Calculation of Molality of 20% w/v H2SO4 Solution

Step 1: Determine the mass of H2SO4 present in 100 mL of the solution.

Given, the density of the solution (D) = 1.5 g/mL

Therefore, the mass of 100 mL of the solution = D x V
= 1.5 g/mL x 100 mL
= 150 g

As the solution is 20% w/v, the mass of H2SO4 present in this solution can be calculated as follows:

Mass of H2SO4 = 20% of 150 g
= (20/100) x 150 g
= 30 g

Step 2: Calculate the moles of H2SO4 in 1000 g (1 kg) of solvent (water).

The molar mass of H2SO4 = 98 g/mol

Therefore, the moles of H2SO4 in 30 g of H2SO4 can be calculated as follows:

Moles of H2SO4 = Mass of H2SO4 / Molar mass of H2SO4
= 30 g / 98 g/mol
= 0.306 moles

The mass of solvent (water) required to prepare this solution can be calculated as follows:

Mass of solvent = 1000 g - 150 g (mass of solution)
= 850 g

Step 3: Calculate the molality of the solution.

Molality is defined as the number of moles of solute (H2SO4) present in 1 kg of solvent (water).

Therefore, the molality of the solution can be calculated as follows:

Molality = Moles of solute / Mass of solvent (in kg)
= 0.306 moles / 0.85 kg
= 0.36 mol/kg

Therefore, the molality of the 20% w/v H2SO4 solution is 0.36 mol/kg.

Explanation:

Molality is defined as the number of moles of solute per kilogram of solvent. In this problem, we are given the concentration of the solution in terms of weight/volume (w/v) and the density of the solution. We first calculate the mass of H2SO4 present in 100 mL of the solution using the density of the solution. Then, we calculate the moles of H2SO4 present in 1 kg of solvent (water) using the molar mass of H2SO4. Finally, we divide the moles of H2SO4 by the mass of solvent (in kg) to obtain the molality of the solution.