Answer:
0.101 M
0.1 mol/kg
0.644
Step-by-step explanation:
To calculate the molarity, molality, and mole fraction of Na2SO4 in a solution, you need to know the moles of Na2SO4 in the solution and the volume or mass of the solution.
A) Molarity: Molarity (M) is defined as the number of moles of solute per liter of solution. To calculate molarity, we need to divide the number of moles of Na2SO4 by the volume of the solution in liters.
First, calculate the number of moles of Na2SO4:
mass of Na2SO4 = 755 g
molecular weight of Na2SO4 = 142 g/mol
number of moles = mass/molecular weight = 755 g / 142 g/mol = 5.34 moles
Next, calculate the volume of the solution:
mass of water = 53,100 g
density of water = 1 g/mL
volume of water = mass/density = 53,100 g / 1 g/mL = 53,100 mL = 53.1 L
Finally, calculate the molarity:
molarity = number of moles / volume of solution = 5.34 moles / 53.1 L = 0.101 M
B) Molality: Molality (m) is defined as the number of moles of solute per kilogram of solvent. To calculate molality, we need to divide the number of moles of Na2SO4 by the mass of the solvent in kilograms.
mass of water = 53,100 g
mass of solvent in kilograms = mass in grams / 1000 g/kg = 53,100 g / 1000 g/kg = 53.1 kg
Finally, calculate the molality:
molality = number of moles / mass of solvent = 5.34 moles / 53.1 kg = 0.1 mol/kg
C) Mole fraction: The mole fraction (X) is defined as the ratio of the number of moles of solute to the total number of moles of solute and solvent in a solution. To calculate the mole fraction of Na2SO4, we need to divide the number of moles of Na2SO4 by the total number of moles of Na2SO4 and water.
number of moles of Na2SO4 = 5.34 moles
number of moles of water = 53.1 kg * 1000 g/kg / 18.015 g/mol = 2.96 moles
total number of moles = number of moles of Na2SO4 + number of moles of water = 5.34 moles + 2.96 moles = 8.30 moles
Finally, calculate the mole fraction:
mole fraction of Na2SO4 = number of moles of Na2SO4 / total number of moles = 5.34 moles / 8.30 moles = 0.644
The molarity of Na2SO4 in the solution is 0.101 M, the molality is 0.1 mol/kg, and the mole fraction of Na2SO4 is 0.644.