Final answer:
To determine the formula of the hydrate, we can compare the mass of the original hydrated compound with the mass of the anhydrous compound. In this case, the formula of the hydrate is CaSO_4·0.24H2O.
Step-by-step explanation:
The formula of a hydrate can be determined by comparing the mass of the original hydrated compound with the mass of the anhydrous compound left after heating. In this case, a 34.01 gram sample of a hydrate of CaSO_4 was heated and only 26.89 grams of the dehydrated compound remained.
To find the formula of the hydrate, we need to calculate the mass of the water that was lost during heating.
Mass of water = Mass of hydrate - Mass of anhydrous compound = 34.01g - 26.89g = 7.12g.
The formula of the hydrate can be written as CaSO_4·xH2O, where x is the number of water molecules per formula unit of CaSO_4. To find x, we can divide the mass of water lost by the mass of the anhydrous compound and multiply by the molar mass of water.
x = (Mass of water lost / Mass of anhydrous compound) * (Molar mass of water / Molar mass of CaSO_4) = (7.12g / 26.89g) * (18.015g/mol / 136.14g/mol) ≈ 0.24.
Therefore, the formula of the hydrate is CaSO_4·0.24H2O.