Note that there are 3 significant figures stated in the question. Therefore, the answers provided will be kept to 3 significant figures.
Balance the equation first:
[tex] \underline{?} Zn+S_8 \Rightarrow ZnS [/tex]
One mole of Zinc reacts with one mole of octasulfur to create a mole of zinc sulfide. There is one part zinc and 8 parts of sulfur, and it results in 8 parts of zinc sulfide, so you will need to create eight parts of zinc. The following chemical equation is balanced:
[tex] 8 \ Zn + S_8 \Rightarrow 8 \ ZnS [/tex]
5.88 grams of zinc react with 5.03 grams of octasulfur to produce 7.25 grams of zinc sulfide. To find the theoretical yield of the reaction, convert the grams into moles by dividing the grams present by the molar mass and moles in the equation:
[tex] \text{Molar mass of zinc: 65.38 grams} [/tex]
[tex] \text{8 moles of zinc in equation} [/tex]
[tex] 5.88 \div 65.38 = 0.0889 \ \text{mol} [/tex]
[tex] 0.0889 \div 8 = 0.0112 [/tex]
There are 0.0889 moles of zinc in this equation, and it will react with 0.0112 moles of octasulfur.
[tex] \text{Molar mass of octasulfur: 256.52 grams} [/tex]
[tex] \text{One mole of octasulfur in equation} [/tex]
[tex] 5.03 \div 256.52 = 0.0196 \ \text{mol} [/tex]
There are 0.0196 moles of octasulfur in this equation.
There is an excess of octasulfur, as you need more moles of octasulfur than moles of zinc to complete the equation. Therefore, you will use moles of zinc to find the theoretical yield:
[tex] \text{Molar mass of zinc sulfide: 97.474 grams} [/tex]
[tex] 0.0899 \times 97.474 = 8.76 \ \text{grams} [/tex]
The theoretical yield is 8.76 grams of zinc sulfide.
To find the percent yield, divide the result from the question by the theoretical yield:
[tex] 7.25 \div 8.76 = 0.828 [/tex]
Multiply this decimal by 100 for the percentage:
[tex] 0.828 \times 100 = \boxed{82.8} [/tex]
The percent yield is 82.8%.
