A substance \(\mathrm{X}_{2} \mathrm{Z}\) has the composition (by mass) of 40.0\% X and 60.0\(\% \mathrm{Z}\) . What is the composition (by mass) of the compound \(\mathrm{XZ}_{2} ?\)

Given the compound X₂Z, we have a mass composition of 40% X and 60% Z. We can assume a 100 g sample to simplify calculations. In this case, we have 40 g of element X and 60 g of element Z.

To determine the composition of the compound XZ₂, we need to find the moles of each element in the 100 g sample. We do not know the atomic masses of elements X and Z, so let's assume the atomic mass of X is Mₓ and that of Z is Mz. Now we can determine the moles of each element using their mass and atomic mass: Moles of X = mass of X / atomic mass of X = 40 g / Mₓ Moles of Z = mass of Z / atomic mass of Z = 60 g / Mz

We know the compound X₂Z has two moles of element X and one mole of element Z. Based on the moles of the elements, we can write the mole ratios: Moles of X : Moles of Z in XZ₂ To obtain the moles of X and Z in compound XZ₂, we divide the moles of X in X₂Z by 2 since XZ₂ contains only one mole of X: Moles of X in XZ₂ = (40 g / Mₓ) / 2 = 20 g / Mₓ For the moles of Z, the compound XZ₂ contains two moles of Z, which is double the amount in X₂Z. To find the moles of Z in XZ₂, we multiply the moles of Z in X₂Z by 2: Moles of Z in XZ₂ = 2 × (60 g / Mz) = 120 g / Mz

We have obtained the moles of X and Z in compound XZ₂. Now, we can find the mass of each element in XZ₂: Mass of X in XZ₂ = Moles of X in XZ₂ × Mₓ = (20 g / Mₓ) × Mₓ = 20 g Mass of Z in XZ₂ = Moles of Z in XZ₂ × Mz = (120 g / Mz) × Mz = 120 g Now, we'll sum the masses of X and Z in XZ₂ to find the total mass: Total mass of XZ₂ = mass of X in XZ₂ + mass of Z in XZ₂ = 20 g + 120 g = 140 g Finally, we'll determine the mass composition by finding the percentage contribution of each element in XZ₂: Mass percent of X in XZ₂ = (mass of X in XZ₂ / total mass of XZ₂) × 100% = (20 g / 140 g) × 100% = 14.2857% Mass percent of Z in XZ₂ = (mass of Z in XZ₂ / total mass of XZ₂) × 100% = (120 g / 140 g) ×100% = 85.7143% Thus, the composition (by mass) of the compound XZ₂ is 14.29% X and 85.71% Z.