Q70P - Chemistry: Molecular Nature Of Matter And Change

Question

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?

Step-by-Step Solution

Answer

The mass of ${\mathbf{F}}_{\mathbf{2}}$is 63.29 g.

Step 1: Chemical equation of the reaction of with 17.8g

When octatomic molecules, $S_8$react with ${\mathbf{F}}_{\mathbf{2}}$ and forms ${\mathbf{SF}}_{\mathbf{6}}$

The chemical reaction is:

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

Step 2: Balance the chemical equation

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:

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

Step 3: Relation between mass and number of moles

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.

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

Step 4: Calculate the number of moles of S 8

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

Step 5: Relation between number of moles of S 8 and F 2

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

Thus,

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

Step 6: Calculate the number of moles of F 2

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

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

Step 7: Calculate the mass of F 2

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