Answer:
The atomic mass of X is 204.5 amu.
Explanation:
We know that metals react with oxygen forming a metallic oxide, according to the following equation:
4 X + O₂ ⇄ 2 X₂O
The oxide is formed just by <em>just</em> two elements, the metal and oxygen. The total mass of the oxide is 1.4158g and the mass of the metal in the oxide must be 1.3625g because of the Law of conservation of mass. Then, we can substract the mass of the metal to obtain the mass of oxygen.
mass O + mass X = mass X₂O
mass O = mass X₂O - mass X = 1.4158g - 1.3625g = 0.0533g
So, for every 0.0533g of oxygen there are 1.3625 g of the metal X. In the formula X₂O there is 1 mol of atoms of oxygen, which has a molar mass of 16 g/mol. We can use this data to find out the mass of the metal in the oxide.
Given in the formula there are 2 moles of atoms of X, the molar mass should be half of 409g, i.e., 204.5g/mol. If a mol of X has a mass of 204.5 g, an atom of X has a mass of 204.5 amu, according to its definition.