Understanding Molarity and Molality: Conversion Examples

In this guide, we will explore the concepts of molarity and molality, and learn how to convert between these two important concentration units. By the end, you'll have a clear understanding of how to perform these conversions with practical examples.
By Jamie

Molarity (M) and molality (m) are two key concepts in chemistry used to express the concentration of solutions. While both measure how much solute is present, they do so in different ways:

  • Molarity (M): Moles of solute per liter of solution.
  • Molality (m): Moles of solute per kilogram of solvent.

Converting between molarity and molality requires knowledge of the solution’s density and temperature, as these factors can affect the measurements. Below are clear examples to help you understand this process.

Example 1: Converting Molarity to Molality

Problem:

A solution has a molarity of 2.0 M NaCl (sodium chloride) and a density of 1.05 g/mL. What is its molality?

Solution:

  1. Calculate the mass of the solution:

    • Molarity (M) = 2.0 moles/L
    • Volume of 1 L solution = 1000 mL
    • Mass of the solution = Density × Volume
    • Mass = 1.05 g/mL × 1000 mL = 1050 g

  2. Calculate moles of solute (NaCl):

    • Molar mass of NaCl = 58.44 g/mol
    • Moles = 2.0 moles

  3. Calculate mass of solute:

    • Mass of NaCl = Moles × Molar mass
    • Mass = 2.0 moles × 58.44 g/mol = 116.88 g

  4. Calculate mass of solvent (water):

    • Mass of solvent = Mass of solution - Mass of solute
    • Mass = 1050 g - 116.88 g = 933.12 g = 0.93312 kg

  5. Calculate molality (m):

    • Molality = Moles of solute / Mass of solvent (kg)
    • Molality = 2.0 moles / 0.93312 kg = 2.14 m

Result: The molality of the solution is approximately 2.14 m.

Example 2: Converting Molality to Molarity

Problem:

A solution has a molality of 3.0 m and a density of 1.20 g/mL. What is its molarity?

Solution:

  1. Calculate the mass of solvent:

    • Assume 1 kg of solvent for ease of calculation.

  2. Calculate moles of solute:

    • Moles = Molality × Mass of solvent (kg)
    • Moles = 3.0 m × 1.0 kg = 3.0 moles

  3. Calculate the total mass of the solution:

    • Mass of the solute (assuming NaCl) = 3.0 moles × 58.44 g/mol = 175.32 g
    • Mass of the solution = Mass of solvent + Mass of solute
    • Mass = 1000 g + 175.32 g = 1175.32 g

  4. Convert mass of solution to volume:

    • Volume = Mass / Density
    • Volume = 1175.32 g / 1.20 g/mL = 979.43 mL = 0.97943 L

  5. Calculate molarity (M):

    • Molarity = Moles of solute / Volume of solution (L)
    • Molarity = 3.0 moles / 0.97943 L = 3.06 M

Result: The molarity of the solution is approximately 3.06 M.

Conclusion

Converting between molarity and molality involves understanding the relationship between the mass of solute, the mass of the solvent, and the volume of the solution. By using the examples above, you should now have a better grasp of how to perform these conversions effectively.