<u>Answer:</u> The atom percent of silver, gold and copper in the alloy is 43.08 %, 44.93 % and 11.99 % respectively
<u>Explanation:</u>
To convert the given masses into grams, we use the conversion factor:
1 lb = 453.6 grams
To calculate the number of moles, we use the equation:
......(1)
To calculate the atom percent of substance in sample, we use the equation:
......(2)
where,
= Avogadro's number
Mass of silver = 44.5 lb = 20185.2 grams
We know that:
Molar mass of silver = 107.87 g/mol
Putting values in equation 1, we get:
![\text{Moles of silver}=\frac{20185.2g}{107.87g/mol}=187.12mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20silver%7D%3D%5Cfrac%7B20185.2g%7D%7B107.87g%2Fmol%7D%3D187.12mol)
Mass of gold = 84.7 lb = 38419.9 grams
We know that:
Molar mass of gold = 196.97 g/mol
Putting values in equation 1, we get:
![\text{Moles of gold}=\frac{38419.9g}{196.97g/mol}=195.05mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20gold%7D%3D%5Cfrac%7B38419.9g%7D%7B196.97g%2Fmol%7D%3D195.05mol)
Mass of copper = 7.3 lb = 3311.3 grams
We know that:
Molar mass of copper = 63.55 g/mol
Putting values in equation 1, we get:
![\text{Moles of copper}=\frac{3311.3g}{63.55g/mol}=52.10mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20copper%7D%3D%5Cfrac%7B3311.3g%7D%7B63.55g%2Fmol%7D%3D52.10mol)
Total moles of the sample =
Moles of silver = 187.12 moles
Total moles = [187.12 + 195.05 + 52.10] = 434.27 moles
Putting values in equation 2, we get:
![\%\text{ composition of silver}=\frac{187.12\times N_A}{434.27\times N_A}\times 100\\\\\%\text{ composition of silver}=43.08\%](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20silver%7D%3D%5Cfrac%7B187.12%5Ctimes%20N_A%7D%7B434.27%5Ctimes%20N_A%7D%5Ctimes%20100%5C%5C%5C%5C%5C%25%5Ctext%7B%20composition%20of%20silver%7D%3D43.08%5C%25)
Moles of gold = 195.05 moles
Total moles = [187.12 + 195.05 + 52.10] = 434.27 moles
Putting values in equation 2, we get:
![\%\text{ composition of gold}=\frac{195.05\times N_A}{434.27\times N_A}\times 100\\\\\%\text{ composition of gold}=44.93\%](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20gold%7D%3D%5Cfrac%7B195.05%5Ctimes%20N_A%7D%7B434.27%5Ctimes%20N_A%7D%5Ctimes%20100%5C%5C%5C%5C%5C%25%5Ctext%7B%20composition%20of%20gold%7D%3D44.93%5C%25)
Moles of copper = 52.10 moles
Total moles = [187.12 + 195.05 + 52.10] = 434.27 moles
Putting values in equation 2, we get:
![\%\text{ composition of copper}=\frac{52.10\times N_A}{434.27\times N_A}\times 100\\\\\%\text{ composition of copper}=11.99\%](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20copper%7D%3D%5Cfrac%7B52.10%5Ctimes%20N_A%7D%7B434.27%5Ctimes%20N_A%7D%5Ctimes%20100%5C%5C%5C%5C%5C%25%5Ctext%7B%20composition%20of%20copper%7D%3D11.99%5C%25)
Hence, the atom percent of silver, gold and copper in the alloy is 43.08 %, 44.93 % and 11.99 % respectively