Answer:
To calculate the molality, normality, and mole fraction of a solution, we'll use the given information.
Molality (m):
Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solute is H₂SO4 and the solvent is water.
To find the molality, we need to know the mass of the solute (H₂SO4) and the mass of the solvent (water). We can calculate the mass of H₂SO4 using its molarity and molar mass.
Given:
Molarity (M) = 5.35 M
Density = 1.22 g/cm³
First, let's find the molar mass of H₂SO4:
Molar mass of H₂SO4 = 2(1.01 g/mol) + 32.07 g/mol + 4(16.00 g/mol) = 98.09 g/mol
To calculate the mass of H₂SO4 in a 1 L solution (1000 mL), we can use the molarity and molar mass:
Mass of H₂SO4 = Molarity × Volume × Molar mass
Mass of H₂SO4 = 5.35 mol/L × 1000 mL × 98.09 g/mol = 5233.795 g
Since the density of the solution is given as 1.22 g/cm³, we can calculate the volume of the solution using the mass and density:
Volume of the solution = Mass of the solution / Density
Volume of the solution = 5233.795 g / 1.22 g/cm³ = 4289.346 cm³
Now, we need to convert the volume of the solution to kilograms:
Volume of the solution in kg = Volume of the solution in cm³ × (1 mL / 1 cm³) × (1 L / 1000 mL) × (1 kg / 1000 g)
Volume of the solution in kg = 4289.346 cm³ × (1 mL / 1 cm³) × (1 L / 1000 mL) × (1 kg / 1000 g) = 4.289346 kg
Finally, we can calculate the molality:
Molality (m) = Moles of solute / Mass of solvent (in kg)
Molality (m) = 5.35 mol / 4.289346 kg = 1.247 m (approximately)
Normality (N):
Normality is the measure of the concentration of acid or base in a solution. In this case, since we have H₂SO4, which is a diprotic acid, the normality will be twice the molarity.
Normality (N) = 2 × Molarity
Normality (N) = 2 × 5.35 M = 10.7 N
Mole Fraction:
The mole fraction (χ) of a solute in a solution is the ratio of the moles of the solute to the total moles of all components in the solution.
Mole fraction (χ) = Moles of solute / (Moles of solute + Moles of solvent)
Since the solute is H₂SO4 and the solvent is water, we need to calculate the moles of H₂SO4 and the moles of water.
Moles of H₂SO4 = Molarity × Volume
Moles of H₂SO4 = 5.35 mol/L × 1 L = 5.35 mol
Moles of water can be calculated using the mass of water and its molar mass:
Mass of water = Mass of solution - Mass of
H₂SO4
Mass of water = 5233.795 g - 4289.346 g = 943.449 g
Moles of water = Mass of water / Molar mass of water
Molar mass of water = 18.02 g/mol
Moles of water = 943.449 g / 18.02 g/mol = 52.39 mol
Now, we can calculate the mole fraction:
Mole fraction (χ) = Moles of H₂SO4 / (Moles of H₂SO4 + Moles of water)
Mole fraction (χ) = 5.35 mol / (5.35 mol + 52.39 mol) = 0.092 (approximately)
So, the answers to the questions are:
a. The molality of the 5.35 M H₂SO4 solution is approximately 1.247 m.
b. The normality of the solution is 10.7 N.
c. The mole fraction of the H₂SO4 solute is approximately 0.092.