Question

A physician has ordered \(325 \mathrm{mg}\) of atropine to be given to a patient intramuscularly. If atropine were available as a solution that contained \(5000 \mu\) \(\mathrm{g} / \mathrm{mL}\), how many milliliters would you need to give the patient?

Short answer

To find the volume of the atropine solution needed to deliver the ordered amount of 325 mg, first convert the ordered amount to µg: 325 mg * 1000 µg/mg = 325,000 µg. Then, use dimensional analysis to find the volume: \( \frac{325,000 ~µg}{5000 ~µg/mL} = 65 ~mL \). Therefore, the patient would need 65 milliliters of the atropine solution.

Step-by-step solution

Convert the amount of atropine ordered into the same unit as the concentration of the solution

Since the concentration is given in µg/mL and the ordered amount of atropine is given in mg, let's convert the ordered amount from mg to µg. We know that 1 mg = 1000 µg. Multiply the ordered amount by this factor to make the units consistent. Ordered amount in µg = 325 mg * 1000 µg/mg

Calculate the volume of atropine solution needed to deliver the ordered amount

Now that both the ordered amount and concentration are in the same unit (µg), we can use dimensional analysis to find the volume. \( \frac{Ordered ~amount}{Concentration} = Volume \) \( \frac{325,000 ~µg}{5000 ~µg/mL} = Volume ~in ~mL \)

Solve for the volume

Divide 325,000 µg by 5000 µg/mL to calculate the volume in milliliters: \( Volume = \frac{325,000 ~µg}{5000 ~µg/mL} = 65 ~mL \) The volume of atropine solution needed to deliver the ordered amount of 325 mg is 65 milliliters.

Key concepts

Dimensional Analysis

Dimensional analysis is a crucial mathematical method used to convert one unit of measure to another, ensuring that equations balance dimensionally. In the context of healthcare and medication dosing, this technique is essential for patient safety, as it helps to accurately calculate the correct dosage of a drug.

For instance, in the exercise, we used dimensional analysis to convert the physician's order from milligrams to micrograms. The process required understanding the relationship between these units: one milligram equals one thousand micrograms. This concept is fundamental when dealing with medication dosages, as drug concentrations can be provided in various units.

Unit Conversion

Unit conversion plays a pivotal role in various scientific calculations, including medicine. To convert units, we apply a conversion factor that mathematically relates two units. In healthcare, performing accurate unit conversions can mean the difference between an effective dose and a potentially dangerous overdose or underdose.

In the provided example, the conversion factor was 1000 micrograms per milligram, which allowed us to seamlessly transition from milligrams, a larger unit, to micrograms, a smaller unit. Mathematicians and scientists always aim to perform calculations with uniform units to simplify and avoid errors in the final results.

Medical Dosing

Medical dosing entails measuring the appropriate amount of a drug to administer to a patient based on doctor's orders. This process necessitates a deep understanding of dosage calculations, which include unit conversions and dimensional analysis, to ensure patient safety and drug efficacy.

The key to successful medical dosing lies in precision and accuracy. As demonstrated in the solution to the exercise, we calculated the exact volume required to achieve the prescribed dose. This precise measurement ensures that the patient receives the right amount of the medication, neither too much nor too little.

Chemistry Pharmacology

Chemistry pharmacology encapsulates the study of drugs and their interactions with living systems. In this field, knowing how to perform dosage calculations is essential, as it involves understanding both the chemical properties of drugs and their physiological effects on the body.

The exercise showcases an application of chemistry pharmacology where the concentration of a pharmaceutical substance (atropine) in a solution is given, and a healthcare provider must compute how to administer the medication properly. Through correct dosage calculation, healthcare professionals can ensure the safety and effectiveness of drug treatments.