Elemental sulfur occurs as octatomic molecules, ${\mathit{S}}_{\mathbf{8}}$. What mass of fluorine gas is needed to react completely with 17.8 g of sulfur to form sulfur hexafluoride?

When octatomic molecules, $S_8$react with ${\mathbf{F}}_{\mathbf{2}}$and formslocalid="1657092468626" ${\mathbf{SF}}_{\mathbf{6}}$

The chemical reaction is:

${\mathbf{S}}_{\mathbf{8}}\left(S\right)\mathbf{+}{\mathbf{F}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{SF}}_{\mathbf{6}}\left(g\right)$

In a balanced chemical equation, the number of atoms on the reactant side should be same with the number of atoms on the product side for a particular atom. For balancing the reaction, the atoms are multiplied by the stochiometric coefficient.

So, the balanced chemical equation is:

${\mathbf{S}}_{\mathbf{8}}\mathbf{\left(}\mathbf{S}\mathbf{\right)}\mathbf{+}\mathbf{24}{\mathbf{F}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{8}{\mathbf{SF}}_{\mathbf{6}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

The number of moles is calculated by the mass and Molar mass. The relationship between the number of moles, mass, and molar mass is given below.

$\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{moles}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{M}\mathbf{}\mathbf{olar}\mathbf{}\mathbf{mass}}$

$$\begin{gathered} \mathrm{The}\mathrm{mass}\mathrm{of}{\mathrm{S}}_8=17.8\mathrm{g}. \\ \mathrm{The}\mathrm{molar}\mathrm{mass}\mathrm{of}{\mathrm{S}}_8=256.48\mathrm{g}/\mathrm{mol}. \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}{\mathrm{S}}_8\mathrm{is}\mathrm{calculated}\mathrm{as}: \\ \mathbf{moles}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{S}}_{\mathbf{8}}\mathbf{=}\frac{\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{S}}_{\mathbf{8}}}{\mathbf{Molar}\mathbf{}\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{S}}_{\mathbf{8}}}\mathbf{}\mathbf{}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{17}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{g}}{\mathbf{256}\mathbf{.}\mathbf{48}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}{\mathrm{S}}_8\mathrm{is}0.0694\mathrm{mol}. \end{gathered}$$

In the given reaction, 1 mol of${\mathbf{S}}_{\mathbf{8}}$ is reacted with 24 mol of${\mathbf{F}}_{\mathbf{2}}$.

Thus,

$\mathbf{1}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{S}}_{\mathbf{8}}\mathbf{=}\mathbf{24}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}}$

The number of moles of ${\mathbf{F}}_{\mathbf{2}}$is:

$$\begin{gathered} \mathbf{1}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{S}}_{\mathbf{8}}\mathbf{=}\mathbf{24}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}} \\ \mathbf{0}\mathbf{.}\mathbf{0694}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{S}}_{\mathbf{8}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0694}\mathbf{\times }\mathbf{24}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6656}\mathbf{m}\mathbf{}\mathbf{ol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}} \end{gathered}$$

$$\begin{gathered} \mathrm{The}\mathrm{molar}\mathrm{mass}\mathrm{of}{\mathbf{F}}_{\mathbf{2}}=37.9968\mathrm{g}/\mathrm{mol}. \\ \mathrm{The}\mathrm{mass}\mathrm{of}{\mathbf{F}}_{\mathbf{2}\mathbf{}}\mathrm{is}\mathrm{calculated}\mathrm{as}: \\ \mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}}\mathbf{=}\mathbf{moles}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}}\mathbf{\times }\mathbf{Molar}\mathbf{}\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{F}}_{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{.}\mathbf{6656}\mathbf{mol}\mathbf{\times }\mathbf{37}\mathbf{.}\mathbf{9968}\mathbf{}\mathbf{g}\mathbf{/}\mathbf{mol} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{63}\mathbf{.}\mathbf{2875}\mathbf{}\mathbf{g} \\ \mathrm{Therefore},\mathrm{the}\mathrm{mass}\mathrm{of}{\mathbf{F}}_{\mathbf{2}\mathbf{}}\mathrm{is}\mathrm{approximately}63.29\mathrm{g}. \end{gathered}$$