Question

Calculate the following medication dosages using the dimensional analysis method. Use medication labels or information provided. Label answers correctly: tab, caps, mL. Answers expressed in milliliters should be expressed to the nearest tenth, except where indicated. Order: Diphenhydramine \(60 \mathrm{mg}\) IM stat. Available: Diphenhydramine labeled \(50 \mathrm{mg}\) per \(\mathrm{mL}\) ______

Short answer

Administer 1.2 mL of Diphenhydramine.

Step-by-step solution

Define the Variables

Identify the variables involved in the problem. The physician has ordered Diphenhydramine in a dose of \(60 \, \mathrm{mg}\) to be administered intramuscularly (IM). The available medication provides \(50 \, \mathrm{mg}\) of Diphenhydramine per \(1 \, \mathrm{mL}\).

Set Up Dimensional Analysis

To find out how many milliliters you need, start by setting up the conversion ratio: \( \frac{50 \, \mathrm{mg}}{1 \, \mathrm{mL}} \). Then, you'll use this to convert the ordered dose of \(60 \, \mathrm{mg}\) into milliliters.

Perform the Conversion

Use the conversion factor to find how many milliliters are needed: \[\text{mL needed} = 60 \, \mathrm{mg} \times \frac{1 \, \mathrm{mL}}{50 \, \mathrm{mg}}\]It simplifies to:\[\text{mL needed} = \frac{60}{50} \, \mathrm{mL} = 1.2 \, \mathrm{mL}\]

Round Appropriately

Round the calculated milliliters to the nearest tenth as per the problem's instructions. In this case, \(1.2 \, \mathrm{mL}\) is already to the nearest tenth.

Box the Answer

Conclude by writing the final answer clearly: \[1.2 \, \mathrm{mL}\] of Diphenhydramine is the amount to be administered.

Key concepts

Medication Dosage Calculation

Calculating the correct medication dosage is a critical skill for healthcare professionals. This ensures that patients receive the proper amount of medication to effectively treat their conditions. The process often involves converting a prescribed dose into a measurable quantity, such as milliliters. Dimensional analysis is a powerful method used to achieve this conversion. It enables you to work through unit conversions systematically, ensuring accuracy and consistency. The key steps in this process are:

• Identify the prescribed dose and the concentration of available medication.
• Set up a conversion factor. For example, if you have 50 mg/mL and need to deliver 60 mg, you'll reframe the equation to solve for mL.
• Perform the calculation precisely and ensure all units are properly canceled out, leaving you with the desired unit.
• Round the result to the appropriate decimal place as instructed, often to the nearest tenth for milliliters.

By following these steps, you can efficiently convert and calculate medication dosages, reducing the risk of medication errors. This accuracy is especially critical in environments where precise dosages are necessary to avoid adverse effects.

Pharmacology

Pharmacology is the branch of medicine that focuses on the use and effects of drugs in the treatment of illnesses. A fundamental aspect of pharmacology includes understanding how drugs interact with the body to produce their effects. Each medication has a particular way it should be administered, and specific effects it aims to achieve.
The cornerstone of pharmacology is the concept of dosage. The effectiveness and safety of treatment are closely linked to the correct dosage of medication prescribed. Factors influencing dosage include the patient’s age, weight, liver and kidney function, and specific health conditions the drug targets.

• Understanding these factors ensures that healthcare providers prescribe the right amount of medication.
• Ensuring the correct route of administration, such as intramuscular, is also part of pharmacological expertise.

This knowledge helps in forecasting how medicines will work in diverse populations, thus allowing for tailored and effective patient care.

Intramuscular Injection

Intramuscular injection (IM) is a method of delivering medication deep into the muscles. This technique is employed when medications need to be absorbed quickly and efficiently into the bloodstream. IM injections are commonly used for drugs like vaccines, hormones, and antibiotics.
There are several advantages and considerations with this route of administration:

• IM injections provide faster absorption than subcutaneous methods because muscles have a more abundant blood supply.
• The injection site should be chosen carefully to avoid nerves and blood vessels; common sites include the deltoid (upper arm) and the gluteus medius (buttocks).
• A proper technique helps minimize patient discomfort and the risk of complications, like infection or tissue damage.

It's crucial for healthcare providers to be adept at administering IM injections, informed by a thorough understanding of muscle anatomy and appropriate injection techniques.