Question

Calculate the volume necessary (in milliliters) to provide the dosage ordered, using medication labels where available. Express your answer as a decimal fraction to the nearest tenth where indicated. Order: Luminal (phenobarbital) \(90 \mathrm{mg}\) IM stat. Available: Luminal \(130 \mathrm{mg}\) per \(\mathrm{ml}\) _______.

Short answer

0.7 ml

Step-by-step solution

Understand the Problem

We are given an order for Luminal (phenobarbital) at a dosage of \(90 \, \text{mg}\). The medication available is \(130 \, ext{mg/ml}\). We need to find out how many milliliters are needed to deliver the ordered \(90 \, \text{mg}\) dose.

Set Up the Calculation

Use the formula \( \text{Volume} = \frac{\text{Ordered Dose}}{\text{Concentration}} \). This means we will divide the ordered dose (\(90 \, \text{mg}\)) by the concentration (\(130 \, \text{mg/ml}\)).

Perform the Calculation

Calculate the volume by dividing \(90 \, \text{mg}\) by \(130 \, \text{mg/ml}\) to find out how many milliliters are needed: \[ \text{Volume} = \frac{90}{130} \]

Simplify and Round to Required Precision

Perform the division to get \(0.6923\ldots\). Round this decimal to the nearest tenth, which results in \(0.7\, \text{ml}\).

Key concepts

Volume Calculation in Pharmacy

In the pharmacy, calculating the right volume of medication is crucial to ensuring a patient receives the correct dose. When we are given a medication's concentration (in this case, 130 mg/ml for Luminal) and a specific dose (here, 90 mg), our goal is to determine how much liquid form of the medication is required to deliver the needed dose.

The core formula used in volume calculation is \[ \text{Volume} = \frac{\text{Ordered Dose}}{\text{Concentration}} \] Think of it as dividing the desired amount of active ingredient by how much active ingredient each unit of liquid contains. This division provides us with an answer in milliliters, which indicates how much of the liquid medication must be administered. This formula is a fundamental tool in ensuring that pharmacists and healthcare providers can accurately respond to dosage instructions.

Accurate volume calculations help maintain safety and efficacy in medication administration. Errors in this step can lead to underdosing or overdosing, both of which can have serious consequences. Thus, practicing these calculations and understanding the underlying principles are essential skills for anyone involved in medical dosage preparation.

Unit Conversion in Medicine

In the world of medicine, converting units is a frequent requirement, as medications can be ordered in milligrams, grams, micrograms, and more. In this problem, we worked with milligrams and needed to convert this to milliliters based on given concentration. It's not just about knowing the units but understanding how they interrelate.

For example, a medical order might specify a dosage in mg, while the medication label provides a concentration in mg/ml. To determine the correct volume to administer, conversions between these units become necessary. Such conversions are often performed using straightforward mathematical operations, based on the relationships between the units. Understanding these relationships is key: for every 1 ml of medication, there are 130 mg present. This makes it simpler to calculate the needed volume for a given mg order.

Unit conversion ensures that everyone involved in a patient's care is speaking the same 'language' concerning doses. Whether a healthcare provider is measuring liquids or discussing dosages with colleagues, accurate unit conversions are vital to safe patient outcomes. This attention to detail helps prevent misunderstandings and potential medication errors.

Rounding Decimal Fractions in Dosage Calculations

Rounding decimal fractions is an important practice in dosage calculations, especially when dealing with very precise medication volumes. In the medical context, rounding to the nearest tenth is common. This ensures that the dose is both safely and practically measurable while minimizing potential confusion.

In our example, after finding that the necessary volume of Luminal was approximately 0.6923 ml, it was rounded to the nearest tenth, resulting in 0.7 ml. Rounding helps streamline the measurement process: using simple, whole or decimal fractions makes it easier for administering personnel to draw up the medication without the need for ultra-precise equipment.

Proper rounding also plays a role in reducing errors. If decimal points were carried out too far in medical settings, the risk of miscalculating a dose increases. By convention, rounding provides a balance between accuracy and practicality, ensuring that dosage calculations remain feasible and safe across different healthcare environments.