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 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 * 1021 kg?

There are 4.5 x 10⁴⁶molecules of water in the world's oceans

Explanation:

The mass of the water molecule is the sum of the masses of each atom that composes the molecule:

The water molecule has 2 H (hydrogen) atoms and 1 O (oxygen) atom (H₂O₁ but the "1" in oxygen is never written, so you have H₂O).

The mass of a single H₂O molecule is then:

mass H₂O = 2 (mass H) + mass O = 2 * 1.0 u + 16 u = 18u

The "u" stands for "atomic mass unit" and 1 u = 1.7 x 10⁻²⁷ Kg (rounded to two significant figures, since all numbers in the question have 2 significant figures: 1.0, 1.4 x 10²¹ and 16).

The mass of 1 water molecule in Kg is:

mass of H2O (kg) = 18 u * (1.7 x 10⁻²⁷ Kg/1.0 u) = 3.1 x 10⁻²⁶ kg

Now, we have the mass of a single water molecule and the mass of the world's oceans:

3.1 x 10⁻²⁶ kg ⇒ 1 water molecule

1.4 x 10²¹ kg ⇒ x = 1.4 x 10²¹ kg * 1 molecule / 3.1 x 10⁻²⁶ kg

= 4.5 x 10⁴⁶molecules of water