Problem 45 - Calculate With Confidence

Question

Calculate the volume necessary (in milliliters) to provide the dosage ordered, using medication labels where available. Express your answer as a decimal fraction to the nearest tenth where indicated. Order: Meperidine hydrochloride \(50 \mathrm{mg}\) IM q4h p.r.n. for pain. Available: Meperidine \(75 \mathrm{mg}\) per \(\mathrm{mL}\) _______.

Step-by-Step Solution

Answer

Administer 0.7 mL of the medication.

Step 1: Understand the Order

The order prescribes Meperidine hydrochloride 50 mg to be administered intramuscularly every 4 hours as needed for pain. This means that each dose should be 50 mg of the medication.

Step 2: Examine Available Medication

The available concentration of Meperidine is 75 mg per mL. This means that each milliliter of the solution contains 75 mg of Meperidine.

Step 3: Set Up the Proportion

To find out how much volume is needed for 50 mg, we set up a proportion using the available concentration: \[ \frac{75 \, \text{mg}}{1 \, \text{mL}} = \frac{50 \, \text{mg}}{x \, \text{mL}} \] where \( x \) is the volume in mL that we need to find.

Step 4: Solve for x

Cross-multiply to solve for \( x \):\[ 75x = 50 \times 1 \] \[ 75x = 50 \] Now, divide both sides of the equation by 75:\[ x = \frac{50}{75} \] Calculating this gives \( x \approx 0.6667 \) mL.

Step 5: Round the Result

Round 0.6667 mL to the nearest tenth as instructed, which results in 0.7 mL.

Key Concepts

Understanding Medication Labels

Medication labels are essential for safe and effective dosage calculation. These labels provide vital information, such as the concentration of the medication. For instance, in our example, the medication Meperidine is provided at a concentration of 75 mg per mL. This denotes how much of the drug's active ingredient is present in a specific volume.
It is crucial when dosing, especially in precise administration requirements like intramuscular injections. Always double-check the medication label to ensure the correct concentration is used.
Correct interpretation prevents errors and ensures that the patient receives the proper amount of medication.

Utilizing the Proportion Method

The proportion method is a reliable mathematical tool utilized in dosage calculations in healthcare. When you deal with different medication strengths, especially as seen in our problem, you need to convert the ordered dose into the available dose.
Given the available concentration of Meperidine being 75 mg/mL, and the requirement being 50 mg, the proportion method helps determine the exact volume needed.
Here, you'll set up the equation:

• The known ratio: 75 mg / 1 mL.
• The unknown ratio: 50 mg / x mL, where x is the unknown volume you'll calculate.

By cross-multiplying and solving for x, you can find out how much volume is necessary for the ordered dose. This systematic approach lends confidence in achieving accurate dosing without guesswork.

Importance of Rounding Decimals

Decimal rounding is a critical final step in dosage calculation. It ensures the measurement is practical and suitable for administration.
Here, the calculation yields approximately 0.6667 mL. Rounding decimals comes into play as it simplifies the volume to a measurable and reasonable amount for practitioners.
According to the problem, you must round to the nearest tenth for simplicity and accuracy, resulting in 0.7 mL.
Always refer to guidelines or standard practices for rounding, as precision in medication administration is paramount to patient safety and effectiveness.