Calculate the number of H2O molecules in a human body of mass 65.9 kg. Assume that, on average, water makes up 62% of the mass of a human body. (Use 1.0 u for the atomic mass of hydrogen, and 16.0 u for the atomic mass of oxygen.)
To calculate the number of H2O molecules in a human body, we need to follow these steps:
1. Calculate the mass of water in the human body:
- Given that water makes up 62% of the body mass, we can calculate the mass of water using the formula:
Mass of water = (62/100) * Mass of human body
Here, the Mass of human body is 65.9 kg.
Mass of water = (62/100) * 65.9 kg = 40.758 kg
2. Calculate the number of moles of water:
- We can use the formula:
Moles = Mass / Molar mass
The molar mass of H2O is (2 * atomic mass of hydrogen) + atomic mass of oxygen.
Given that the atomic mass of hydrogen is 1.0 u, and the atomic mass of oxygen is 16.0 u, the molar mass of water is (2 * 1.0 u) + 16.0 u = 18.0 u.
Moles of water = Mass of water / Molar mass of water
Moles of water = 40.758 kg / 18.0 g/mol
The result is in kilograms, so we need to convert it to grams:
Moles of water = 40758 g / 18.0 g/mol = 2264.33 mol (rounded to two decimal places)
3. Calculate the number of molecules:
One mole of any substance contains 6.022 x 10^23 molecules (Avogadro's number).
So, the number of H2O molecules in the human body is:
Number of molecules = Moles of water * 6.022 x 10^23 molecules/mol
Number of molecules = 2264.33 mol * 6.022 x 10^23 molecules/mol = 1.364 x 10^27 H2O molecules
Therefore, the number of H2O molecules in a human body of mass 65.9 kg is approximately 1.364 x 10^27 molecules.