Problem 54 - Calculate With Confidence

Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Procaine penicillin 150,000 units IM q12h. Available: Procaine penicillin 300,000 units per \(\mathrm{mL}\)

Step-by-Step Solution

Answer

Administer 0.5 mL of Procaine penicillin per dose.

Step 1: Understand the Order

The doctor's order is for the patient to receive 150,000 units of Procaine penicillin intramuscularly every 12 hours. This means you need to determine how many milliliters of the solution the patient should receive for each dose.

Step 2: Review Available Dosage

The available Procaine penicillin comes in a concentration of 300,000 units per milliliter. This information helps you calculate the needed volume to reach the prescribed dosage of 150,000 units.

Step 3: Set up the Calculation

You can find out how many milliliters to give by setting up a ratio. You need to determine how many milliliters are required to administer the 150,000 units from the available solution. The relationship is given by:\[\frac{150,000 \text{ units}}{x \text{ mL}} = \frac{300,000 \text{ units}}{1 \text{ mL}}\]

Step 4: Solve for x

Cross-multiply the equation:\[150,000 \times 1 = 300,000 \times x\]which simplifies to: \[150,000 = 300,000x\]. Now, solve for \(x\) by dividing both sides by 300,000:\[x = \frac{150,000}{300,000} = 0.5\]

Step 5: Conclude with the Dosage

The calculation shows that 0.5 milliliters of the available Procaine penicillin solution is required to administer 150,000 units. Finally, round your answer to the nearest tenth if necessary, although in this case, it is already to the nearest tenth.

Key Concepts

Medication Administration

Understanding medication administration is crucial for safe patient care. It involves the correct handling and dispensing of drugs according to a physician's order, ensuring patients get the right medication and dosage.
This process usually includes verifying the medication, calculating the correct dose, and administering it through the appropriate route, such as intramuscularly (IM) in this scenario.
Key points to remember in medication administration:

• Double-check the physician's order to confirm the correct medication and dose.
• Understand the drug formulation and its concentration, as it's essential for dosage calculations.
• Be aware of the patient’s medical history and allergies to prevent adverse reactions.

Unit Conversion

Unit conversion plays a significant role in dosage calculations, especially in fields like pharmacology where medications often come in various strengths or concentrations.
In this exercise, the order requires converting units to milliliters since the medication is provided in a concentration rather than a dosage amount. The basic principle is to create an equation where the units cancel out and leave the desired measurement in milliliters.
Steps for converting dosage units:

• Identify the unit given in the order (e.g., units of penicillin) and the concentration available (e.g., units per milliliter).
• Set up a proportion that equates the ordered dose to the available concentration, allowing for direct conversion to milliliters.
• Cross-multiply to solve for the unknown quantity, ensuring you convert to the proper unit of administration.

Nursing Mathematics

Nursing mathematics involves a variety of calculations, including drug dosage computations, fluid intake, and output measurements. It is a core skill all nurses must master to ensure safe and effective patient care.
This mathematical competence helps nurses avoid dosing errors which can lead to significant health risks. In this exercise, nursing mathematics guides the proportional calculation from units to milliliters.
The importance of accuracy in nursing mathematics:

• Ensures patient safety by preventing underdosing or overdosing.
• Aids in adjusting medication doses for specific patient needs, like children or those with kidney issues.
• Involves vigilant checking and re-calculation to minimize human errors.

Pharmacology

Pharmacology is the science of drug action on biological systems. Understanding pharmacology helps healthcare providers predict the effects of medication, including therapeutic effects and potential side effects.
In the context of this exercise, knowledge of pharmacology ensures that Procaine penicillin is used effectively and safely, considering its mechanism and proper dosage.
Fundamentals of pharmacology in practice:

• Comprehend the drug's therapeutic effects and conditions it's prescribed for, ensuring it's appropriate for the patient.
• Understand drug interactions which could alter its efficacy or increase the risk of adverse effects.
• Educate patients about their medications, including potential side effects and how to take them correctly.