Problem 57 - Calculate With Confidence

Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Meperidine (Demerol) \(20 \mathrm{mg} \mathrm{IM}\) q 4h p.r.n. Available: Meperidine labeled \(25 \mathrm{mg}\) per mL

Step-by-Step Solution

Answer

Give 0.8 mL of Meperidine to deliver a 20 mg dose.

Step 1: Understand the Problem

The doctor has prescribed Meperidine at a dosage of 20 mg per dose. We need to calculate how many milliliters of the available solution should be administered to deliver this 20 mg dose.

Step 2: Determine Concentration Per mL

We know that the available solution is labeled with Meperidine at a concentration of 25 mg per mL. This means every milliliter of the solution contains 25 mg of Meperidine.

Step 3: Set Up the Proportion

To find out how many milliliters contain 20 mg, set up a proportion between the desired dose (20 mg) and the concentration (25 mg/mL): \[ \frac{20 \, \text{mg}}{x \, \text{mL}} = \frac{25 \, \text{mg}}{1 \, \text{mL}} \]

Step 4: Solve the Proportion

Cross-multiply and solve for \(x\):\[ 25x = 20 \times 1 \]\[ 25x = 20 \]\[ x = \frac{20}{25} = 0.8 \]

Step 5: Round the Answer

Since the problem asks for the answer rounded to the nearest tenth, check if rounding is necessary. The value we have calculated is already at the nearest tenth, so no further rounding is needed.

Key Concepts

Pharmacology

Pharmacology is the science of drugs, including their composition, uses, and effects on the body. It is crucial in healthcare as it helps in understanding how drugs interact with the body and how to use them safely and effectively. Pharmacology covers two important concepts:

• Pharmacodynamics: This studies the effects of drugs on the body and how they work to achieve their desired effects.
• Pharmacokinetics: This examines how the body absorbs, distributes, metabolizes, and excretes drugs.

In this exercise, we focus on the dosage calculation of Meperidine, an opioid pain medication used to manage moderate to severe pain. Understanding pharmacology ensures healthcare professionals administer the right drug in the correct dosage, maximizing its therapeutic effect while minimizing side effects.

Proportional Reasoning

Proportional reasoning is a mathematical process used to solve problems that involve ratios or relationships between numbers. It helps us calculate dosages accurately in pharmacology by setting up equations or proportions to solve for unknowns.When calculating Meperidine dosage, we use a proportion to determine how many milliliters are needed to deliver a 20 mg dose, given the available concentration of 25 mg/mL. The proportion is:\[ \frac{20 \, \text{mg}}{x \, \text{mL}} = \frac{25 \, \text{mg}}{1 \, \text{mL}} \]Here, "x" represents the milliliters needed. We solve for "x" by cross-multiplying and dividing, which gives us the dosage required. Solving proportions requires careful attention to ensure correct calculations and accurate medication administration.

Medication Administration

Medication administration is a critical process in healthcare, aiming to ensure safe and accurate delivery of medications to patients. Proper administration involves several steps to guarantee patient safety and treatment efficacy:

• Correct Dosage: Ensure the dose is accurate as per the prescribed amount.
• Right Route: Administer via the correct route such as orally, rectally, or intramuscularly (IM), as specified.
• Proper Timing: Follow the prescribed schedule, for example, 'q 4h p.r.n.' which means every 4 hours as needed.

For Meperidine, the verification of the calculated 0.8 mL of the drug to be administered IM ensures the dose is safely prepared and given correctly. Attention to these steps reduces the risk of errors and enhances patient confidence in their care team.