How many moles and water molecules are in the runner's body?
(b) How many water molecules (H2O) are there?
To determine the number of moles of water in the runner's body, we can use the equation:
Number of moles = Mass / Molar mass
First, we need to find the mass of water in the runner's body. Since 71% of the runner's weight is water, we can calculate this by multiplying the weight of the runner (577 N) by 0.71:
Mass of water = 577 N * 0.71 = 410.67 N
Next, we need to convert the weight of water from newtons to kilograms, as the molar mass of water is given in grams. We know that 1 N = 0.10197 kg, so:
Mass of water (kg) = 410.67 N * 0.10197 kg/N = 41.90 kg
The molar mass of water (H2O) is 18.015 g/mol. Converting the mass of water from kilograms to grams:
Mass of water (g) = 41.90 kg * 1000 g/kg = 41,900 g
Now, we can calculate the number of moles of water:
Number of moles = 41,900 g / 18.015 g/mol = 2322.86 mol
Explanation:
Water Molecules: The number of water molecules (H2O) can be calculated from the number of moles of water found earlier. Each mole of water contains Avogadro's number of molecules, which is approximately 6.022 x 10^23. Therefore, to find the number of water molecules, we multiply the number of moles (2322.86 mol) by Avogadro's number:
Number of water molecules = 2322.86 mol * 6.022 x 10^23 molecules/mol
After performing the calculation, we find that the runner's body contains approximately 1.396 x 10^27 water molecules.
This explains that the runner's body contains approximately 2322.86 moles of water and about 1.396 x 10^27 water molecules.