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: Quinidine gluconate \(200 \mathrm{mg}\) IM \(\mathrm{q} 8 \mathrm{~h}\). Available: Quinidine gluconate labeled \(80 \mathrm{mg}\) per \(\mathrm{mL}\)______

Short answer

Administer 2.5 mL.

Step-by-step solution

Gather Information

We need to administer 200 mg of Quinidine gluconate. The vial available contains Quinidine gluconate in concentration of 80 mg/mL.

Set Up Dimensional Analysis

Use the dimensional analysis method to determine how many mL you'll need to provide 200 mg. Start by writing the prescribed dose as a fraction: \(\frac{200 \, \text{mg}}{1}\). The dose must be converted to mL using the concentration given as a conversion factor: \(\frac{1 \, \text{mL}}{80 \, \text{mg}}\).

Perform the Calculation

Multiply these fractions to cancel out the mg unit. You get: \(\frac{200 \, \text{mg}}{1} \times \frac{1 \, \text{mL}}{80 \, \text{mg}} = \frac{200 \times 1 \, \text{mL}}{80} = \frac{200}{80} \, \text{mL}\).

Solve for mL

Simplify the fraction \(\frac{200}{80}\) to find the volume in mL: \(\frac{200}{80} = 2.5\).

Conclusion

The dosage calculation shows that you need to administer 2.5 mL of Quinidine gluconate to meet the 200 mg order.

Key concepts

Medication Dosage Calculation

Medication dosage calculation is a fundamental skill for healthcare professionals. Accurate dosage ensures that the patient receives the intended therapeutic effect while minimizing the risk of adverse effects. Nurses and pharmacists, especially, rely on precise calculations to deliver safe and effective medication therapy. The primary goal of medication dosage calculation is to determine the correct amount of a drug to administer based on the prescribed order.
When calculating medication dosages, it's essential to understand the relationship between the dose ordered by the physician and what is available in stock. For instance, if a doctor prescribes 200 mg of Quinidine gluconate, and the available medication concentration is 80 mg/mL, healthcare providers must determine how many milliliters of the medication to administer to achieve the prescribed dose. This process not only ensures accuracy but also fosters patient safety.

Dimensional Analysis Method

Dimensional analysis is a mathematical technique used to simplify medication dosage calculations by using ratio and proportion. It's often employed to convert measurements from one unit to another, making it a reliable tool in clinical settings. In essence, dimensional analysis involves multiplying fractions to cancel unwanted units and solve for the desired unit.
To use dimensional analysis in medication dosage calculations, start by expressing the dosage as a fraction. For example, if ordered to give 200 mg of medication, write it as \(\frac{200 \, \text{mg}}{1}\). Next, incorporate a conversion factor that relates milligrams to milliliters, like \(\frac{1 \, \text{mL}}{80 \, \text{mg}}\). When these fractions are multiplied, the mg units cancel out, leading to a simplified calculation that reveals the needed volume in mL. This method is particularly advantageous because it minimizes errors and can be applied consistently to different dosage forms.

Volume Conversion in Medicine

Volume conversion is an essential part of medication dosage calculation, especially when medications are supplied in different forms or concentrations. In many scenarios, healthcare providers need to convert a weight-based dosage, such as milligrams, into a volume measurement like milliliters to administer the appropriate amount of liquid medication.
The conversion process begins with understanding the concentration label on the medication bottle, for example, 80 mg per mL. This label serves as the conversion factor in your calculation. To determine how much of a liquid medication is required to deliver a prescribed dose, use the conversion factor to switch the unit from the drug's weight to its volume. For instance, converting 200 mg of a drug to its volume form when it's available as 80 mg/mL, you divide the ordered milligrams by the concentration to find the volume; hence, 200 divided by 80 results in 2.5 mL. Implementing accurate volume conversions is critical for delivering precise and safe medication dosages.