Final answer:
To find the ∆H for the dissolution of MgSO₄, calculate the heat absorbed using q = mc∆T, convert it to kilojoules, determine the number of moles of MgSO₄, and divide the heat by the moles to get ∆H in kJ/mol.
Step-by-step explanation:
To calculate the ∆H (enthalpy change) for the dissolution of MgSO₄, we need to calculate the amount of heat (q) absorbed by the water when the compound dissolves. We use the formula q = mc∆T, where m = mass of the solution, c= specific heat of water, and ∆T = change in temperature. Given that the specific heat c = 4.184 J/g°C, and ∆T = 6.70°C, and also given that the mass of the solution is the mass of water since the mass of MgSO₄ is negligible in comparison, we have m = 100.0 mL × 1.00 g/mL = 100.0 g.
Therefore, the heat absorbed by the solution is q = 100.0 g × 4.184 J/g°C × 6.70°C = 2803.28 J.
To express this heat in kilojoules, q = 2803.28 J ÷ 1000 = 2.80328 kJ. Next, we convert the mass of MgSO₄ to moles. The molar mass of MgSO₄ is approximately 120.36 g/mol, so 5.31 g corresponds to 5.31 g ÷ 1 mol/120.36 g = 0.04413 mol. Finally, ∆H for the dissolution can be calculated by dividing the heat energy by the number of moles: ∆H = 2.80328 kJ ÷ 0.04413 mol = 63.54 kJ/mol.