Question

Calculate the dosages below. Use the labels where provided. Calculate to the nearest hundredth where necessary. Order: Gentamicin \(7.3 \mathrm{mg}\) IM \(\mathrm{q} 12 \mathrm{~h}\). Available: \(20 \mathrm{mg}\) per \(2 \mathrm{~mL}\)

Short answer

Administer 0.73 mL of Gentamicin solution.

Step-by-step solution

Understand the Problem

We need to administer 7.3 mg of Gentamicin intramuscularly every 12 hours. However, the medication available is provided as a concentration of 20 mg per 2 mL. We need to convert the ordered dose into mL to determine how much volume to administer.

Set Up the Proportion

We create a proportion based on the available medication to find out how many milliliters correspond to 7.3 mg. We set it up like this: \( \frac{20 \, \text{mg}}{2 \, \text{mL}} = \frac{7.3 \, \text{mg}}{x \, \text{mL}} \). The goal is to solve for \( x \), which represents the volume in mL we need to administer.

Cross Multiply

Cross multiply to solve for \( x \). This gives us the equation: \( 20x = 7.3 \times 2 \). Simplify the right side to get \( 20x = 14.6 \).

Solve for x

Divide both sides of the equation by 20 to solve for \( x \): \( x = \frac{14.6}{20} \).

Calculate the Dosage

Perform the division to find \( x = 0.73 \). This means you need to administer 0.73 mL of the Gentamicin solution to provide the correct dosage of 7.3 mg.

Key concepts

Pharmacology

Pharmacology is the branch of medicine concerned with the uses, effects, and modes of actions of drugs. Understanding pharmacology is crucial for healthcare professionals to safely and effectively administer medications. Gentamicin, the drug in question, is an antibiotic used to treat a variety of bacterial infections.
It interacts with bacteria by inhibiting protein synthesis, which leads to the death of susceptible bacterial cells.

In pharmacology, it's important to know that drugs come in various forms and concentrations. The concentration (or strength) of a drug affects how it is dosed and administered.

• Healthcare professionals must identify the appropriate dosage to effectively fight infections while minimizing side effects.
• Each patient's physical condition and age may affect their response to the medication and must be considered with each dosage adjustment.

By understanding the basic principles of pharmacology, healthcare providers can make informed decisions about how best to use drugs like Gentamicin to treat patients.

Mathematics in Medicine

In the field of medicine, mathematics plays a pivotal role, especially in calculating the correct dosages of medications. This ensures patient safety and the intended therapeutic effects. Calculating dosages, like for Gentamicin, typically involves setting up a proportion to determine how much of a drug to give.
In our exercise, the concentration was 20 mg per 2 mL, and the goal was to administer 7.3 mg.

To solve this, a proportion was set up: \( \frac{20 \, \text{mg}}{2 \, \text{mL}} = \frac{7.3 \, \text{mg}}{x \, \text{mL}} \). Here, \( x \) is the unknown volume in milliliters needed. By cross-multiplying, the equation to solve becomes \( 20x = 14.6 \). Dividing both sides by 20, the solution is \( x = 0.73 \) mL.

• Understanding proportions is crucial because similar calculations are used frequently in clinical settings.
• An accurate calculation avoids underdosing, leading to ineffective treatment, or overdosing, leading to toxicity.

By mastering mathematics in medicine, healthcare professionals can ensure accurate and safe dispensing of medications.

Medication Administration

Administering medication accurately is a critical skill for healthcare workers to ensure patient safety and therapeutic efficacy. For medications given intramuscularly (IM), like Gentamicin, proper technique and dosage calculations are essential.
The ordered dose of 7.3 mg translates to administering 0.73 mL of the solution.

Here are important steps and considerations during medication administration:

• Double-check the accuracy of the dose calculation to ensure patient safety.
• Ensure the correct volume is drawn up into the syringe to match the calculated dosage.
• Be familiar with the appropriate injection sites for IM delivery, which include muscles such as deltoid, vastus lateralis, and ventrogluteal.
• Rotate injection sites to prevent tissue irritation or damage.

By following these guidelines, healthcare providers can administer medications effectively, ensuring that patients receive the full benefit of their treatment with minimized risk of side effects or complications.