One molecule of water (H2O) contains two atoms of hydrogen
and one atom of oxygen.A hydrogen atom has a mass of 1.0 u and an
atom of oxygen has a mass of 16 u, approximately. (a) What is the
mass in kilograms of one molecule of water? (b) How many molecules
of water are in the world’s oceans, which have an estimated total
mass of 1.4 * 10^21 kg?
To determine the mass of one molecule of water (H2O), we need to add up the masses of the hydrogen and oxygen atoms.
(a) Mass of one hydrogen atom (H) = 1.0 u (given)
Mass of one oxygen atom (O) = 16 u (given)
In one molecule of water (H2O), there are two hydrogen atoms and one oxygen atom. Therefore, the total mass of one molecule of water can be calculated as:
Total mass of one molecule of water = (2 * Mass of hydrogen atom) + Mass of oxygen atom
= (2 * 1.0 u) + 16 u
= 2 u + 16 u
= 18 u
Now, we need to convert the mass from atomic mass units (u) to kilograms (kg). The conversion factor is:
1 u = 1.66054 x 10^-27 kg (approximately)
Mass of one molecule of water in kg = Total mass of one molecule of water * Conversion factor
Mass of one molecule of water in kg = 18 u * (1.66054 x 10^-27 kg/u)
= 2.98997 x 10^-26 kg (approximately)
Therefore, the mass of one molecule of water is approximately 2.98997 x 10^-26 kg.
(b) To determine the number of water molecules in the world's oceans, we need to divide the total mass of the oceans (1.4 * 10^21 kg) by the mass of one water molecule (2.98997 x 10^-26 kg).
Number of water molecules in the world's oceans = Total mass of oceans / Mass of one water molecule
= (1.4 * 10^21 kg) / (2.98997 x 10^-26 kg)
= 4.67640 x 10^46 molecules (approximately)
Therefore, there are approximately 4.67640 x 10^46 molecules of water in the world's oceans.