Physics for Engineers (PHY052)
Assignment No. 1: Units and Measurements
Problem: Water Molecules
One molecule of water (H2O) contains two atoms of hydrogen and one atom of oxygen. A
hydrogen atom has a mass of 1.0u and an atom of oxygen has a mass of 16u, 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 1.4×1021kg?
(a)
Concept
In computing the mass of the compound H2O (water) in kilograms, we need to understand first
that both the elements (Hydrogen and Oxygen) masses are expressed in terms of atomic mass
unit (amu/u).
Now, since 1 mol = 6.022x1023 atoms, 1g/6.022x1023 mol is equal to 1.6605x10-24 grams,
therefore 1 u = 1g/mol
In other words, the ratio of u/atom is the same as the ratio of g/mol. The definitions of amu and
moles were intentionally chosen to make that happen. This allows us to easily relate masses at
the atomic scale to masses at the macroscopic scale.
Computations and Conclusions
In solving the atomic mass of an element we only take the average. The average atomic mass
of an element is calculated by summing the masses of the elements isotopes, each multiplied
by its natural abundance on Earth. When doing any mass calculations involving elements or
compounds, we always use average atomic mass, which can be seen on the periodic table.
In periodic table, 1 mol of Hydrogen has a mass of 1 u or 1 g/mol and Oxygen has a mass of
16 u or 16g/mol.
MM = Molar Mass
MM of H2O = 2 (MM of Hydrogen) + 1 (MM of Oxygen) = 2(1 u) + 1(16 u) = 18 u = 18 g/mol
MM of H2O (in grams) = (18g/mol) (1.6605x10-24) = 2.9889x10-23 grams
Grams to kilograms
2.9889x10-23 grams x 1kg/1000g = 2.9889x10-23 x 10-3 = 2.9889x10-26 kilograms
Therefore, one molecule of water (H2O) has a mass of approximately 2.9889x10-26 kilograms.
(b)
Concept
The approximate mass of the world’s ocean is 1.4×1021 kg, it is calculated using the density of
water and the volume of the ocean. The volume was calculated by multiplying the surface area
and the average depth of the ocean.
The density of the water used in this calculation was assumed to be pure water, just the molar
mass of H2O and neglecting the masses of other elements and ions present in the sea water.
Computations and Conclusion
MM of H2O = 18 u = 18g/mol
Mass of the Ocean = 1.4×1021kg
Therefore, the number of molecules of water in the world’s oceans is approximately equal to
4.684x1046 molecules.