Question

Calculate the empirical formula of the compound containing $ 37.6\% $ Na, $ 23.{\text{ }}1\% $ Si, and $ 39.3\% $ O. (Atomic weights of O =16, Na = 23, and Si = 28).

Answer 1

Hint: The empirical formula represents the simplest whole number ratio of the atoms that are present in the compound. An example would be that the empirical formula of glucose is $ {\text{C}}{{\text{H}}_{\text{2}}}{\text{O}} $ whose molecular formula is $ {{\text{C}}_{\text{6}}}{{\text{H}}_{12}}{{\text{O}}_{\text{6}}} $ . We shall calculate the relative number of atoms by dividing the mass ratio with atomic mass and then dividing it with the smallest of the three values obtained to get the simplest ratio.

Complete step by step solution:
The empirical formula of the compound can be calculated by the following format:

Element	Atomic mass	Mass ratio	Relative number of atoms	Simplest ratio
Sodium	23	$ 37.6 $	$ \dfrac{{37.6}}{{23}} = 1.63 $	$ \dfrac{{1.63}}{{0.825}} = 2 $
Oxygen	16	$ 39.3 $	$ \dfrac{{39.3}}{{16}} = 2.45 $	$ \dfrac{{2.45}}{{0.825}} = 3 $
Silicon	28	$ 23.1 $	$ \dfrac{{23.1}}{{28}} = 0.825 $	$ \dfrac{{0.825}}{{0.825}} = 1 $

In the above format, the mass ratio is the percentage of an element that is present in a compound, the relative number of the atoms is the ratio of the mass percentage of the elements to their atomic mass, and the simplest ratio is the ratio of the relative number of atoms of the said element to the lowest relative number of atoms of any element.
From the above calculation it is clear that the ratio of Na: O: Si in the compound = 2: 3: 1, hence the empirical formula of the compound is equal to $ {\text{N}}{{\text{a}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{3}}} $ and since the elements are present in this formula is their simplest whole number ratio, the molecular formula of the compound is also the same.

Note:
The empirical formula of a compound is the simplest way to represent a compound and they show the lowest whole number ratio in which the atoms in a molecule can mix with each other to form a chemical compound.