Calculate the molality, molarity, and mole fraction of FeCl3 in a 25.7 mass % aqueous solution (d = 1.204 g/mL).
And you know what about this?
The definitions are
% w/w = grams/100 g solution
m = mols/kg solvent
M = mols/L solution
X = mols solute/total mols.
To calculate the molality, molarity, and mole fraction of FeCl3 in the given solution, we need to use the formulas and equations related to these terms.
1. Molality (m):
Molality is defined as the amount of solute (in moles) dissolved in 1 kilogram (1000 grams) of solvent. The formula for molality is:
molality (m) = moles of solute / mass of solvent (in kg)
2. Molarity (M):
Molarity is defined as the amount of solute (in moles) dissolved in 1 liter of solvent. The formula for molarity is:
molarity (M) = moles of solute / volume of solvent (in L)
3. Mole fraction (χ):
Mole fraction is defined as the ratio of the number of moles of a particular component to the total number of moles of all components in the solution. The formula for mole fraction is:
mole fraction (χ) = moles of solute / total moles of solute and solvent
Now let's calculate each value step by step:
Step 1: Calculate the mass of the solution:
Given mass percentage = 25.7%
Let's assume we have 100 grams of the solution,
Then the mass of the solution = 100 g
Step 2: Calculate the mass of the solute (FeCl3):
Given mass percentage = 25.7%
Mass of the solute = (mass percentage / 100) × mass of the solution
Mass of the solute = (25.7 / 100) × 100 g
Mass of the solute = 25.7 g
Step 3: Calculate the amount of solute in moles:
We need the molar mass of FeCl3, which is 162.2 g/mol.
Amount of solute (moles) = mass of solute / molar mass of solute
Amount of solute (moles) = 25.7 g / 162.2 g/mol
Amount of solute (moles) ≈ 0.1586 mol
Step 4: Calculate molality:
Molality (m) = moles of solute / mass of solvent (in kg)
Given density (d) = 1.204 g/mL, which is the same as 1.204 g/cm³
Mass of solvent = volume of solvent × density
Since we have assumed 100 g of solution, the mass of the solvent can be calculated as follows:
Mass of solvent = mass of solution - mass of solute
Mass of solvent = 100 g - 25.7 g = 74.3 g
Mass of solvent in kg = 74.3 g / 1000 g/kg = 0.0743 kg
Molality (m) = 0.1586 mol / 0.0743 kg = 2.134 mol/kg
Step 5: Calculate molarity:
Molarity (M) = moles of solute / volume of solvent (in L)
Given density (d) = 1.204 g/mL, which is the same as 1.204 g/cm³
Volume of solvent = mass of solvent / density
Volume of solvent = 74.3 g / 1.204 g/cm³ = 61.7 cm³
Volume of solvent in L = 61.7 cm³ / 1000 cm³/L = 0.0617 L
Molarity (M) = 0.1586 mol / 0.0617 L = 2.573 mol/L
Step 6: Calculate mole fraction:
Total moles of solute and solvent = moles of solute
Mole fraction (χ) = moles of solute / total moles of solute and solvent
Mole fraction (χ) = 0.1586 mol / 0.1586 mol = 1
Therefore, the molality (m) of FeCl3 in the solution is 2.134 mol/kg, the molarity (M) is 2.573 mol/L, and the mole fraction (χ) is 1.