Question

You have just purchased a \(500-\mathrm{mL}\) bottle of a decongestant medication. The doctor prescribed 2 teaspoons 4 times a day for 10 days. Have you purchased enough medication? \((1\) teaspoon \((\mathrm{tsp})=5 \mathrm{~mL})\)

Short answer

Yes, you've purchased enough medication.

Step-by-step solution

Determine the daily dosage in milliliters

First, calculate how many milliliters are taken per dose. Since 1 teaspoon is equal to 5 mL, and each dose is 2 teaspoons, we multiply: \[ 2 \text{ tsp} \times 5 \text{ mL/tsp} = 10 \text{ mL/dose} \] Next, calculate the total daily dosage by multiplying the amount per dose by the number of doses per day (4 times): \[ 10 \text{ mL/dose} \times 4 \text{ doses/day} = 40 \text{ mL/day} \]

Determine the total amount needed for 10 days

Multiply the daily dosage by the number of days (10 days) to find the total amount of medication needed: \[ 40 \text{ mL/day} \times 10 \text{ days} = 400 \text{ mL} \]

Compare the total amount needed with the bottle size

You bought a 500 mL bottle. Compare it with the total amount needed: Total amount needed: 400 mL Bottle size: 500 mL Since 400 mL < 500 mL, the bottle contains enough medication.

Key concepts

unit conversion

Understanding unit conversion is a key skill in calculating medication dosages. In this exercise, we converted teaspoons to milliliters because the prescription was given in teaspoons, but we needed to know the total amount in milliliters.

To start, we use the given conversion factor: 1 teaspoon equals 5 milliliters.

By knowing this, we convert the prescribed 2 teaspoons per dose to milliliters: \( 2 \text{ tsp} \times 5 \text{ mL/tsp} = 10 \text{ mL/dose} \).

Mastering unit conversions enables precise dosage calculations and is crucial for ensuring safe and effective treatment. Always double-check conversion factors, especially in medical contexts where accuracy is paramount.

daily dosage

Calculating the daily dosage is essential for determining if the medication purchased will last the prescribed period. Here, we first calculated the amount per dose and then the number of doses per day.

The prescription was for 2 teaspoons, 4 times a day. Converting teaspoons to milliliters, we found: \( 2 \text{ tsp} \times 5 \text{ mL/tsp} = 10 \text{ mL/dose} \).

Next, we multiplied the dosage per administration by the frequency of doses: \( 10 \text{ mL/dose} \times 4 \text{ doses/day} = 40 \text{ mL/day} \).

Knowing the daily dosage helps in understanding the overall medication requirement and aids in verifying if the quantity purchased matches the prescribed treatment duration.

prescription compliance

Prescription compliance ensures that patients follow the prescribed dosage accurately, impacting the effectiveness of the treatment.

In our exercise, compliance involves taking 2 teaspoons of medication 4 times a day for 10 days. Properly calculating the dose and ensuring the correct quantity of medication helps avoid missed doses and potential over or under medication.

Adhering strictly to the dosage regimen is crucial for achieving the desired therapeutic effects. Providing clear instructions and understanding the prescription fully can prevent errors and improve overall health outcomes.

problem-solving in chemistry

Problem-solving in chemistry often involves applying theoretical knowledge to practical scenarios like medication dosage calculations.

Our exercise demonstrates how to break down a complex problem into manageable steps: calculating unit conversions, determining daily dosage, and ensuring adequate medication supply. Identifying the right mathematical operations and applying them correctly is key to finding the solution.

This structured approach is useful not only in chemistry but also in various real-life situations requiring accurate calculations and logical reasoning. Developing strong problem-solving skills builds confidence in handling diverse tasks and making informed decisions.