Final answer:
The composition of an alloy containing silver, gold, and copper in atom percent is calculated by converting the pound-mass to grams, finding the number of moles of each, and then determining the atom percent, which is approximately 44.79% Ag, 46.16% Au, and 9.06% Cu.
Step-by-step explanation:
The composition of an alloy in atom percent can be calculated by first finding the mass of each element in the alloy, then determining the number of moles of each element, and finally calculating the atom percent for each element.
The masses given are:
- 44.5 lbm of silver (Ag)
- 83.7 lbm of gold (Au)
- 5.3 lbm of copper (Cu)
We first need to convert the masses from pounds-mass (lbm) to grams since the atomic mass unit (amu) is based on grams. There are 453.59237 grams in a pound-mass:
- 44.5 lbm Ag × 453.59237 g/lbm = 20159.68055 g Ag
- 83.7 lbm Au × 453.59237 g/lbm = 37952.63003 g Au
- 5.3 lbm Cu × 453.59237 g/lbm = 2404.03916 g Cu
Next, calculate the number of moles for each element using their atomic masses (approximations):
- Ag = 107.8682 amu
- Au = 196.96657 amu
- Cu = 63.546 amu
Number of moles:
- ≈ 20159.68055 g Ag / 107.8682 g/mol = 186.882 mol Ag
- ≈ 37952.63003 g Au / 196.96657 g/mol = 192.665 mol Au
- ≈ 2404.03916 g Cu / 63.546 g/mol = 37.817 mol Cu
Then, calculate the total number of moles in the alloy:
Total moles = 186.882 mol Ag + 192.665 mol Au + 37.817 mol Cu = 417.364 mol
Calculate the atom percent for each element:
- Atom percent Ag ≈ (186.882 mol Ag / 417.364 mol) × 100% = 44.79%
- Atom percent Au ≈ (192.665 mol Au / 417.364 mol) × 100% = 46.16%
- Atom percent Cu ≈ (37.817 mol Cu / 417.364 mol) × 100% = 9.06%
Therefore, the composition of the alloy in atom percent is approximately 44.79% Ag, 46.16% Au, and 9.06% Cu.