A runner weighs 560 N (about 130 lb), and 74% of this weight is water.
(a) How many moles of water are in the runner's body?
moles
(b) How many water molecules (H2O) are there?
molecules
runner's mass = 560N/g = 560/9.8 kg
weight of water =(560/9.8)*74% kg
=(560/9.8)*.74*1000 g
atomic mass of hydrogen=1g/mol
atomic mass of oxygen=16g/mol, so
atomic mass of water=2x1+16=18g/mol
moles water=(560/9.8)*.74/18
molecules=[moles water]*6x10^23
To find the number of moles of water in the runner's body, we need to convert their weight into grams and then divide by the molar mass of water.
First, let's convert the weight from newtons to kilograms:
Weight = 560 N
Weight = 560 N * (1 kg / 9.8 N)
Weight = 56.29 kg
We know that 74% of the runner's weight is water. So we can find the mass of water by multiplying the runner's weight by 74%:
Mass of water = 56.29 kg * 0.74
Mass of water = 41.66 kg
Now we need to convert the mass of water from kilograms to grams because the molar mass of water is usually given in grams:
Mass of water = 41.66 kg * (1000 g / 1 kg)
Mass of water = 41660 g
The molar mass of water (H2O) is 18.015 g/mol. Therefore, we can find the number of moles of water by dividing the mass of water by the molar mass:
Number of moles of water = 41660 g / 18.015 g/mol
(a) The number of moles of water in the runner's body is approximately equal to 2314 moles.
To find the number of water molecules (H2O), we need to multiply the number of moles of water by Avogadro's number.
Avogadro's number is approximately equal to 6.022 x 10^23 molecules/mol.
Number of water molecules = Number of moles of water * Avogadro's number
(b) The number of water molecules in the runner's body is approximately equal to (2314 mol) * (6.022 x 10^23 molecules/mol), which is equal to 1.393 x 10^27 molecules.