A 1.00% by mass MgSO4 solution has a freezing point of -.192°C. Water has a Kf of 1.86 (KxKg)/mol.
a.) Estimate the van’t Hoff i factor from the data.
b.)Determine the total molality of all solute species.
c.) Calculate the percentage dissociation of MgSO4 in this solution.
I understand part A and got i=1.23 but I don’t understand part B or part C.
To calculate the total molality of all solute species, you need to consider the moles of each individual species in the solution. In the case of a 1.00% by mass MgSO4 solution, you can assume that the entire mass of the solution is 100 g. Since the solution is 1.00% by mass, this means that you have 1.00 g of MgSO4 in the solution.
To calculate the molality, you need to determine the moles of MgSO4 in the solution. To do this, you need to know the molar mass of MgSO4, which is 120.37 g/mol. Using this molar mass, you can calculate the number of moles of MgSO4:
moles of MgSO4 = mass of MgSO4 / molar mass of MgSO4
= 1.00 g / 120.37 g/mol
≈ 0.00831 mol
Next, you need to calculate the total molality. Molality is defined as the moles of solute per kilogram of solvent. Since the solvent in this case is water, you need to consider the mass of water in the solution. The mass of water can be calculated by subtracting the mass of MgSO4 from the total mass of the solution:
mass of water = total mass of solution - mass of MgSO4
= 100 g - 1.00 g
= 99.00 g
Converting the mass of water to kilograms:
mass of water = 99.00 g / 1000 g/kg
= 0.099 kg
Finally, you can calculate the total molality:
molality = moles of solute / mass of solvent (in kg)
= 0.00831 mol / 0.099 kg
≈ 0.0840 mol/kg
For part C, to calculate the percentage dissociation of MgSO4 in the solution, you need to consider the van't Hoff factor (i) and the total molality of the solute species.
The percentage dissociation can be calculated using the formula:
% dissociation = (i - 1) / (i × molality) × 100
In this case, the van't Hoff factor (i) has been estimated as 1.23, and the total molality is approximately 0.0840 mol/kg. Plugging these values into the formula:
% dissociation = (1.23 - 1) / (1.23 × 0.0840) × 100
= 0.23 / 0.10332 × 100
≈ 2.22%
Therefore, the estimated percentage dissociation of MgSO4 in this solution is approximately 2.22%.