Answer : The mass of [tex]S_8[/tex] required is 18.238 grams.
Explanation : Given,
Mass of [tex]SF_6[/tex] = 83.10 g
Molar mass of [tex]SF_6[/tex] = 146 g/mole
Molar mass of [tex]S_8[/tex] = 256.52 g/mole
The balanced chemical reaction is,
[tex]S_8+24F_2\rightarrow 8SF_6[/tex]
First we have to determine the moles of [tex]SF_6[/tex].
[tex]\text{Moles of }SF_6=\frac{\text{Mass of }SF_6}{\text{Molar mass of }SF_6}=\frac{83.10g}{146g/mole}=0.569moles[/tex]
Now we have to determine the moles of [tex]S_8[/tex].
From the balanced chemical reaction we conclude that,
As, 8 moles of [tex]SF_6[/tex] produced from 1 mole of [tex]S_8[/tex]
So, 0.569 moles of [tex]SF_6[/tex] produced from [tex]\frac{0.569}{8}=0.0711[/tex] mole of [tex]S_8[/tex]
Now we have to determine the mass of [tex]S_8[/tex].
[tex]\text{Mass of }S_8=\text{Moles of }S_8\times \text{Molar mass of }S_8[/tex]
[tex]\text{Mass of }S_8=(0.0711mole)\times (256.52g/mole)=18.238g[/tex]
Therefore, the mass of [tex]S_8[/tex] required is 18.238 grams.
