Question

A children’s pain relief elixir contains 80. mg acetaminophen per 0.50 teaspoon. The dosage recommended for a child who weighs between 24 and 35 lb is 1.5 teaspoons. What is the range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and 35 lb?

Short answer

The range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and 35 lb is approximately $15.11\frac{mg}{kg}$ to $22.06\frac{mg}{kg}$.

Step-by-step solution

Convert weight from lb to kg

To convert the weight of the children from pounds to kilograms, we can use the conversion factor: 1 lb = 0.453592 kg. For 24 lb: $24lb\times \frac{0.453592kg}{1lb}\approx 10.88kg$ For 35 lb: $35lb\times \frac{0.453592kg}{1lb}\approx 15.88kg$

Calculate total acetaminophen per dose

The children's pain relief elixir has a concentration of 80 mg acetaminophen per 0.5 teaspoon. The recommended dosage for the given weight range is 1.5 teaspoons. To find the total amount of acetaminophen in the dose, we can use: Total acetaminophen (mg) = (1.5 teaspoons) × (80 mg acetaminophen / 0.5 teaspoon) Total acetaminophen (mg) = $1.5tsp\times \frac{80mg}{0.5tsp}=240mg$

Determine the dosage range in mg/kg

Now that we have the total acetaminophen in mg and the children's weight range in kg, we can calculate the dosage range in mg/kg. For the lower weight (10.88 kg): $\frac{240mg}{10.88kg}\approx 22.06\frac{mg}{kg}$ For the upper weight (15.88 kg): $\frac{240mg}{15.88kg}\approx 15.11\frac{mg}{kg}$ So the range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and 35 lb is approximately $15.11\frac{mg}{kg}$ to $22.06\frac{mg}{kg}$.

Key concepts

Unit Conversion

Understanding unit conversion is crucial, especially when dealing with medication dosages. In our exercise, the weight of the children is given in pounds, but medical dosages often use the metric system, particularly kilograms. Knowing how to convert between these units ensures accuracy in dosage calculations.

To convert pounds to kilograms, you use the conversion factor where 1 pound equals approximately 0.453592 kilograms.

• For a child weighing 24 lbs, the weight in kilograms is calculated as: $24\text{lb}\times 0.453592\text{kg/lb}\approx 10.88\text{kg}$
• For a child weighing 35 lbs, it is $35\text{lb}\times 0.453592\text{kg/lb}\approx 15.88\text{kg}$

This conversion is essential, as it allows us to determine how much medication per kilogram a child needs, facilitating the prevention of overdoses or under-doses.

Acetaminophen Dosage

Calculating the correct dosage of acetaminophen is vital to ensuring its effectiveness while avoiding potential harm. The problem at hand required determining the amount of acetaminophen per dose. The pain relief elixir specified has 80 mg of acetaminophen per 0.5 teaspoon. With a recommended dose of 1.5 teaspoons, it's crucial to understand how much acetaminophen is being administered.

You can determine the total dosage using a multiplication approach:

• First, convert the dosage from teaspoons to the concentration found in the elixir: $1.5\text{tsp}\times \frac{80\text{mg}}{0.5\text{tsp}}=240\text{mg}$

Thus a single dose delivers 240 mg of acetaminophen. This understanding helps in planning the dosage schedule and ensuring the child receives effective pain relief.

Medication for Children

Administering medication to children requires special consideration. Children are more sensitive to medications, so precise dosage is necessary to avoid adverse effects. In the case of acetaminophen, it’s especially important because overdosing can lead to severe health consequences.

• The exercise aims to determine the range of acetaminophen dosage based on the child's weight. For safe medication practice, the correct dosage is calculated based on mg per kilogram of body weight.
• For a child weighing 24 lbs (approximately 10.88 kg), the dose is $\frac{240\text{mg}}{10.88\text{kg}}\approx 22.06\text{mg/kg}$.
• For a child weighing 35 lbs (approximately 15.88 kg), it is $\frac{240\text{mg}}{15.88\text{kg}}\approx 15.11\text{mg/kg}$.

By understanding how much medication per kilogram is suitable, caregivers can administer the drug safely, ensuring that each child receives the optimum balance of efficacy and safety. The dosage range ensures that even the smallest or largest children within this weight category receive an effective and safe amount of acetaminophen.