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Answer :
Final answer:
To calculate the composition of the alloy in atom percent, we need to find the number of moles of each element and divide them by the total moles of the alloy. Then, we multiply by 100 to get the atom percent. The composition of the alloy in atom percent is approximately 49.84% copper, 49.84% zinc, and 0.318% lead.
Explanation:
To find the composition of the alloy in atom percent, we need to calculate the number of moles of each element. First, we convert the given quantities of each element into grams using their molar masses. Then, we divide the grams by the molar mass to find the number of moles. Finally, we divide the number of moles of each element by the total number of moles present in the alloy and multiply by 100 to get the atom percent.
Let's start with copper: 99.7 lbm = 45.18 kg (1 lbm = 0.4536 kg). The molar mass of copper is 63.5 g/mol. So, the number of moles of copper is 45.18 kg / 63.5 g/mol = 0.71 mol.
We can follow the same steps for zinc and lead. Zinc: 102 lbm = 46.27 kg. The molar mass of zinc is 65.4 g/mol. So, the number of moles of zinc is 46.27 kg / 65.4 g/mol = 0.71 mol. Lead: 2.1 lbm = 0.95 kg. The molar mass of lead is 207 g/mol. So, the number of moles of lead is 0.95 kg / 207 g/mol = 0.0046 mol.
Now, we can calculate the atom percent of each element. Atom percent of copper = (0.71 mol / (0.71 mol + 0.71 mol + 0.0046 mol)) * 100 = 49.84%. Atom percent of zinc = (0.71 mol / (0.71 mol + 0.71 mol + 0.0046 mol)) * 100 = 49.84%. Atom percent of lead = (0.0046 mol / (0.71 mol + 0.71 mol + 0.0046 mol)) * 100 = 0.318%. So, the composition of the alloy in atom percent is approximately 49.84% copper, 49.84% zinc, and 0.318% lead.
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