Problem 16 - Calculate With Confidence

Question

Order: Elixophyllin Elixir \(300 \mathrm{mg}\) by nasogastric tube b.i.d. Available: Elixophyllin liquid labeled \(160 \mathrm{mg}\) per \(15 \mathrm{~mL}\)

Step-by-Step Solution

Answer

Administer 28.13 mL of Elixophyllin each dose.

Step 1: Understand the Medication Order

The doctor has ordered Elixophyllin Elixir at a dosage of 300 mg to be administered twice a day (b.i.d.) via a nasogastric tube.

Step 2: Determine the Concentration of Available Medication

The available Elixophyllin liquid has a concentration of 160 mg per 15 mL, which means that every 15 mL contains 160 mg of the medication.

Step 3: Set Up a Proportion to Find Required Volume

We need to determine how many mL contain 300 mg of Elixophyllin. Set up the proportion: \( \frac{160 \text{ mg}}{15 \text{ mL}} = \frac{300 \text{ mg}}{x \text{ mL}} \), where \( x \) is the volume we need to find.

Step 4: Solve the Proportion

Cross-multiply to find \( x \): \( 160x = 4500 \). Solve for \( x \) by dividing both sides by 160: \( x = \frac{4500}{160} \approx 28.125 \text{ mL} \).

Step 5: Conclusion

To administer a dose of 300 mg, approximately 28.13 mL of the Elixophyllin liquid should be given each time.

Key Concepts

Proportional Reasoning in Dosage Calculation

In medication dosage calculation, proportional reasoning is a vital skill. It helps in determining the correct volume of medication needed based on its concentration. By setting up a proportion, we can easily calculate the unknown quantity when the dosage prescribed does not match the available concentration. For our example, we know that 160 mg of Elixophyllin is present in 15 mL. The goal is to find out how much volume contains 300 mg. This is where proportional reasoning shines. We set up the proportion as:

• Given concentration: \( \frac{160 \text{ mg}}{15 \text{ mL}} \)
• Required concentration: \( \frac{300 \text{ mg}}{x \text{ mL}} \)

Then we solve for \( x \) using cross multiplication. This method ensures precision and consistency in calculation, which is crucial for patient safety.

Understanding Medication Orders

Medication orders are instructions provided by a healthcare provider that detail specific information on how a medication should be given. They specify the medication's name, dosage, administration route, frequency, and sometimes the duration of treatment. Understanding these details is essential for safe administration. In our exercise, the order is for "Elixophyllin Elixir 300 mg, administered b.i.d (twice a day) by nasogastric tube." This tells us exactly what medication and dosage to prepare, how it should be given, and how often. It's important always to check these details carefully to ensure you administer the patient's medication as prescribed without errors.

Nasogastric Tube Administration

Administering medication through a nasogastric (NG) tube involves giving medication directly into the stomach through a tube inserted via the nose. This method is often used for patients who cannot take medication orally. Steps typically involve:

• Checking the tube placement and ensuring it's correctly positioned in the stomach.
• Flushing the tube with a small amount of water before and after medication administration to ensure the tube is clear.
• Administering the correct volume of medication in liquid form.

NG tube administration requires careful attention to preparation and hygiene to prevent complications.

Concentration and Volume Calculation

When calculating how much of a liquid medication to administer, it’s crucial to understand its concentration, which tells how much of the active ingredient is present per specific unit of fluid. For Elixophyllin, the concentration is given as 160 mg per 15 mL.To calculate the required volume for a different dosage, such as 300 mg, follow these steps:1. Set up a proportion where the concentrations match the dosages.2. Solve for the unknown volume needed to match the prescribed dosage.Using the formula: \[ \frac{160 \text{ mg}}{15 \text{ mL}} = \frac{300 \text{ mg}}{x \text{ mL}} \]Cross-multiply to find the solution. This method ensures you give the precise amount of medication, maintaining efficacy and safety.