Question

Silicon reacts with sulfur at elevated temperatures. If \({\bf{0}}.{\bf{0923}}{\rm{ }}{\bf{g}}\) of silicon reacts with sulfur to give \({\bf{0}}.{\bf{3030}}{\rm{ }}{\bf{g}}\) of silicon sulfide, determine the empirical formula of silicon sulfide.

Short answer

The empirical formula of silicone sulfide is\({\rm{Si}}{{\rm{S}}_2}.\)

Step-by-step solution

Empirical formula

An empirical formula is a type of chemical formula in which elements’ simplest ratio are taken and not the total count of atoms that happen in the molecular formulas.

Number of moles of silicon

The standard atomic weight of silicon is\(28.085\;{\rm{g}}/{\rm{mol}}{\rm{.}}\)

The standard atomic weight of sulfur is\(32.06\;{\rm{g}}/{\rm{mol}}{\rm{.}}\)

We will first calculate the number of moles that are stored in a \(0.0923\;{\rm{g}}\) of silicon.

\(\begin{aligned}{}Number{\rm{ }}of{\rm{ }}moles{\rm{ of silicon}} = \frac{{{\rm{Given mass}}}}{{{\rm{Molar mass}}}}\\ = \frac{{0.0923}}{{28.085}}\\ = 0.00329\;\;{\rm{mol}}{\rm{.}}\end{aligned}\)

Determination of the empirical formula of silicon sulfide 

We must calculate the mass of the sulfur by subtracting the mass of the silicon from the total mass of the silicon sulfide.

\(0.3030\;{\rm{g}} - 0.0923\;{\rm{g}} = 0.2107\;{\rm{g}}{\rm{.}}\)

Now, we can calculate the number of moles that are stored in a \(0.2107\;{\rm{g}}\) of sulfur:

\(\begin{aligned}{}Number{\rm{ }}of{\rm{ }}moles{\rm{ of sulfur}} = \frac{{{\rm{Given mass}}}}{{{\rm{Molar mass}}}}\\ = \frac{{0.2107}}{{32.06}}\\ = 0.00657\;\;{\rm{mol}}{\rm{.}}\end{aligned}\)

Since \(0.00329\)mols of silicon react with \(0.00657\)mols of sulfur in a ratio approximate to\(1:2\), we can conclude that the empirical formula of silicone sulfide is\({\rm{Si}}{{\rm{S}}_2}.\)