Problem 30 - Chemistry The Science in Context

Question

Dilution of Adult-Strength Cough Syrup A standard dose of an over-the-counter cough suppressant for adults is \(20.0 \mathrm{mL} .\) A portion this size contains \(35 \mathrm{mg}\) of the active pharmaceutical ingredient (API). Your pediatrician says you may give this medication to your 6-year-old child, but the child may take only \(10.0 \mathrm{mL}\) at a time and receive a maximum of 4.00 mg of the API. What is the concentration in \(\mathrm{mg} / \mathrm{mL}\) of the adult-strength medication, and how many millimeters of it would you need to dilute to make 100.0 mL of child-strength cough syrup?

Step-by-Step Solution

Answer

Answer: The concentration of the adult-strength cough syrup is 1.75 mg/mL. To create 100.0 mL of child-strength cough syrup, approximately 22.86 mL of adult-strength cough syrup would be needed.

Step 1: Find the concentration of the adult-strength cough syrup

To find the concentration of the adult-strength cough syrup, we can use the following formula: Concentration = Amount of API / Volume of Syrup Given: Volume of adult-strength cough syrup = 20.0 mL Amount of API in adult-strength cough syrup = 35 mg Concentration of adult-strength = (35 mg) / (20.0 mL) = 1.75 mg/mL

Step 2: Find the API quantity in child-strength cough syrup

We know that the child can take a maximum of 4.00 mg API in a 10.0 mL dose. So, we can calculate the amount of API in 100.0 mL of child-strength cough syrup based on this proportion: API in child-strength (100.0 mL) = (4.00 mg API / 10.0 mL) * 100.0 mL = 40 mg API

Step 3: Determine the mL of adult-strength cough syrup needed for child-strength cough syrup

To make 100.0 mL of child-strength cough syrup using the adult-strength medication, we need to dilute the adult-strength cough syrup until the required API quantity for the child is achieved. Adult-strength concentration = 1.75 mg/mL Child-strength API needed = 40 mg Using the concentration formula: Volume of adult-strength = Amount of API / Concentration = 40 mg / 1.75 mg/mL = 22.86 mL (approximately) So, to make 100.0 mL of child-strength cough syrup, we would need to dilute approximately 22.86 mL of adult-strength cough syrup.

Key Concepts

Concentration

Concentration is a fundamental concept in chemistry and pharmacology. It refers to the amount of a substance in a given volume of solution. Here, we are dealing with the concentration of an active pharmaceutical ingredient (API) in cough syrup.

You can calculate concentration using the formula:

• Concentration = Amount of API / Volume of Syrup

For example, if a cough syrup contains 35 mg of an API in 20 mL of solution, the concentration is found by dividing the amount of API by the volume of the liquid, which gives you 1.75 mg/mL.

This measurement helps determine how much of a drug is in each dose and ensures that each dose delivers the required therapeutic effect without exceeding safety limits. Proper understanding of concentration is crucial for anyone involved in administering or preparing medications.

Cough Syrup

Cough syrup is a common over-the-counter medication used to relieve symptoms of cough and sore throat. Typically, cough syrup contains active ingredients, like dextromethorphan, that suppress the cough reflex.

When designing cough syrup for children, it's essential to adjust the concentration of the API to be safe for a child's body weight and metabolism. Adult cough syrups are often too potent for children, so they need to be diluted correctly to prevent overdose risks.

• Overdose can lead to harmful side effects, especially in younger patients.
• Proper dosing helps avoid these risks while still providing symptomatic relief.

Understanding the specific needs for pediatric formulations highlights the importance of precise dilution and measurement in pharmaceutical calculations.

Pharmaceutical Calculations

Pharmaceutical calculations are essential in ensuring that medications are both safe and effective. They involve determining the correct dose, figuring out how much of each ingredient is needed to prepare a mixture, and ensuring the concentration is within safe limits for patients.

In the context of the exercise, pharmaceutical calculations were used to ensure that the cough syrup dosage is appropriate for a child. We determined the amount of adult-strength syrup required to make a safe child dosage by calculating:

• The concentration of the adult syrup (1.75 mg/mL).
• The total API needed for a child-safe dose (40 mg).
• The volume of undiluted syrup to be used (22.86 mL) for the specified total volume (100 mL).

Performing these calculations helps pharmacists and healthcare providers formulate treatments appropriately, ensuring both safety and efficacy for patients. Accuracy in pharmaceutical calculations is vital to patient care and medication management.