Question

The nurse has an order to administer meperidine (Demerol) \(75 \mathrm{mg}\) IM for pain. The drug is available Demerol \(100 \mathrm{mg}\) in \(2 \mathrm{mLs}\). How many \(\mathrm{mL}(\mathrm{S})\) will the nurse administer? A. \(1.0 \mathrm{~mL}\) B. \(1.3 \mathrm{~mL}\) C. \(1.5 \mathrm{~mL}\) D. \(1.7 \mathrm{~mL}\)

Short answer

Answer: 1.5 mL

Step-by-step solution

Identify the known and unknown quantities

The known quantities are: - The required dosage is 75 mg - The available concentration is 100 mg in 2mL The unknown quantity: the amount of solution to administer in mL.

Set up a proportion equation

A proportion equation can be set up according to the problem. Since we know that 100 mg corresponds to 2 mL of the solution, and we want to find out the volume equivalent to 75 mg, we write the proportion as follows: \[\frac{100mg}{2mL} = \frac{75mg}{xmL}\] Where \(x\) is the unknown quantity to be found, which is the volume of the solution to be administered to the patient.

Solving the proportion equation

Cross-Multiply and solve for \(x\) to find out the volume that would contain 75 mg of meperidine: \[100mg * xmL = 75mg * 2mL\] \[100x = 150\] \[x = \frac{150}{100}\] \[x = 1.5 mL\]

Choose the answer

According to the calculation, 1.5 mL of the given solution will provide the required 75 mg of meperidine. Therefore, the correct answer is (C) \(1.5 \mathrm{mL}\)

Key concepts

Nursing Mathematics

Nursing mathematics is an essential skill that every nurse must master. This includes understanding basic arithmetic to perform calculations related to medication doses, intravenous fluids, and other treatments. Nurses often deal with medication calculations that require precision and accuracy, as any errors can have serious consequences for patient care.

In the case of the nurse administering meperidine, they need to utilize several math skills effectively:

• First, understanding and interpreting prescription details to identify necessary dosages.
• Next, utilizing conversion factors and proportional reasoning based on the concentration of medication available.
• Finally, applying arithmetic operations like multiplication and division to solve equations accurately.

By practicing these skills, nurses can ensure they administer the right amount of medication, optimizing therapeutic outcomes and minimizing risks.

Dosage Proportion

The concept of dosage proportion is crucial in nursing for calculating how much medicine to give a patient. It's a method of using ratios to determine the correct dose from what's available. If the drug's concentration is different from what's prescribed, nurses calculate the proportion to find the correct volume or number of tablets to administer.

In this specific example, the nurse has a medication order for 75 mg of meperidine. However, the available solution is 100 mg per 2 mL. The nurse must set up a proportion using the known concentration (100 mg per 2 mL) and the required dose (75 mg), leading to the equation:\[\frac{100 \ mg}{2 \ mL} = \frac{75 \ mg}{x \ mL}\]

Solving this proportion through cross-multiplication allows the nurse to find that 1.5 mL contains the necessary 75 mg dose. Understanding dosage proportion ensures that patients receive accurate medication amounts safely.

Intramuscular Injection Calculations

Intramuscular injection calculations specifically refer to determining the correct volume of medication when administering drugs via the intramuscular route. This form of drug delivery is widely used due to its fast absorption and effectiveness.

The steps for intramuscular injection dosage involve:

• Accurately identifying the prescribed dosage of medication needed.
• Confirming the concentration and total volume of the available medication.
• Setting up a calculation, often in the form of a proportion, to find the volume to administer.
• Cross-checking calculations to prevent errors.

For instance, our example involves the nurse calculating how much meperidine to administer intramuscularly by solving a proportion equation. By mastering these calculations, nurses can maintain the balance between effective treatment and patient safety.