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Chapter 1: Problem 48

A children's pain relief elixir contains \(80 . \mathrm{mg}\) acetaminophen per \(0.50\) teaspoon. The dosage recommended for a child who weighs between 24 and \(35 \mathrm{lb}\) 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 \(35 \mathrm{lb}\) ?

Short Answer

Expert verified
The range of acetaminophen dosages for children who weigh between 24 and 35 lb is 15.12 to 22.04 mg/kg.

Step by step solution

01

Calculate the acetaminophen in the recommended dosage

First, we need to find the quantity of acetaminophen in 1.5 teaspoons. We are given that the elixir contains 80 mg of acetaminophen per 0.5 teaspoon. So, the amount of acetaminophen in 1.5 teaspoons can be found by using a proportion: \[\frac{80\,\text{mg}}{0.5\,\text{tsp}} = \frac{x\,\text{mg}}{1.5\,\text{tsp}}\] Now, we will solve for x: \(x = \frac{(80\,\text{mg} \times 1.5\,\text{tsp})}{0.5\,\text{tsp}}\)
02

Calculate the total amount of acetaminophen in the recommended dosage

Now we will calculate x's value: \(x = \frac{120\,\text{mg}}{0.5}\) \(x = 240\,\text{mg}\) Therefore, the recommended dosage contains 240 mg of acetaminophen.
03

Convert pounds to kilograms

To express the acetaminophen dosage in terms of mg/kg, we need to convert the given child's weight range from pounds(lb) to kilograms(kg). The conversion rate is 1 lb = 0.453592 kg. So, Minimum weight in kg: \(24\text{lb} \times 0.453592 = 10.886208\,\text{kg}\) Maximum weight in kg: \(35\text{lb} \times 0.453592 = 15.87572\,\text{kg}\)
04

Find the range of acetaminophen dosages

Now, we will calculate the range of acetaminophen dosages by dividing the total amount of acetaminophen (240 mg) by the minimum and maximum weights in kg: Minimum dosage: \(\frac{240\,\text{mg}}{10.886208\,\text{kg}} = 22.04 \frac{\text{mg}}{\text{kg}}\) Maximum dosage: \(\frac{240\,\text{mg}}{15.87572\,\text{kg}} = 15.12 \frac{\text{mg}}{\text{kg}}\)
05

Express the range in the required format

Finally, we will express the range of acetaminophen dosages in mg/kg: The range of acetaminophen dosages for children who weigh between 24 and 35 lb is 15.12 to 22.04 mg/kg.

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Most popular questions from this chapter

For a material to float on the surface of water, the material must have a density less than that of water \((1.0 \mathrm{~g} / \mathrm{mL})\) and must not react with the water or dissolve in it. A spherical ball has a radius of \(0.50 \mathrm{~cm}\) and weighs \(2.0 \mathrm{~g} .\) Will this ball float or sink when placed in water? (Note: Volume of a sphere \(=\frac{4}{3} \pi r^{3} .\) )

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(212.2+26.7+402.09\) b. \(1.0028+0.221+0.10337\) c. \(52.331+26.01-0.9981\) d. \(2.01 \times 10^{2}+3.014 \times 10^{3}\) e. \(7.255-6.8350\)

The density of osmium (the densest metal) is \(22.57 \mathrm{~g} / \mathrm{cm}^{3} .\) If \(\mathrm{a}\) \(1.00-\mathrm{kg}\) rectangular block of osmium has two dimensions of \(4.00 \mathrm{~cm} \times 4.00 \mathrm{~cm}\), calculate the third dimension of the block.

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(6.022 \times 10^{23} \times 1.05 \times 10^{2}\) b. \(\frac{6.6262 \times 10^{-34} \times 2.998 \times 10^{8}}{2.54 \times 10^{-9}}\) c. \(1.285 \times 10^{-2}+1.24 \times 10^{-3}+1.879 \times 10^{-1}\) d. \(\frac{(1.00866-1.00728)}{6.02205 \times 10^{23}}\) e. \(\frac{9.875 \times 10^{2}-9.795 \times 10^{2}}{9.875 \times 10^{2}} \times 100(100\) is exact \()\) f. \(\frac{9.42 \times 10^{2}+8.234 \times 10^{2}+1.625 \times 10^{3}}{3}(3\) is exact)

Perform the following unit conversions. a. Congratulations! You and your spouse are the proud parents of a new baby, born while you are studying in \(\Omega\) country that uses the metric system. The nurse has informed you that the baby weighs \(3.91 \mathrm{~kg}\) and measures \(51.4 \mathrm{~cm}\). Convert your baby's weight to pounds and ounces and her length to inches (rounded to the nearest quarter inch). b. The circumference of the earth is \(25,000 \mathrm{mi}\) at the equator. What is the circumference in kilometers? in meters? c. A rectangular solid measures \(1.0 \mathrm{~m}\) by \(5.6 \mathrm{~cm}\) by \(2.1 \mathrm{dm}\). Express its volume in cubic meters, liters, cubic inches, and cubic feet.
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