Final answer:
To calculate the molality of the solution, you need to find the number of moles of K₂CO₃ present in the solution and the mass of the solvent. The molality is found by dividing the moles of solute by the mass of the solvent in kilograms. For this question, the molality of the solution is 0.0865 mol/kg.
Step-by-step explanation:
To calculate the molality of the solution, we need to first find the number of moles of K₂CO₃ present in the solution. The given solution is 13.0% by mass, so for every 100g of solution, there are 13.0g of K₂CO₃. We can assume that the density of the solution is equal to that of water, which is 1.09 g/cm³. Therefore, the mass of 1000 cm³ of the solution (1 liter) is 1090g.
To find the number of moles of K₂CO₃, we can use its molar mass, which is 138.20 g/mol. The number of moles of K₂CO₃ in 13.0g is calculated as:
Moles of K₂CO₃ = mass / molar mass = 13.0g / 138.20 g/mol = 0.094 mol
Finally, we can calculate the molality of the solution by dividing the moles of solute (K₂CO₃) by the mass of the solvent (water) in kilograms. Since 1 liter of water weighs 1090g, or 1.09kg, the molality is:
Molality = moles of solute / mass of solvent (kg) = 0.094 mol / 1.09 kg = 0.0865 mol/kg