Final answer:
By calculating the mass of water lost when Epsom salt is heated and comparing it to the mass of remaining anhydrous MgSO4, we find there are approximately 7 moles of water for every mole of MgSO4, indicating the formula is likely MgSO4 · 7H2O. However, this option is not provided in the question, implying an error in the question or options.
Step-by-step explanation:
To find the formula of Epsom salt, MgSO4 · X H2O, when it is heated to 250°C and all the water of hydration is lost, we must compare the mass of the anhydrous magnesium sulphate with the original hydrated mass.
Given that the original sample weighed 1.687 g and the remaining anhydrous MgSO4 weighed 0.824 g after heating, the mass of the water lost is:
Mass of water = Original mass - Mass of anhydrous MgSO4 = 1.687 g - 0.824 g = 0.863 g of water
The molar mass of water (H2O) is approximately 18.015 g/mol. Next, we need to calculate the moles of water lost during the heating process:
Moles of water = Mass of water / Molar mass of water = 0.863 g / 18.015 g/mol ≈ 0.0479 mol
The molar mass of MgSO4 is approximately 120.36 g/mol. We now calculate the moles of anhydrous MgSO4 that remain:
Moles of MgSO4 = Mass of anhydrous MgSO4 / Molar mass of MgSO4 = 0.824 g / 120.36 g/mol ≈ 0.0068 mol
Since the molar ratio of MgSO4 to H2O in the hydrated compound should be 1:1 (as they are combined in whole number ratios in a compound), we can approximate the number of water molecules in the hydrate by dividing the moles of water by the moles of MgSO4:
X = Moles of water / Moles of MgSO4 ≈ 0.0479 mol / 0.0068 mol ≈ 7
Therefore, the formula of the hydrated Epsom salt is MgSO4 · 7H2O. The correct answer is not provided among the options, suggesting there might be a mistake in the question or options provided.