Question

Children's ibuprofen is a solution containing \(20 \mathrm{mg} / \mathrm{mL}\). The recommended dose for a two-year-old child is \(75 \mathrm{mg}\). How many milliliters should be given to the child?

Short answer

3.75 mL of the ibuprofen solution should be given to the child.

Step-by-step solution

Identify the dosage concentration

The concentration of the children's ibuprofen is given as 20 milligrams of ibuprofen per milliliter of solution, expressed as 20 mg/mL.

Determine the recommended dose

The recommended dose of ibuprofen for a two-year-old child is 75 mg.

Calculate the volume of solution required

To find out how many milliliters of the solution are required to achieve the recommended dose, divide the dose by the concentration. The calculation is as follows: \[ \text{Volume (mL)} = \frac{\text{Dose (mg)}}{\text{Concentration (mg/mL)}} \] Substitute the known values: \[ \text{Volume} = \frac{75 \text{ mg}}{20 \text{ mg/mL}} \] \[ \text{Volume} = 3.75 \text{ mL} \] This is the volume of the solution needed to administer the recommended dose.

Key concepts

Solution Concentration

When dealing with medications in liquid form, it's essential to understand solution concentration. This term refers to the amount of a substance (such as ibuprofen) dissolved in a specific volume of liquid. Usually, this is expressed in milligrams per milliliter (mg/mL), as seen in the original exercise.

Grasping the notion of concentration is much like knowing how strong your coffee is based on the amount of coffee grounds per cup of water. In the exercise, the 'strength' of the ibuprofen is 20 mg for every mL of solution. If you imagine a box filled with tiny 20 mg packets of ibuprofen, each of these packets would perfectly fit into 1 mL of the liquid solution it's in.

Why Understanding Concentration Matters

Understanding the concentration is vital for calculating the right dosage, ensuring that a patient receives the appropriate amount of medication—not too little, which may be ineffective, and not too much, which can be harmful.

Medicinal Dosage

Medicinal dosage refers to the exact amount of a drug that should be taken to achieve the desired therapeutic effect. For example, our exercise involves determining the correct dose of children's ibuprofen for a two-year-old child—75 mg. It is similar to following a recipe where the dose is like measuring specific ingredients to bake a cake; too much or too little can lead to a different, potentially unwanted result.

Healthcare professionals calculate the correct dosage based on factors such as age, weight, and the severity of the condition being treated. It's crucial to adhere to these recommendations for safety and efficacy.

Importance of Precise Dosage in Pediatrics

This is especially important in pediatrics, where the margin for error is low, and the consequence of incorrect dosing can be significant. That's why the calculation in our exercise is so critical; it ensures the child gets just the right amount of medication.

Unit Conversion Chemistry

Unit conversion in chemistry is a fundamental skill, as it allows you to translate one type of measurement into another. This can involve converting between units of volume, mass, length, temperature, and more. In the context of our exercise, we're converting a medicinal dose measured in milligrams (mg) to a volume measured in milliliters (mL).

Think of unit conversion like using a currency converter to understand how much money you have while traveling in a foreign country. In chemistry and medicine, it ensures precise communication and understanding, as a misunderstanding could lead to errors in medication dosing.

Unit Conversion in the Exercise

In our child's ibuprofen example, we needed to find how many milliliters of solution equate to the required 75 mg dose. The conversion was straightforward: divide the dose in milligrams by the concentration in mg/mL. This is an essential skill in both educational settings and professional practice.