Calculation of Molality of Sulphuric Acid Solution:

Molality is defined as the number of moles of solute dissolved in 1 kg of solvent. The formula for molality is:

Molality (m) = Number of moles of solute / Mass of solvent in kg

To calculate the molality of sulphuric acid solution, we need to know the number of moles of sulphuric acid and the mass of water in the solution.

Calculating the Number of Moles of Sulphuric Acid:

The mole fraction of water (Xw) is given as 0.85. This means that the mole fraction of sulphuric acid (Xs) is:

Xs = 1 - Xw = 1 - 0.85 = 0.15

The total number of moles of the solution can be calculated as:

n = n(H2O) + n(H2SO4)

where n(H2O) is the number of moles of water and n(H2SO4) is the number of moles of sulphuric acid.

Since the mole fraction of water is 0.85, we can assume that there are 0.85 moles of water for every 1 mole of sulphuric acid. Therefore:

n(H2O) = 0.85n(H2SO4)

Substituting this into the equation for total number of moles, we get:

n = 0.85n(H2SO4) + n(H2SO4)
n = 1.85n(H2SO4)

The mole fraction of sulphuric acid (Xs) is given as 0.15. Therefore:

Xs = n(H2SO4) / n
0.15 = n(H2SO4) / (1.85n(H2SO4))
0.15 = 1 / 1.85
n(H2SO4) = 0.0811 moles

Calculating the Mass of Solvent (Water):

To calculate the mass of water in the solution, we need to know the density of the solution and the mass of the solution.

Assuming that the density of the solution is 1 g/mL, the mass of the solution can be calculated as:

Mass of solution = Volume of solution x Density of solution

Assuming that we have 1 L of the solution, the volume of the solution is 1 L. Therefore, the mass of the solution is:

Mass of solution = 1 L x 1000 g/L = 1000 g

Since the mole fraction of water is 0.85, we can assume that there are 0.85 g of water for every 1 g of the solution. Therefore:

Mass of water = 0.85 x 1000 g = 850 g

Converting the mass of water to kg, we get:

Mass of water = 850 g / 1000 = 0.85 kg

Calculating the Molality:

Now that we know the number of moles of sulphuric acid and the mass of water in the solution, we can calculate the molality of the solution using the formula:

Molality (m) = Number of moles of solute / Mass of solvent in kg

9.8m