Question

The physician ordered penicillin (Penicilin G) 250,000 units intravenously. The nurse has on hand penicillin 20,000,000 units in \(20 \mathrm{ml}\). How many ml contains the ordered dose? a. \(0.25 \mathrm{ml}\) b. \(4 \mathrm{ml}\) c. \(16 \mathrm{ml}\) d. \(25 \mathrm{ml}\)

Short answer

0.25 ml

Step-by-step solution

Understand the Problem

The task is to calculate the volume in milliliters (ml) of penicillin needed to obtain the ordered dose of 250,000 units from a solution that contains 20,000,000 units in 20 ml.

Set up the Proportion

Using a proportion, which is a statement that two ratios are equal, we set up the following equation: \(\frac{250,000 \text{ units}}{x \text{ ml}} = \frac{20,000,000 \text{ units}}{20 \text{ ml}}\) where \(x\) is the volume in ml that contains 250,000 units of penicillin.

Solve for x

Cross-multiply to solve for the unknown volume (x): \(250,000 \text{ units} \times 20 \text{ ml} = 20,000,000 \text{ units} \times x \text{ ml}\).Now divide both sides of the equation by 20,000,000 to isolate x: \(x = \frac{250,000 \times 20}{20,000,000}\).

Calculate the Volume

Carry out the division to find the volume of penicillin required in ml:\(x = \frac{250,000 \times 20}{20,000,000} = \frac{5,000,000}{20,000,000} = 0.25 \text{ ml}\).

Key concepts

Medication Dosage Calculation

Understanding medication dosage calculation is crucial for administeringe the correct amount of medication to patients. It involves mathematics and attention to detail. The goal is to ensure patient safety by accurately calculating dosages based on a doctor's order, the concentration of the medication available, and the appropriate formula.

Let's look at a practical scenario: A physician orders 250,000 units of penicillin intravenously, and a nurse has penicillin with a concentration of 20,000,000 units in 20 ml at hand. To find the volume of penicillin needed, the nurse must perform a dosage calculation. This process entails setting up a proportional relation between the available concentration and the desired dose. In this case, we set up a proportion as follows: \(\frac{250,000 \text{ units}}{x \text{ ml}} = \frac{20,000,000 \text{ units}}{20 \text{ ml}}\).

By cross-multiplying and solving for x, the unknown volume, the nurse calculates that 0.25 ml of penicillin contains the ordered dose. Such calculations are everyday tasks in nursing practice, and mastering them ensures effective and safe patient care.

Nursing Pharmacology

Nursing pharmacology encompasses the understanding of how medications affect the human body and managing their administration. Nurses must be familiar with different types of medications, their uses, side effects, and how they interact with other drugs.

Administering penicillin—as with any medication—also requires knowledge of pharmacokinetics (how the body absorbs, distributes, metabolizes, and excretes a drug) and pharmacodynamics (the drug's actions and effects within the body). Understanding these principles helps the nurse anticipate how quickly a drug will take effect and how long it will last in the system, which is critical for determining proper dosage intervals. Moreover, nurses must recognize symptoms of allergic reactions or overdose.

By integrating their knowledge of pharmacology with accurate dosage calculations, nurses ensure medications achieve the desired therapeutic effect while minimizing potential risks to patients.

Proportion Calculations in Nursing

Proportion calculations in nursing are used to find out how much of a medication to give a patient, as demonstrated in the penicillin dosage example. To perform proportion calculations effectively, nurses should remember the key formula: \(\frac{dose \text{ ordered}}{quantity \text{ have}} = \frac{dose \text{ on hand}}{volume \text{ on hand}}\). After setting up the proportion, it involves cross-multiplication and solving for the unknown variable, which represents the amount of medication to administer.

Nurses need to be comfortable with these calculations, often under time constraints or in stressful situations, to ensure quick and accurate medication administration. Regular practice and adopting a step-by-step approach to calculations can prevent medication errors and ensure patient safety and quality care.