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Answer :
To solve the problem of determining the mass of gold (Au) produced when 0.0500 moles of Au₂S₃ are reduced completely with excess hydrogen (H₂), we can follow these steps:
1. Understand the Chemical Reaction: The compound Au₂S₃ decomposes to produce gold (Au) and sulfur (S) when reduced with hydrogen. The balanced chemical equation for the reaction can be written as:
[tex]\( \text{Au}_2\text{S}_3 + \text{H}_2 \rightarrow 2\text{Au} + \text{Sulfur Compounds} \)[/tex]
From the stoichiometry of the equation, 1 mole of Au₂S₃ produces 2 moles of Au.
2. Calculate Moles of Au Produced: If you start with 0.0500 moles of Au₂S₃, then the moles of Au produced can be calculated using the stoichiometry:
[tex]\[ \text{Moles of Au} = 2 \times \text{Moles of Au₂S₃} = 2 \times 0.0500 \, \text{moles} = 0.100 \text{ moles of Au} \][/tex]
3. Molar Mass of Au: The molar mass of gold (Au) is approximately 196.97 grams per mole.
4. Calculate the Mass of Au Produced: To find the mass of gold produced, use the formula:
[tex]\[ \text{Mass of Au} = \text{Moles of Au} \times \text{Molar Mass of Au} \][/tex]
[tex]\[ \text{Mass of Au} = 0.100 \, \text{moles} \times 196.97 \, \text{g/mol} \][/tex]
[tex]\[ \text{Mass of Au} = 19.697 \, \text{g} \][/tex]
Therefore, the mass of gold produced when 0.0500 moles of Au₂S₃ are reduced completely is approximately 19.7 grams. The closest option that matches this result is 19.7 g.
1. Understand the Chemical Reaction: The compound Au₂S₃ decomposes to produce gold (Au) and sulfur (S) when reduced with hydrogen. The balanced chemical equation for the reaction can be written as:
[tex]\( \text{Au}_2\text{S}_3 + \text{H}_2 \rightarrow 2\text{Au} + \text{Sulfur Compounds} \)[/tex]
From the stoichiometry of the equation, 1 mole of Au₂S₃ produces 2 moles of Au.
2. Calculate Moles of Au Produced: If you start with 0.0500 moles of Au₂S₃, then the moles of Au produced can be calculated using the stoichiometry:
[tex]\[ \text{Moles of Au} = 2 \times \text{Moles of Au₂S₃} = 2 \times 0.0500 \, \text{moles} = 0.100 \text{ moles of Au} \][/tex]
3. Molar Mass of Au: The molar mass of gold (Au) is approximately 196.97 grams per mole.
4. Calculate the Mass of Au Produced: To find the mass of gold produced, use the formula:
[tex]\[ \text{Mass of Au} = \text{Moles of Au} \times \text{Molar Mass of Au} \][/tex]
[tex]\[ \text{Mass of Au} = 0.100 \, \text{moles} \times 196.97 \, \text{g/mol} \][/tex]
[tex]\[ \text{Mass of Au} = 19.697 \, \text{g} \][/tex]
Therefore, the mass of gold produced when 0.0500 moles of Au₂S₃ are reduced completely is approximately 19.7 grams. The closest option that matches this result is 19.7 g.
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