To determine the atomic mass of the metal in the trivalent metal oxide, we need to use the information that the oxide contains 68.4% oxygen.
Let's assume we have 100 grams of the trivalent metal oxide. This means that 68.4 grams of this compound consist of oxygen.
To find the mass of the metal, we can subtract the mass of oxygen from the total mass of the compound:
Mass of metal = Total mass of compound - Mass of oxygen
Since we assumed the total mass of the compound to be 100 grams, we can calculate the mass of the metal as follows:
Mass of metal = 100 grams - 68.4 grams = 31.6 grams
Now, we know that the atomic mass of an element is the mass of one mole of that element. To determine the atomic mass of the metal, we need to convert the mass of the metal from grams to moles.
We can do this by using the molar mass of the metal. Let's denote the molar mass of the metal as "M."
To convert the mass of the metal from grams to moles, we divide the mass by the molar mass:
Moles of metal = Mass of metal / M
Since we found the mass of the metal to be 31.6 grams, the number of moles of metal can be calculated as follows:
Moles of metal = 31.6 grams / M
Now, we know that the trivalent metal has a valence of +3, which means it forms three positive charges in its ionic state. This indicates that the metal's molar mass is three times the atomic mass of oxygen (O), as it combines with three oxygen atoms.
The atomic mass of oxygen (O) is approximately 16 grams/mole. Therefore, the molar mass of the metal (M) is approximately 3 times the atomic mass of oxygen:
M ≈ 3 * 16 grams/mole = 48 grams/mole
Now, we can substitute the molar mass value into the equation for moles of metal:
Moles of metal = 31.6 grams / 48 grams/mole
By performing this calculation, we find:
Moles of metal ≈ 0.6583 moles
Therefore, the atomic mass of the metal is approximately 0.6583 moles.