An aqueous KNO₃ solution is made using 72.5 g of KNO₃ diluted to a total solution volume of 2.00 L. Calculate the molality of the solution. (Assume a density of 1.05 g/mL for the solution.)

Verified step by step guidance

1. Step 1: Convert the mass of KNO3 to moles. The molar mass of KNO3 is approximately 101.1 g/mol. So, the number of moles of KNO3 can be calculated by dividing the given mass of KNO3 by its molar mass.
2. Step 2: Convert the volume of the solution to kilograms. Since the density of the solution is given as 1.05 g/mL, you can first convert the volume of the solution from liters to milliliters, and then multiply by the density to find the mass in grams. Finally, convert the mass from grams to kilograms by dividing by 1000.
3. Step 3: Calculate the molality of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solute is KNO3 and the solvent is water. So, the molality can be calculated by dividing the number of moles of KNO3 by the mass of the water in kilograms.
4. Step 4: Remember that the volume of the solution is not the same as the volume of the solvent. In this case, the volume of the solution is given, but the volume of the solvent (water) is not. However, because the solution is dilute, we can assume that the volume of the water is approximately equal to the total volume of the solution.
5. Step 5: Finally, express your answer in the appropriate units. Molality is typically expressed in moles per kilogram (mol/kg).

Key Concepts

Molarity and Molality

Molarity (M) is defined as the number of moles of solute per liter of solution, while molality (m) is the number of moles of solute per kilogram of solvent. Understanding the difference between these two concentration units is crucial for solving problems involving solutions, especially when the volume and mass of the solvent are involved.

Calculating Moles from Mass

To find the number of moles of a substance, you can use the formula: moles = mass (g) / molar mass (g/mol). For KNO3, the molar mass is approximately 101.1 g/mol. This calculation is essential for determining the concentration of the solution in terms of molality.

Density and Volume Relationships

Density is defined as mass per unit volume (g/mL or g/cm³). In this problem, the density of the solution is given as 1.05 g/mL, which allows us to convert the total volume of the solution into mass. This conversion is necessary to calculate the mass of the solvent, which is required for determining molality.