

Step-by-step solution

Identify Given Information

The nurse needs to administer 500 mg of ampicillin in a 50 ml bag over 20 minutes. The IV drop factor is 15 gtts/ml.

Determine the Volume to be Infused

The volume to be infused is 50 ml because the ampicillin is in a 50 ml bag of D5W.

Calculate the Infusion Rate in Drops per Minute

Use the formula for drops per minute: \[ \text{Drops per minute} = \frac{\text{Volume (ml)} \times \text{Drop factor (gtts/ml)}}{\text{Time (minutes)}} \] Substitute the given values: \[ \text{Drops per minute} = \frac{50 \text{ ml} \times 15 \text{ gtts/ml}}{20 \text{ minutes}} = \frac{750 \text{ gtts}}{20 \text{ minutes}} = 37.5 \text{ gtts/minute} \]

Round to the Nearest Whole Number

Since 37.5 drops per minute is not feasible, round it to the nearest whole number, which is 38 drops per minute.

Select the Closest Correct Answer

The closest answer to 38 drops per minute in the options provided is 40 gtts/min. Therefore, the correct answer is C: 40 gtts/min.

Key concepts

IV infusion rate

When administering IV medication, it's important to calculate the infusion rate correctly. This rate tells us how fast the IV fluid should be administered to the patient. Infusion rate can be calculated based on the volume of the fluid and the time over which it needs to be delivered. The formula for calculating the infusion rate in drops per minute (gtts/min) is: \[ \text{Drops per minute} = \frac{\text{Volume (ml)} \times \text{Drop factor (gtts/ml)}}{\text{Time (minutes)}} \] For example, if you have 50 ml to be administered over 20 minutes with a drop factor of 15 gtts/ml, substituting these values into the formula gives: \[ \text{Drops per minute} = \frac{50 \text{ ml} \times 15 \text{ gtts/ml}}{20 \text{ minutes}} = 37.5 \text{ gtts/minute} \] Rounding to the nearest whole number, we get 38 drops per minute. Thus, it is crucial to understand and apply this concept accurately to ensure safe medication administration.

Drop factor

The drop factor is a key element in IV calculations. It represents the number of drops (gtts) that make up 1 milliliter of fluid. Different IV tubing systems have different drop factors, and this information is usually provided in the IV set packaging. Common drop factors are 10, 15, 20, or 60 gtts/ml.
Using the correct drop factor is crucial. For example, if the drop factor is 15 gtts/ml, this means that 15 drops will equal 1 ml of fluid. If we were to use a different drop factor, say 20 gtts/ml, the number of drops required to administer the same volume would change.
Incorrectly using the wrong drop factor can lead to both underdosing and overdosing, posing significant risks to patient health. Always double-check the drop factor on the IV tubing package before starting the infusion.

Medication dosage calculation

Proper medication dosage calculation is essential in nursing to ensure patients receive the correct amount of medication. For IV infusions, you need to calculate how much of a medication is in a certain volume of IV fluid.
In our example, the nurse needs to administer 500 mg of ampicillin within a 50 ml bag over 20 minutes. The key steps include identifying the medication dose, the volume of the IV fluid, and the time over which the medication should be administered.
By understanding these factors, we can determine the correct infusion rate so the patient receives 500 mg of ampicillin safely over the intended time period. Accurate calculation helps prevent medication errors and ensures effective treatment.

Nursing math skills

Nursing math skills are indispensable for safe and effective patient care. These skills encompass a range of calculations such as medication dosages, IV infusion rates, conversion of units, and interpreting lab values.
Let's consider our IV infusion rate calculation again. The steps included understanding the problem, identifying given information, using the appropriate formula, and applying the drop factor correctly. This multi-step process showcases how fundamental math skills are for nurses to ensure patients receive precise and accurate care.
Practicing these calculations regularly and double-checking your work can help boost your confidence and competence in administering medications. Mastery of nursing math skills is an invaluable part of a nurse’s toolkit in providing high-quality healthcare.