8.0575 X 10-2 kg of Glauber’s salt is dissolved in water to obtain 1 dm3 of a solution of density 1077.2 kg m-3. Calculate the molarity, molality & mole fraction of Na2SO4 in the solution.

To tackle the problem of calculating the molarity, molality, and mole fraction of Na2SO4 in the given solution, we need to break down the information provided and apply the relevant formulas step by step. Let’s go through each calculation methodically.

Understanding the Given Data

We have the following information:

• Mass of Glauber’s salt (Na2SO4) = 8.0575 x 10^-2 kg
• Volume of solution = 1 dm³ (which is equivalent to 1 L)
• Density of solution = 1077.2 kg/m³

Calculating Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. To find this, we first need to determine the number of moles of Na2SO4.

Step 1: Calculate Moles of Na2SO4

The molar mass of Na2SO4 can be calculated as follows:

• Na: 22.99 g/mol × 2 = 45.98 g/mol
• S: 32.07 g/mol
• O: 16.00 g/mol × 4 = 64.00 g/mol

Adding these together gives:

Molar mass of Na2SO4 = 45.98 + 32.07 + 64.00 = 142.05 g/mol

Now, convert the mass of Na2SO4 to grams:

8.0575 x 10^-2 kg = 80.575 g

Next, calculate the number of moles:

Number of moles = mass (g) / molar mass (g/mol) = 80.575 g / 142.05 g/mol ≈ 0.567 moles

Step 2: Calculate Molarity

Since the volume of the solution is 1 L, the molarity is simply:

Molarity (M) = moles of solute / volume of solution (L) = 0.567 moles / 1 L = 0.567 M

Calculating Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. To find this, we need to determine the mass of the solvent (water) in the solution.

Step 1: Calculate Mass of the Solution

Using the density of the solution:

Density = mass/volume, thus mass = density × volume

Mass of solution = 1077.2 kg/m³ × 1 dm³ = 1077.2 kg

Step 2: Calculate Mass of the Solvent

Mass of solvent (water) = mass of solution - mass of solute

Mass of solvent = 1077.2 kg - 0.080575 kg = 1077.119425 kg

Step 3: Calculate Molality

Now we can calculate molality:

Molality (m) = moles of solute / mass of solvent (kg) = 0.567 moles / 1.077119425 kg ≈ 0.526 m

Finding Mole Fraction

Mole fraction (X) is the ratio of the number of moles of a component to the total number of moles in the solution.

Step 1: Calculate Moles of Water

The molar mass of water (H2O) is approximately 18.02 g/mol. First, convert the mass of water to grams:

Mass of water = 1077.119425 kg = 1077119.425 g

Now, calculate the number of moles of water:

Moles of water = mass (g) / molar mass (g/mol) = 1077119.425 g / 18.02 g/mol ≈ 59745.5 moles

Step 2: Calculate Total Moles in the Solution

Total moles = moles of Na2SO4 + moles of water = 0.567 + 59745.5 ≈ 59746.067 moles

Step 3: Calculate Mole Fraction of Na2SO4

Mole fraction (X) of Na2SO4 = moles of Na2SO4 / total moles = 0.567 / 59746.067 ≈ 9.49 x 10^-6

Summary of Results

To summarize, we have calculated:

• Molarity of Na2SO4 = 0.567 M
• Molality of Na2SO4 = 0.526 m
• Mole fraction of Na2SO4 = 9.49 x 10^-6

These calculations provide a comprehensive understanding of the concentration of Na2SO4 in the solution. If you have any further questions or need clarification on any of the steps, feel free to ask!