Answer :
The molality is approximately 3.60 mol/kg, the molarity is approximately 4.47 M, and the mole fraction of FeCl3 is approximately 0.0607.
To calculate the molality, molarity, and mole fraction of FeCl3 in the solution, we need to follow these steps:
1. Determine the mass of FeCl3 and water in the solution.
2. Convert the mass of FeCl3 to moles.
3. Calculate molality using moles of solute (FeCl3) per kilogram of solvent (water).
4. Convert the mass of water to volume using the density provided.
5. Calculate molarity using moles of solute per liter of solution.
6. Calculate mole fraction of FeCl3.
Let's go through these steps:
1. Determine the mass of FeCl3 and water:
Given that the solution is 36.9% FeCl3 by mass, and the density is 1.243 g/mL, let's assume we have 100 g of solution.
Mass of FeCl3 = 36.9 g
Mass of water = 100 g - 36.9 g = 63.1 g
2. Convert the mass of FeCl3 to moles:
The molar mass of FeCl3 is:
Fe: 55.845 g/mol
Cl: 3 * 35.453 g/mol = 106.359 g/mol
Total: 162.204 g/mol
Moles of FeCl3 = Mass / Molar Mass
= 36.9 g / 162.204 g/mol
≈ 0.227 moles
3. Calculate molality:
Molality (m) = moles of solute / mass of solvent (in kg)
= 0.227 mol / (63.1 g / 1000)
≈ 3.60 mol/kg
4. Convert the mass of water to volume:
Volume of water = Mass / Density
= 63.1 g / 1.243 g/mL
≈ 50.75 mL
5. Calculate molarity:
Molarity (M) = moles of solute / volume of solution (in L)
= 0.227 mol / (50.75 mL / 1000)
≈ 4.47 M
6. Calculate mole fraction of FeCl3:
Mole fraction of FeCl3 = moles of FeCl3 / total moles in solution
= 0.227 mol / (0.227 mol + (mass of water in kg) / (molar mass of water))
= 0.227 mol / (0.227 mol + (0.0631 kg / 18.015 g/mol))
≈ 0.227 / (0.227 + 3.502)
≈ 0.0607
The complete question is:
Calculate the molality, molarity, and mole fraction of FeCl3 in a 36.9 mass % aqueous solution (d = 1.243 g/mL).