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
I was able to get part (a), but I'm not sure how to get part (b)
multiply the number of moles by avagradro's number.
I'm getting 1.415*10^27, but my homework is telling me its wrong. Isn't Avogadro's number 6.022*10^23
To find the number of water molecules (H2O) in the runner's body, we need to convert the weight percentage of water to moles and then calculate the number of molecules.
(a) We already know that 74% of the runner's weight is water. We can convert this percentage to grams by multiplying it by the runner's weight:
Weight of water = (74% of runner's weight) = (74/100) * 560 N = 414.4 N
To convert the weight of water to grams, we can use the conversion factor 1 N = 1 kg*m/s^2, and 1 kg = 1000 g:
Weight of water in grams = (414.4 N) * (1 kg/1 N) * (1000 g/1 kg) = 414,400 g
Next, we need to convert the weight of water in grams to moles. To do this, we can use the molar mass of water, which is approximately 18 g/mol. The molar mass represents the mass of one mole of a substance.
Number of moles of water = (weight of water in grams) / (molar mass of water)
= 414,400 g / 18 g/mol
≈ 23,022 moles
Therefore, there are approximately 23,022 moles of water in the runner's body.
(b) To calculate the number of water molecules, we need to use Avogadro's number, which defines the number of particles (atoms, molecules, or ions) in one mole of a substance. Avogadro's number is approximately 6.022 × 10^23 per mole.
Number of water molecules = (number of moles of water) * (Avogadro's number)
= 23,022 moles * (6.022 × 10^23 molecules/mol)
≈ 1.386 × 10^26 molecules
Therefore, there are approximately 1.386 × 10^26 water molecules in the runner's body.