A metallurgist decomposes an unknown ore to the following metals. What is the chemical formula of the ore?
(Show all the chemical equation and solution steps)
ore = x
metal products from ore decomposition:
Al: 162.0 grams
Sb: 730.8 grams
Ag: 1,294 grams
To determine the chemical formula of the ore, we need to analyze the mass of each element present in the metal products from the ore decomposition. In this case, we have the following metals and their corresponding masses:
Aluminum (Al): 162.0 grams
Antimony (Sb): 730.8 grams
Silver (Ag): 1,294 grams
To find the chemical formula, we need to convert these masses into moles by using the molar mass of each element. The molar mass of aluminum is 26.98 g/mol, the molar mass of antimony is 121.76 g/mol, and the molar mass of silver is 107.87 g/mol.
1. Let's start with Aluminum (Al):
Mass of Al = 162.0 g
Molar mass of Al = 26.98 g/mol
Number of moles of Al = Mass of Al / Molar mass of Al
= 162.0 g / 26.98 g/mol
≈ 6.00 mol
2. Now let's move on to Antimony (Sb):
Mass of Sb = 730.8 g
Molar mass of Sb = 121.76 g/mol
Number of moles of Sb = Mass of Sb / Molar mass of Sb
= 730.8 g / 121.76 g/mol
≈ 6.00 mol
3. Lastly, let's calculate Silver (Ag):
Mass of Ag = 1,294 g
Molar mass of Ag = 107.87 g/mol
Number of moles of Ag = Mass of Ag / Molar mass of Ag
= 1,294 g / 107.87 g/mol
≈ 12.00 mol
Now, we need to find the ratio of each element to determine the chemical formula. We can divide each element's mole value by the smallest mole value obtained above (in this case, 6.00 mol):
Al: 6.00 mol / 6.00 mol = 1
Sb: 6.00 mol / 6.00 mol = 1
Ag: 12.00 mol / 6.00 mol = 2
The ratio of Al, Sb, and Ag in the unknown ore is 1:1:2. Therefore, the chemical formula of the ore can be written as AlSbAg2.