. 20 g of a solute whose density is 2.0 g/cc is dissolved in water and the solution is made upto one litre. If the molecular weight of the solute is 100, what is the molality of the solution? a) 0.2020 b) 0.4040 c) 0.2000 d) 0.0200

To determine the molality of the solution, we first need to understand what molality is. Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula for calculating molality is:

Molality Formula

Molality (m) = Moles of solute / Mass of solvent (kg)

Step 1: Calculate the Moles of Solute

We know the mass of the solute is 20 g and its molecular weight is 100 g/mol. To find the number of moles, we use the formula:

Moles of solute = Mass of solute (g) / Molecular weight (g/mol)

Moles of solute = 20 g / 100 g/mol = 0.2 moles

Step 2: Determine the Mass of the Solvent

Next, we need to find out how much water (the solvent) is present in the solution. Since the solution is made up to one liter, we need to calculate the volume of the solute and then subtract that from the total volume to find the volume of the solvent.

Given the density of the solute is 2.0 g/cc, we can convert this to volume:

Volume of solute = Mass of solute / Density of solute

Volume of solute = 20 g / 2.0 g/cc = 10 cc (or 10 mL)

Since 1 liter = 1000 mL, the volume of the solvent (water) is:

Volume of solvent = Total volume - Volume of solute

Volume of solvent = 1000 mL - 10 mL = 990 mL

Now, we convert this volume into kilograms:

Mass of solvent = 990 mL × (1 g/mL) = 990 g = 0.990 kg

Step 3: Calculate the Molality

Now that we have both the moles of solute and the mass of the solvent, we can calculate the molality:

Molality (m) = Moles of solute / Mass of solvent (kg)

Molality (m) = 0.2 moles / 0.990 kg ≈ 0.2020

Final Answer

The molality of the solution is approximately 0.2020. Therefore, the correct answer is option a) 0.2020.

Approved