Askiitians Tutor Team
Last Activity: 5 Days ago
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.