To determine the amount of [tex]\( O_2 \)[/tex] needed to consume [tex]\( 0.04 \)[/tex] grams of [tex]\( ZnS \)[/tex], we’ll perform a series of calculations based on stoichiometry. Here are the steps:
1. Determine the molar mass of [tex]\( ZnS \)[/tex]:
- Zinc (Zn) has a molar mass of approximately [tex]\( 65.38 \, \text{g/mol} \)[/tex]
- Sulfur (S) has a molar mass of approximately [tex]\( 32.07 \, \text{g/mol} \)[/tex]
- Therefore, the molar mass of [tex]\( ZnS \)[/tex] is [tex]\( 65.38 \, \text{g/mol} + 32.07 \, \text{g/mol} = 97.46 \, \text{g/mol} \)[/tex]
2. Calculate the moles of [tex]\( ZnS \)[/tex] given:
- Given mass of [tex]\( ZnS \)[/tex] is [tex]\(\ 0.04 \, \text{g} \)[/tex]
- Number of moles of [tex]\( ZnS \)[/tex] = [tex]\(\frac{\text{mass}}{\text{molar mass}} = \frac{0.04 \, \text{g}}{97.46 \, \text{g/mol}} \approx 0.000410 \, \text{moles} \)[/tex]
3. Use the balanced chemical equation to find the moles of [tex]\( O_2 \)[/tex] needed:
[tex]\[
2 ZnS + 3 O_2 \rightarrow 2 ZnO + 2 SO_2
\][/tex]
- According to the balanced equation, [tex]\( 2 \)[/tex] moles of [tex]\( ZnS \)[/tex] require [tex]\( 3 \)[/tex] moles of [tex]\( O_2 \)[/tex]
- Therefore, the moles of [tex]\( O_2 \)[/tex] required per mole of [tex]\( ZnS \)[/tex] is [tex]\(\frac{3}{2} \)[/tex]
4. Calculate the moles of [tex]\( O_2 \)[/tex] needed for the given moles of [tex]\( ZnS \)[/tex]:
- Moles of [tex]\( O_2 \)[/tex] = [tex]\( 0.000410 \, \text{moles of } ZnS \times \frac{3}{2} = 0.000615 \, \text{moles} \)[/tex]
5. Determine the molar mass of [tex]\( O_2 \)[/tex]:
- Oxygen (O) has a molar mass of [tex]\( 16.00 \, \text{g/mol} \)[/tex]
- Therefore, the molar mass of [tex]\( O_2 \)[/tex] is [tex]\( 32.00 \, \text{g/mol} \)[/tex]
6. Calculate the mass of [tex]\( O_2 \)[/tex] needed:
- Mass of [tex]\( O_2 \)[/tex] = [tex]\(\text{moles} \times \text{molar mass} = 0.000615 \, \text{moles} \times 32.00 \, \text{g/mol} = 0.0197 \, \text{g} \)[/tex]
Therefore, approximately [tex]\( 0.0197 \)[/tex] grams of [tex]\( O_2 \)[/tex] are needed to consume [tex]\( 0.04 \)[/tex] grams of [tex]\( ZnS \)[/tex].
