To determine the value of X in the formula of rust (Fe2O3.XH2O), we can use the given information about the mass of the sample of rust and the mass of iron (III) oxide obtained after heating.
Let's break down the steps to solve the problem:
Calculate the mass of water lost during heating: Mass of water lost = Mass of rust - Mass of iron (III) oxide = 10.7g - 8.0g = 2.7g
Determine the molar mass of water (H2O): Molar mass of water = 2(1.00784 g/mol of H) + 15.999 g/mol of O = 18.015 g/mol
Convert the mass of water lost to moles: Moles of water lost = Mass of water lost / Molar mass of water = 2.7g / 18.015 g/mol ≈ 0.1498 mol
Calculate the molar ratio between water and iron (III) oxide in rust: In rust (Fe2O3.XH2O), the molar ratio of water to iron (III) oxide is 1:1. This means that for every 1 mole of iron (III) oxide, there is 1 mole of water.
Determine the moles of iron (III) oxide obtained: Moles of iron (III) oxide = Mass of iron (III) oxide / Molar mass of iron (III) oxide = 8.0g / (2(55.845 g/mol of Fe) + 3(15.999 g/mol of O)) ≈ 0.0571 mol
Use the mole ratio to find the value of X: Since the molar ratio of water to iron (III) oxide is 1:1 in rust, the moles of water lost (0.1498 mol) is equal to the moles of iron (III) oxide obtained (0.0571 mol) multiplied by the value of X. Therefore, 0.1498 mol = 0.0571 mol * X
Solving for X: X = (0.1498 mol) / (0.0571 mol) X ≈ 2.62
The value of X in the formula of rust (Fe2O3.XH2O) is approximately 2.62. Since X is expected to be a whole number, we round it to the nearest whole number. Therefore, X = 3.