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Answer :
To find the mass of Au produced when 0.0500 mol of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] is reduced completely with excess [tex]\( \text{H}_2 \)[/tex], follow these steps:
1. Understand the Chemical Reaction:
The balanced chemical equation for the reduction of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] with hydrogen is:
[tex]\[
\text{Au}_2\text{S}_3 + 3\text{H}_2 \rightarrow 2\text{Au} + 3\text{H}_2\text{S}
\][/tex]
From this equation, you can see that 1 mole of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] produces 2 moles of Au.
2. Calculate the Moles of Au Produced:
Since you start with 0.0500 moles of [tex]\( \text{Au}_2\text{S}_3 \)[/tex], and each mole of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] produces 2 moles of Au, you will have:
[tex]\[
\text{Moles of Au} = 2 \times 0.0500 = 0.1000 \ \text{mol}
\][/tex]
3. Calculate the Mass of Au Produced:
The molar mass of Au (gold) is approximately 196.97 g/mol. Therefore, to find the mass of gold produced:
[tex]\[
\text{Mass of Au} = 0.1000 \ \text{mol} \times 196.97 \ \text{g/mol} = 19.697 \ \text{g}
\][/tex]
4. Select the Closest Answer:
Rounding to an appropriate level of precision, the mass of Au produced is approximately 19.7 g.
Thus, the correct answer is B: 19.7 g.
1. Understand the Chemical Reaction:
The balanced chemical equation for the reduction of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] with hydrogen is:
[tex]\[
\text{Au}_2\text{S}_3 + 3\text{H}_2 \rightarrow 2\text{Au} + 3\text{H}_2\text{S}
\][/tex]
From this equation, you can see that 1 mole of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] produces 2 moles of Au.
2. Calculate the Moles of Au Produced:
Since you start with 0.0500 moles of [tex]\( \text{Au}_2\text{S}_3 \)[/tex], and each mole of [tex]\( \text{Au}_2\text{S}_3 \)[/tex] produces 2 moles of Au, you will have:
[tex]\[
\text{Moles of Au} = 2 \times 0.0500 = 0.1000 \ \text{mol}
\][/tex]
3. Calculate the Mass of Au Produced:
The molar mass of Au (gold) is approximately 196.97 g/mol. Therefore, to find the mass of gold produced:
[tex]\[
\text{Mass of Au} = 0.1000 \ \text{mol} \times 196.97 \ \text{g/mol} = 19.697 \ \text{g}
\][/tex]
4. Select the Closest Answer:
Rounding to an appropriate level of precision, the mass of Au produced is approximately 19.7 g.
Thus, the correct answer is B: 19.7 g.
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