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Chapter 13: Problem 31

Estimate the number of \(\mathrm{H}_{2} \mathrm{O}\) molecules in a human body of mass \(80.2 \mathrm{kg} .\) Assume that, on average, water makes up about $62 \%$ of the mass of a human body.

Short Answer

Expert verified
Answer: \(1.66 \times 10^{27}\) water molecules

Step by step solution

01

Calculate the mass of water in the body

To calculate the mass of water in an 80.2 kg human body, we need to find 62% of the body's mass: Total mass of water = (62/100) × 80.2 kg Total mass of water ≈ 49.724 kg
02

Find the number of moles of water

We can determine the number of moles of water (H2O) present in 49.724 kg by using the molecular weight of water, which is 18.015 g/mol. First, we need to convert the mass of water from kg to g to match the unit of molecular weight: Total mass of water = 49.724 kg * 1000 g/kg ≈ 49724 g Now, we will divide the mass by the molecular weight of water: Number of moles of H2O = 49724 g / 18.015 g/mol ≈ 2758.34 moles
03

Calculate the number of water molecules

Final step is to convert the number of moles of water into the number of molecules using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol): Number of molecules of H2O = 2758.34 moles × \(6.022 \times 10^{23}\) molecules/mol ≈ \(1.66 \times 10^{27}\) molecules So, there are approximately \(1.66 \times 10^{27}\) water molecules in a human body of mass 80.2 kg.

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