Certainly! Let's go through the steps to determine the number of water molecules in the body of a person weighing 80 kg, assuming that the body is 80% water by mass.
### Step-by-Step Solution:
1. Determine the mass of water in the body:
- We know that 80% of the body mass is composed of water.
- The mass of the person is 80 kg.
[tex]\[
\text{Mass of water} = \text{Body mass} \times \text{Water percentage}
\][/tex]
[tex]\[
\text{Mass of water} = 80 \, \text{kg} \times 0.80 = 64 \, \text{kg}
\][/tex]
2. Convert the mass of water from kilograms to grams:
- Knowing that 1 kg equals 1000 grams.
[tex]\[
\text{Mass of water in grams} = 64 \, \text{kg} \times 1000 \, \dfrac{\text{grams}}{\text{kg}} = 64000 \, \text{grams}
\][/tex]
3. Calculate the number of moles of water:
- The molar mass of water ([tex]\(\text{H}_2\text{O}\)[/tex]) is 18 grams/mol.
[tex]\[
\text{Number of moles of water} = \dfrac{\text{Mass of water in grams}}{\text{Molar mass of water}}
\][/tex]
[tex]\[
\text{Number of moles of water} = \dfrac{64000 \, \text{grams}}{18 \, \dfrac{\text{grams}}{\text{mol}}} \approx 3555.56 \, \text{mol}
\][/tex]
4. Calculate the number of water molecules:
- Avogadro's number tells us the number of molecules in one mole, which is [tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol.
[tex]\[
\text{Number of water molecules} = \text{Number of moles of water} \times \text{Avogadro's number}
\][/tex]
[tex]\[
\text{Number of water molecules} \approx 3555.56 \, \text{mol} \times 6.022 \times 10^{23} \, \dfrac{\text{molecules}}{\text{mol}} \approx 2.14116 \times 10^{27} \, \text{molecules}
\][/tex]
### Summary:
- Mass of water in the body: [tex]\(64 \, \text{kg}\)[/tex]
- Mass of water in grams: [tex]\(64000 \, \text{grams}\)[/tex]
- Number of moles of water: [tex]\(\approx 3555.56 \, \text{mol}\)[/tex]
- Number of water molecules: [tex]\(\approx 2.14116 \times 10^{27} \, \text{molecules}\)[/tex]
Therefore, the number of water molecules in the body of a person weighing 80 kg is approximately [tex]\(2.14116 \times 10^{27}\)[/tex] molecules.
