The empirical formula of a compound gives the simplest whole number ratio of atoms of each element in a compound.

To calculate the empirical formula, we assume that we have \(100\) g of the compound. Therefore, we will have:\(57\) g \(S\) and \(43\) g \(O\).

Calculate the number of moles of \(S\):

$$57\ g\ S \times \frac{1\ mole\ S}{32\ g\ S} = 1.78 \ mole \ S$$

Calculate the number of moles of \(O\):

$$43\ g\ O \times \frac{1\ mol \ O}{16\ g\ O} = 2.7 \ mol\ O$$

We divide the number of moles of each element by the smallest number of moles, which is \(1.78\) mol:

$$1.78 \ mol \ S /1.78 \ mol = 1\ S$$

$$2.70 \ mol \ O /1.78 \ mol = 1.521 \approx 3 \ O$$

Therefore, the empirical formula is \(SO_{3}\)