Calculate the molality, molarity, and mole fraction of FeCl3 in a 39.2 mass % aqueous solution (d = 1.238 g/mL).

m = mols/kg solvent

M = mols/L soln
X = n of X/total mols.

39.2 mass% means 39.2 g FeCl3 per 100 g solution.
mols FeCl3 = 39.2g/molar mass
Use density to convert 100 g to volume in mL, convert to L, and mols/L = M

You try the others. Just use the definition to go from unit to unit.

To calculate the molality, molarity, and mole fraction of FeCl3 in a 39.2 mass % aqueous solution, we need to follow a step-by-step process. Here's how you can do it:

Step 1: Determine the mass of the solution
Given that the density (d) of the solution is 1.238 g/mL, we can assume we have 1 L of the solution and calculate the mass using the formula:
mass of solution = volume × density
mass of solution = 1 L × 1.238 g/mL = 1.238 kg

Step 2: Calculate the mass of FeCl3 in the solution
To find the mass of FeCl3 in the solution, we multiply the mass of the solution by the mass percent of the solute:
mass of FeCl3 = mass of solution × mass percent of FeCl3
mass of FeCl3 = 1.238 kg × 39.2% = 0.484 kg

Step 3: Calculate the number of moles of FeCl3
To find the number of moles of FeCl3, we need to divide the mass of FeCl3 by its molar mass. The molar mass of FeCl3 can be found by adding the atomic masses of iron (Fe) and chlorine (Cl):
molar mass of FeCl3 = atomic mass of Fe + 3 × atomic mass of Cl
molar mass of FeCl3 = 55.85 g/mol + 3 × 35.45 g/mol = 162.2 g/mol
number of moles of FeCl3 = mass of FeCl3 / molar mass of FeCl3
number of moles of FeCl3 = 0.484 kg / 162.2 g/mol = 0.00299 mol

Step 4: Calculate the molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water. Since we know the number of moles of FeCl3 and the mass of the solvent (1.238 kg), we can calculate the molality using the formula:
molality = moles of solute / mass of solvent in kg
molality = 0.00299 mol / 1.238 kg = 0.00242 mol/kg

Step 5: Calculate the molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. In this case, the solution is the entire 1 L, and we already know the number of moles of FeCl3 (0.00299 mol). Therefore, we can calculate the molarity using the formula:
molarity = moles of solute / volume of solution in L
molarity = 0.00299 mol / 1 L = 0.00299 mol/L

Step 6: Calculate the mole fraction
Mole fraction (X) is defined as the number of moles of a component divided by the total number of moles of all components in the solution. In this case, we only have one component, FeCl3, so its mole fraction will be equal to 1. To calculate the mole fraction, we can use the formula:
mole fraction = moles of component / total moles of all components
mole fraction = 0.00299 mol / 0.00299 mol = 1

Therefore, the molality of FeCl3 in the solution is 0.00242 mol/kg, the molarity is 0.00299 mol/L, and the mole fraction is 1.