Final answer:
To calculate the value of x in MgSO₄.H₂O, use the ideal gas law to determine the moles of water vapor produced from heating, then find the mass of the water and compare it to the mass of the anhydrous salt to find the moles of water per mole of MgSO₄.
Step-by-step explanation:
A student asked how to calculate the number of moles of water (x) in the hydrate MgSO₄.H₂O using the mass lost upon heating and the properties of the water vapor released. To solve for x in the given hydrate, we must first use the ideal gas law, PV = nRT, to find the number of moles of water vapor (n) produced during the heating process.
The ideal gas law states that PV = nRT, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the gas constant (0.0821 L·atm/mol·K), and T is the absolute temperature in Kelvin. The student is provided with all necessary values: P = 24.8 atm, V = 2.0 L, and T = 393.15 K (120°C + 273.15).
After calculating the moles of water vapor, we then find the mass of just the water that was in the hydrate by multiplying the moles by the molar mass of water (18.015 g/mol). The difference between the initial mass of the hydrate and the mass of the anhydrous salt (MgSO₄) gives the total mass of water lost. Comparing this mass to the mass of water calculated from the vapor allows us to find x, which represents the number of moles of water per mole of MgSO₄ in the original hydrate.