Molality and Osmolality: Concentration Units in Solution Chemistry

Molality and Osmolality

Molality (m)

Molality is a concentration unit used in chemistry to express the amount of solute dissolved in a given mass of solvent. Unlike molarity, molality is independent of temperature because it is based on mass, not volume.

• Definition: Molality (m) is the number of moles of solute per kilogram of solvent.

• Formula:

$m = \frac{\text{mol solute}}{\text{kg solvent}}$

• Key Properties:

  • Temperature independent (mass does not change with temperature).

  • Useful for colligative property calculations (e.g., boiling point elevation, freezing point depression).

Example Calculation

Example: A solution contains 24.8 g of sucrose (C12H22O11) dissolved in 550.0 g of water. Calculate the molality of the solution.

• Step 1: Calculate moles of sucrose:

  • Molar mass of sucrose = 342.3 g/mol

  • Moles of sucrose = $\frac{24.8\ \text{g}}{342.3\ \text{g/mol}} = 0.07245\ \text{mol}$

• Step 2: Convert solvent mass to kg:

  • 550.0 g water = 0.550 kg

• Step 3: Calculate molality:

  • $m = \frac{0.07245\ \text{mol}}{0.550\ \text{kg}} = 0.132\ m$

Practice Problems

• Practice 1: A solution is prepared by dissolving 43.0 g potassium chlorate (KClO3) in enough water to make 100.0 mL of solution. If the density of the solution is 1.76 g/mL, what is the molality of KClO3 in the solution?

  • Answer: 2.64 m

• Practice 2: The density of a 15.7 M methanol (CH3OH) solution is 0.858 g/mL. If H2O is the solvent, what is the molality of the solution?

  • Answer: 31.2 m

Osmolality

Osmolality is a measure of the total number of dissolved particles (ions or molecules) in a solution per kilogram of solvent. It is especially important in biological and medical contexts.

• Definition: Osmolality is the number of osmoles (total dissolved particles) per kilogram of solvent.

• Formula:

$\text{Osmolality} = (\text{number of ions per formula unit}) \times m$

• Key Properties:

  • Accounts for dissociation of ionic compounds.

  • For covalent compounds, the number of particles is typically 1 (no dissociation).

Example Calculation

Example: What is the osmolality of total ions in an aqueous solution prepared by dissolving 0.400 moles of Pb(NO3)2 in 750.0 g water?

• Step 1: Calculate molality:

  • $m = \frac{0.400\ \text{mol}}{0.750\ \text{kg}} = 0.533\ m$

• Step 2: Count total ions per formula unit:

  • Pb(NO3)2 dissociates into 1 Pb2+ and 2 NO3- ions = 3 ions

• Step 3: Calculate osmolality:

  • $\text{Osmolality} = 3 \times 0.533\ m = 1.60\ m$

Practice Problems

• Practice: What is the ionic molality of sodium ions in a solution of 25.7 g NaNO3 dissolved in enough water to make a 150.0 mL solution? Density of the solution is 1.02 g/mL.

  • Answer: 2.57 m

Comparison Table: Molality vs. Osmolality

Property	Molality (m)	Osmolality
Definition	Moles of solute per kg solvent	Total number of dissolved particles per kg solvent
Formula	$m = \frac{\text{mol solute}}{\text{kg solvent}}$	$\text{Osmolality} = (\text{number of ions}) \times m$
Temperature Dependence	Independent	Independent
Application	Chemical calculations, colligative properties	Biological, medical, and chemical applications

Additional info: Osmolality is especially important in physiology and medicine, where the concentration of dissolved particles affects osmotic pressure and cell function.