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Chapter 1: Problem 52

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

Expert verified
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

01

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: \(24 \, lb \times \frac{0.453592 \, kg}{1 \, lb} \approx 10.88 \, kg\) For 35 lb: \(35 \, lb \times \frac{0.453592 \, kg}{1 \, lb} \approx 15.88 \, kg\)
02

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) = \(1.5 \, tsp \times \frac{80 \, mg}{0.5 \, tsp} = 240 \, mg\)
03

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): \(\frac{240 \, mg}{10.88 \, kg} \approx 22.06 \, \frac{mg}{kg}\) For the upper weight (15.88 kg): \(\frac{240 \, mg}{15.88 \, kg} \approx 15.11 \, \frac{mg}{kg}\) 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 \(22.06 \, \frac{mg}{kg}\).

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