Question

Calculate the heat of hydration of magnesium sulfate (MgSO4) given that 4.17 g of MgSO4 is dissolved in 50.0 ml of water at 25°C, and the resulting solution cools from 25°C to 20°C. The specific heat capacity of the solution is 4.18 J/(g·°C), and the density of the solution is 1.00 g/ml. Don't forget to include the units in your final answer.

Answer 1

To calculate the heat of hydration of magnesium sulfate, we first need to determine the heat released during the dissolution process. We can do this using the formula:q = mcTwhere q is the heat released, m is the mass of the solution, c is the specific heat capacity, and T is the change in temperature.First, we need to find the mass of the solution. Since the density of the solution is 1.00 g/ml, the mass of the 50.0 ml solution is:mass_solution = density  volume = 1.00 g/ml  50.0 ml = 50.0 gNow we can calculate the heat released:T = T_initial - T_final = 25C - 20C = 5Cq = mcT =  50.0 g  4.18 J/ gC   5C  = 1045 JNow we need to find the heat of hydration per mole of MgSO4. First, we need to find the molar mass of MgSO4:Mg = 24.31 g/molS = 32.07 g/molO = 16.00 g/molMolar mass of MgSO4 = 24.31 + 32.07 +  4  16.00  = 120.38 g/molNow we can find the moles of MgSO4:moles_MgSO4 = mass_MgSO4 / molar_mass_MgSO4 = 4.17 g / 120.38 g/mol = 0.0346 molFinally, we can calculate the heat of hydration per mole of MgSO4:heat_of_hydration = q / moles_MgSO4 = 1045 J / 0.0346 mol = 30200 J/molThe heat of hydration of magnesium sulfate is 30,200 J/mol.