Question

At high temperatures, the compound $S_{4} N_{4}$ decomposes completely into $N_{2}$ and sulphur vapour. If all measurements were made under the same conditions of temperature and pressure, it is found that for each volume of $S_{4} N_{4}$ decomposed $2.5$ volumes of gaseous products are formed. What is the molecular formula of sulphur?

Answer 1

It means that 1 vol. of $S_{4} N_{4}$ produces $(2 \cdot 5-2)$ vol. of sulphur vapour (vol. of nitrogen being subtracted).

That is, 1 vol. of $S_{4} N_{4}$ produces $\frac{1}{2}$ vol. of sulphur vapour. By Avogadro's hypothesis :

$\frac{1}{2}$ molecule of sulphur vapour came from 1 molecule of $S_{4} N_{4}$. That is :

(One molecule of sulphur vapour came from 2 molecules of $S_{4} N_{4}$. But two moleculs of $S_{4} N_{4}$ contain $(4 \times 2)$ atoms of sulphur. Then it is clear that one molecule of sulphur vapour (which is obtained from $S_{4} N_{4}$ ) contains 8 atoms of sulphur.

Hence, molecular formula of sulphur $= S _{ 8 }$.