Problem 49 - Calculate With Confidence

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: Morphine \(10 \mathrm{mg}\) subcut stat. (Express answer in hundredths.) Available: Morphine \(15 \mathrm{mg}\) per mL. _______.

Step-by-Step Solution

Answer

Administer 0.67 mL of Morphine.

Step 1: Identify the Dosage Ordered

The order is for Morphine, with a required dosage of 10 mg.

Step 2: Identify the Medication Concentration Available

You have available Morphine at a concentration of 15 mg per mL.

Step 3: Set Up the Ratio Equation

To find out how many milliliters are needed, set up the equation: \( \frac{15 \, \text{mg}}{1 \, \text{mL}} = \frac{10 \, \text{mg}}{x \, \text{mL}} \), where \(x\) is the amount in mL we need to determine.

Step 4: Solve for x

Cross-multiply to solve for \(x\): \(15x = 10 \times 1\). Thus, \(15x = 10\). Divide both sides by 15: \(x = \frac{10}{15} = \frac{2}{3}\) mL.

Step 5: Express the Solution to the Nearest Hundredth

Convert the fraction \(\frac{2}{3}\) to a decimal to find \(x\) approximately \(0.67\) when rounded to the nearest hundredth.

Key Concepts

Medication Concentration

Medication concentration refers to the amount of active drug available in a given volume of solution. In our exercise, the concentration of Morphine available is 15 mg per milliliter (mL). This means that for every 1 mL of the solution, there are 15 milligrams of Morphine. Understanding this concept is crucial because it allows healthcare providers to accurately administer the correct dose of medication based on the orders given by a physician.
When calculating doses, always pay close attention to the medication labels, as they provide you with the concentration needed to perform dosage calculations correctly. Here, we have identified the concentration as 15 mg/mL, which will be used in the ratio equation later.

Dosage Ordered

The dosage ordered is the specific amount of medication that a doctor has prescribed for a patient. In this case, the doctor has ordered 10 mg of Morphine to be administered subcutaneously and immediately (stat). This ordered dosage is the target amount of medication that needs to be delivered to ensure proper treatment, without under-dosing or overdosing the patient.
It's essential to carefully read and understand the dosage ordered, as this will be the basis for setting up your calculations. You will use this information to determine how much of the medication solution you should administer, based on its concentration.

Ratio Equation

A ratio equation is a mathematical method used to solve problems involving proportions or relationships between quantities. In the context of medical calculations, it helps us determine how much of a medicine solution to use in order to deliver the ordered dosage. For our exercise, the ratio equation is set up by comparing the known medication concentration to the dosage ordered.
To express this, we use the equation:

• Available: \( \frac{15 \, \text{mg}}{1 \, \text{mL}} \)
• Needed: \( \frac{10 \, \text{mg}}{x \, \text{mL}} \)

Here, \( x \) represents the amount in mL needed to achieve the ordered dose. Establishing this equation allows us to solve for \( x \), giving us the exact volume of the solution to prepare.

Solution to Nearest Unit

The final step in our calculation is to express the solution to the nearest unit, in this case, the nearest hundredth of a milliliter. After setting up and solving the ratio equation, we find \( x = \frac{2}{3} \, \text{mL} \). To make it more practical for dosing, fractions are often converted to decimal form. By dividing 2 by 3, we obtain approximately 0.66666..., which when rounded to the nearest hundredth, becomes 0.67 mL.
Rounding is essential in ensuring that doses are not only precise but also practical to measure and administer. Keeping calculations accurate to the necessary decimal place helps maintain the safety and effectiveness of medication administration.