To find the atomic mass of silver (Ag) based on the given information about cuprous sulfide (Cu₂S) and silver sulfide (Ag₂S), we can follow these steps:
### Step 1: Understand the Composition of Cu₂S
- The percentage composition of sulfur in Cu₂S is given as 20.14%.
- This means that in 100 g of Cu₂S, there are 20.14 g of sulfur (S).
### Step 2: Calculate the Mass of Copper in Cu₂S
- The mass of copper in 100 g of Cu₂S can be calculated as:
\[
\text{Mass of Cu} = 100 \, \text{g} - 20.14 \, \text{g} = 79.86 \, \text{g}
\]
### Step 3: Calculate the Moles of Copper in Cu₂S
- The molar mass of copper (Cu) is given as 63.57 g/mol.
- The number of moles of copper in Cu₂S can be calculated using the formula:
\[
\text{Moles of Cu} = \frac{\text{Mass of Cu}}{\text{Molar mass of Cu}} = \frac{79.86 \, \text{g}}{63.57 \, \text{g/mol}} \approx 1.255 \, \text{mol}
\]
### Step 4: Relate Moles of Copper to Moles of Sulfur in Cu₂S
- In Cu₂S, there are 2 moles of copper for every mole of sulfur. Therefore, the moles of sulfur can be calculated as:
\[
\text{Moles of S} = \frac{1.255 \, \text{mol Cu}}{2} \approx 0.6275 \, \text{mol S}
\]
### Step 5: Calculate the Molar Mass of Sulfur
- The molar mass of sulfur can be calculated using the mass of sulfur:
\[
\text{Molar mass of S} = \frac{\text{Mass of S}}{\text{Moles of S}} = \frac{20.14 \, \text{g}}{0.6275 \, \text{mol}} \approx 32.1 \, \text{g/mol}
\]
### Step 6: Understand the Composition of Ag₂S
- The percentage composition of sulfur in Ag₂S is given as 12.94%.
- This means that in 100 g of Ag₂S, there are 12.94 g of sulfur.
### Step 7: Calculate the Mass of Silver in Ag₂S
- The mass of silver in 100 g of Ag₂S can be calculated as:
\[
\text{Mass of Ag} = 100 \, \text{g} - 12.94 \, \text{g} = 87.06 \, \text{g}
\]
### Step 8: Calculate the Moles of Silver in Ag₂S
- Let the molar mass of silver be \( y \).
- The number of moles of silver in Ag₂S can be calculated as:
\[
\text{Moles of Ag} = \frac{87.06 \, \text{g}}{y}
\]
### Step 9: Relate Moles of Silver to Moles of Sulfur in Ag₂S
- In Ag₂S, there are 2 moles of silver for every mole of sulfur. Therefore, the moles of sulfur can be calculated as:
\[
\text{Moles of S} = \frac{1}{2} \times \frac{87.06 \, \text{g}}{y}
\]
### Step 10: Set Up the Equation Using Molar Mass of Sulfur
- We know the moles of sulfur from the previous calculation:
\[
\frac{1}{2} \times \frac{87.06}{y} = \frac{12.94}{32.1}
\]
- Cross-multiplying gives:
\[
87.06 \times 32.1 = 12.94 \times 2y
\]
- Simplifying this:
\[
2790.066 = 25.88y
\]
- Therefore, solving for \( y \):
\[
y = \frac{2790.066}{25.88} \approx 107.74 \, \text{g/mol}
\]
### Conclusion
The atomic mass of silver (Ag) is approximately **107.74 g/mol**.
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