First, we need to calculate the molar mass of silver oxide (Ag2O\mathrm{Ag}_{2} \mathrm{O}Ag2O). The molar masses of the elements involved are:
The molar mass of Ag2O\mathrm{Ag}_{2} \mathrm{O}Ag2O is: 2×107.87 g/mol+16.00 g/mol=231.74 g/mol 2 \times 107.87 \, \text{g/mol} + 16.00 \, \text{g/mol} = 231.74 \, \text{g/mol} 2×107.87g/mol+16.00g/mol=231.74g/mol
Next, we use the given mass of Ag2O\mathrm{Ag}_{2} \mathrm{O}Ag2O to find the number of moles. The formula to convert grams to moles is: moles=massmolar mass \text{moles} = \frac{\text{mass}}{\text{molar mass}} moles=molar massmass
Given mass of Ag2O\mathrm{Ag}_{2} \mathrm{O}Ag2O is 47.6 grams: moles of Ag2O=47.6 g231.74 g/mol=0.2054 moles \text{moles of } \mathrm{Ag}_{2} \mathrm{O} = \frac{47.6 \, \text{g}}{231.74 \, \text{g/mol}} = 0.2054 \, \text{moles} moles of Ag2O=231.74g/mol47.6g=0.2054moles
Since each molecule of Ag2O\mathrm{Ag}_{2} \mathrm{O}Ag2O contains 2 atoms of Ag, the number of moles of Ag is twice the number of moles of Ag2O\mathrm{Ag}_{2} \mathrm{O}Ag2O: moles of Ag=2×0.2054=0.4108 moles \text{moles of Ag} = 2 \times 0.2054 = 0.4108 \, \text{moles} moles of Ag=2×0.2054=0.4108moles
0.4108 moles \boxed{0.4108 \, \text{moles}} 0.4108moles
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