41. A 13.0% solution of K2CO3 by mass has a density of 1.09 g/cm3. Calculate the molality of the solution.

1.08 m is the molality of the solution.

Explanation:

1st step: Determine the mass of solvent.

13% by mass means that 13 g are contained in 100 g of solution.

Solution mass = Solute mass + solvent mass

100 g = 13 g + Solvent mass

Solvent mass = 100 g - 13 g → 87 g

Second Step: Let's determine the moles of our solute mass (mass / molar mass)

13 g / 138.2 g/mol = 0.094 moles

Third step: Replace the data to determine molality.

Molality are the moles of solute in 1kg of solvent (mol/kg)

Before this, we must convert the solvent mass to kg

87 g. 1kg / 1000 g = 0.087 kg

molality → 0.094 mol / 0.087 kg = 1.08 m