Problem 30 - Calculate With Confidence

Question

Calculate the following dosages using the medication label or information provided. Label answers correctly: tabs, caps, mL. Answers expressed in milliliters should be rounded to the nearest tenth where indicated. Order: Stadol 1 mg IM q4h p.r.n. for pain. Available: Stadol labeled 2 mg per mL ____________________________

Step-by-Step Solution

Answer

0.5 mL

Step 1: Identify the prescribed dosage

The order states 1 mg of Stadol IM (intramuscular) every 4 hours as needed for pain.

Step 2: Determine concentration from available supply

The available medication is labeled as 2 mg per mL.

Step 3: Set up a proportion

Using the available concentration, set up a proportion to determine how many mL are needed to achieve the prescribed dose: \(\frac{1 \text{ mg}}{x \text{ mL}} = \frac{2 \text{ mg}}{1 \text{ mL}}\).

Step 4: Solve for x

Cross-multiply to solve for \(x\): \(1 \times 1 = 2 \times x\) leads to \(x = \frac{1}{2}\).

Step 5: Calculate the dosage in mL

According to the calculations, \(x = 0.5\), meaning 0.5 mL is needed to administer a 1 mg dose.

Key Concepts

Medication Dosage

Medication dosage refers to the prescribed amount of a drug that a patient needs to take within a specific period. This is critical because administering the correct dose ensures the drug's effectiveness, and minimizes the risk of adverse effects. Dosages are often specified in units such as milligrams (mg), milliliters (mL), tablets (tabs), or capsules (caps). Dosage calculation is an essential skill for healthcare professionals. They must be able to accurately interpret prescriptions, which may state the dosage in terms the availability of the medication on hand. For instance, the prescription might require a specific dose in mg, whereas the medication available might be in mg/mL. It's important to convert and sometimes round the dosage to correctly prepare and administer the medication.

Proportion Method

The proportion method is a widely used mathematical approach in medication dosage calculations. In our case, we are utilizing this technique to convert the available dosage into the required dose.To set up a proper proportion, you need two ratios set equal to each other. For instance, if the medication is labeled as 2 mg per mL, and a 1 mg dose is necessary, create the equation:\[\frac{1 \, \text{mg}}{x \, \text{mL}} = \frac{2 \, \text{mg}}{1 \, \text{mL}}\]Here, \(x\) represents the mL of the solution required to administer the prescribed 1 mg dose. Solving this proportion involves cross-multiplication: - Multiply the means and extremes: \(1 \times 1 = 2 \times x\) - Simplify to find \(x\): \(x = \frac{1}{2}\), which calculates to 0.5 mL.Proportions are especially useful when the available dosage form differs from what is ordered. This method allows for precise and clear conversion of measurements, ensuring safe and effective patient care.

Intramuscular Injection

An intramuscular injection (IM) involves delivering medication directly into a muscle. This method is often chosen for drugs that need to be absorbed quickly into the bloodstream or when the medication cannot be taken orally. Intramuscular injections are typically administered in areas with substantial muscle mass, such as: - Deltoid muscle of the arm - Vastus lateralis muscle on the thigh - Ventrogluteal muscle on the hip - Dorsogluteal site on the buttocks For accurate delivery, healthcare professionals must be trained to select the appropriate site and needle size based on patient size and drug viscosity. Rotating injection sites is advisable to prevent tissue damage and ensure consistent absorption. IM injections are crucial for managing pain effectively, as seen in administering the drug Stadol. This method allows for timely relief, providing essential comfort for the patient.