An oxide XO2 has a vapour density of 32. What is the atomic mass of X?

Answer Details

The given oxide XO2 has a vapor density of 32. Vapor density is the ratio of the molecular weight of a gas to that of hydrogen. So, we can say that the molecular weight of XO2 is 32 times that of hydrogen. The molecular formula of XO2 can be written as XaOb, where 'a' and 'b' are the atomicity of X and O, respectively. The atomicity of oxygen is 2, so we can write the formula as XaO2. Now, the molecular weight of XaO2 can be calculated as follows: Molecular weight of XaO2 = (Atomic mass of X x a) + (Atomic mass of O x 2) We don't know the value of 'a' or the atomic mass of X, so we need to find a way to calculate them. We know that the vapor density of XaO2 is 32 times that of hydrogen. The molecular weight of hydrogen is 2 (since it is a diatomic molecule), so the molecular weight of XaO2 is 32 x 2 = 64. Therefore, we can write the equation as: (Atomic mass of X x a) + (16 x 2) = 64 Atomic mass of X x a = 32 Dividing both sides by 'a', we get: Atomic mass of X = 32/a We don't know the value of 'a', so we need to find it. The formula XaO2 shows that one atom of X combines with two atoms of O. The combining capacity of X is its valency. The valency of O is 2, so the valency of X must be 4 in order to combine with 2 atoms of O. Now, the atomic mass of X can be calculated as follows: Atomic mass of X = 32/a Valency of X = 4 So, the equivalent weight of X = Atomic mass of X / Valency of X = (32/a) / 4 = 8/a The equivalent weight of X must be a whole number, so the value of 'a' must be a factor of 8. The factors of 8 are 1, 2, 4, and 8. If we substitute each value of 'a' into the equation for atomic mass of X, we get: a = 1 -> Atomic mass of X = 32 a = 2 -> Atomic mass of X = 16 a = 4 -> Atomic mass of X = 8 a = 8 -> Atomic mass of X = 4 Out of these values, the only one that makes sense is the atomic mass of X = 16 (when a=2). This is because the atomic mass of X cannot be less than that of oxygen (which is 16), and it is unlikely to be greater than 32 (which is the molecular weight of XaO2). Therefore, the answer is 20. In summary, the atomic mass of X in the oxide XO2 with a vapor density of 32 is 20, and this is because the equivalent weight of X (which is related to its valency) must be a whole number, and the only value of 'a' that makes sense is 2, which leads to an atomic mass of X of 16, and since XO2 has a molecular weight of 64, the atomic mass of O is 16, so the molecular formula is XO2, and the atomic mass of X is 20.