Calculate the empirical formula of a compound having $37.6\%$ sodium, $23.1\%$ silicon and $39.3\%$ oxygen.
$\left[\mathrm{O}=16,\mathrm{Na}=23,\mathrm{Si}=28\right]$

Step 1: Given information

• The percentage of Sodium $\left(\mathrm{Na}\right)$ in the compound is $37.6\%$.
• Atomic weight of Sodium is $23\mathrm{g}$.
• The percentage of Silicon $\left(\mathrm{Si}\right)$ in the compound is $23.1\%$
• Atomic weight of Silicon is $28\mathrm{g}$.
• The percentage of Oxygen $\left(\mathrm{O}\right)$ in the compound is $39.3\%$
• Atomic weight of Oxygen is $16\mathrm{g}$.

Step 2: Formula used to calculate atomic ratio and simplest ratio

• The atomic ratio is calculated by dividing the percentage composition of an element by its atomic weight.

$\mathrm{Atomic}\mathrm{ratio}=\frac{\mathrm{Percentage}\mathrm{composition}\mathrm{of}\mathrm{an}\mathrm{element}}{\mathrm{Atomic}\mathrm{weight}\mathrm{of}\mathrm{an}\mathrm{element}}$

• The simplest ratio is calculated by dividing the atomic ratio of each element by the smallest atomic ratio.

$\mathrm{Simplest}\mathrm{ratio}=\frac{\mathrm{Atomic}\mathrm{ratio}\mathrm{of}\mathrm{an}\mathrm{element}}{\mathrm{Smallest}\mathrm{atomic}\mathrm{ratio}}$

Step 3: Determination of the empirical formula

Element	Percentage composition	Atomic weight	Atomic ratio	Simplest ratio
Na	$37.6$	$23$	$\frac{37.6}{23}=1.63$	$\frac{1.63}{0.82}=2$
Si	$23.1$	$28$	$\frac{23.1}{28}=0.82$	$\frac{0.82}{0.82}=1$
O	$39.3$	$16$	$\frac{39.3}{16}=2.45$	$\frac{2.45}{0.82}=3$

• The simplest ratio of $\mathrm{Na}:\mathrm{Si}:\mathrm{O}=2:1:3$, which is a whole number ratio.

Thus, the empirical formula of the compound is ${\mathrm{Na}}_2{\mathrm{SiO}}_3$.