Question

Children's Tylenol is a solution containing \(32 \mathrm{mg} / \mathrm{mL}\). The recommended dose for a two-year-old child is \(120 \mathrm{mg}\). How many milliliters should be given to the child?

Short answer

3.75 mL of Children's Tylenol should be given to the child.

Step-by-step solution

Identify the Known Variables

The concentration of Children's Tylenol is given as 32 mg per mL. The recommended dose for the child is 120 mg.

Set Up the Equation

To find the volume of Tylenol in milliliters (mL) that contains the recommended dose, use the formula dose (mg) = concentration (mg/mL) * volume (mL).

Solve for the Volume

Rearrange the formula to solve for volume (mL): volume (mL) = dose (mg) / concentration (mg/mL). Substitute the known values to find the volume: volume (mL) = 120 mg / 32 mg/mL.

Calculate the Volume

Perform the division to find the volume in milliliters. volume (mL) = 120 mg / 32 mg/mL = 3.75 mL.

Key concepts

Understanding Medication Dosage Calculation

The accurate calculation of medication dosage is critical, especially when it comes to children's medications where precision is paramount for safety. Dosage calculation involves determining the appropriate amount of medicine based on the strength of the medication's concentration and the recommended dose. In our example, the Children's Tylenol has a concentration of 32 mg/ml and the recommended dose for a two-year-old is 120 mg. To ensure the child receives the right amount of medication without overdose or underdose, the total volume of Tylenol needed is calculated using a simple formula.

To avoid mistakes in the calculation process, always double-check the units and the concentration. This ensures that the amount of medicine given is safe and effective for the child's medical needs.

Concentration of Solutions Explained

The concentration of a solution is a measure of how much solute is dissolved in a given volume of solvent. It is typically expressed as a ratio such as milligrams per milliliter (mg/mL) in medication solutions. Understanding this concept is important not only in healthcare settings for appropriate medication administration but also in various scientific applications.

In our Tylenol example, the solution's concentration is 32 mg/mL, indicating that each milliliter of the Tylenol solution contains 32 milligrams of the active ingredient. When managing health conditions, the right concentration ensures the effectiveness of the treatment while also minimizing the risk of potential side effects. It's important to master solution concentration calculations to handle medications safely.

Dimensional Analysis in Calculating Dosages

Dimensional analysis, also known as unit factor method or the factor-label method, is a powerful tool used in calculations that involve units of measurement. The process involves conversion factors to go from one unit of measure to another.

In the context of our medication dosage problem, dimensional analysis helps to convert the recommended dose, which is in milligrams, to the volume, in milliliters, that should be administered based on the concentration. Following our Tylenol problem, beginning with the 120 mg recommended dose, and knowing the concentration (32 mg/mL), we apply the conversion factor (1 mL/32 mg) to arrive at the volume in mL. This method reduces errors, ensures consistency in calculations, and increases the safety of medication administration by enforcing the right units throughout the problem-solving process. Becoming proficient in dimensional analysis is a valuable skill in both academic and professional settings.