8.4 Colligative properties

Colligative properties are fascinating phenomena that occur in solutions, affecting their behavior based on solute concentration. These properties, including vapor pressure lowering and boiling point elevation, play a crucial role in understanding phase equilibria and diagrams.

In this section, we'll explore how solute particles influence a solution's properties, regardless of their chemical nature. We'll dive into calculating these effects and examine their real-world applications, from antifreeze to drug delivery systems.

Colligative properties and solute concentration

Defining colligative properties

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• Colligative properties are properties of solutions that depend on the concentration of solute particles, but not on the nature of the solute itself
• The four main colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure
• As the concentration of solute particles in a solution increases, the magnitude of the colligative properties also increases

Expressing solute concentration

• The concentration of solute particles is typically expressed in terms of molality (moles of solute per kilogram of solvent) or mole fraction
• Molality is a useful concentration unit for colligative properties because it is independent of temperature, unlike molarity (moles of solute per liter of solution)
• Mole fraction represents the ratio of moles of solute to the total moles of solute and solvent in the solution

Relationship between colligative properties and solute concentration

• Colligative properties arise from the reduced chemical potential of the solvent in the presence of solute particles, which affects the solvent's ability to undergo phase transitions or maintain osmotic equilibrium
• The presence of solute particles decreases the vapor pressure, elevates the boiling point, depresses the freezing point, and creates osmotic pressure in the solution
• The magnitude of these effects is directly proportional to the concentration of solute particles, regardless of their chemical identity

Calculating colligative properties

Vapor pressure lowering

• Raoult's law states that the vapor pressure of a solution (P1) is equal to the vapor pressure of the pure solvent (P1°) multiplied by the mole fraction of the solvent (X1)
• The vapor pressure lowering (ΔP) is the difference between the vapor pressure of the pure solvent and the solution: ΔP = P1° - P1 = P1°(1 - X1)
• Example: If a solution has a solvent mole fraction of 0.9 and the vapor pressure of the pure solvent is 50 mmHg, the vapor pressure of the solution would be 45 mmHg (50 × 0.9), and the vapor pressure lowering would be 5 mmHg (50 - 45)

Boiling point elevation and freezing point depression

• The boiling point elevation (ΔTb) is calculated using the equation ΔTb = Kb × m × i, where Kb is the molal boiling point elevation constant (specific to the solvent), m is the molality of the solution, and i is the van 't Hoff factor
• The freezing point depression (ΔTf) is calculated using the equation ΔTf = Kf × m × i, where Kf is the molal freezing point depression constant (specific to the solvent), m is the molality of the solution, and i is the van 't Hoff factor
• Example: If a solution has a molality of 0.5 m and the solvent has a Kb of 0.52 °C·kg/mol and a van 't Hoff factor of 1, the boiling point elevation would be 0.26 °C (0.52 × 0.5 × 1)

Osmotic pressure

• The osmotic pressure (π) of a solution is calculated using the equation π = MRT, where M is the molarity of the solution, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the absolute temperature in Kelvin
• Example: If a solution has a molarity of 0.1 M and the temperature is 298 K, the osmotic pressure would be 2.44 atm (0.1 × 0.0821 × 298)

Applications of colligative properties

Antifreeze

• The addition of solutes such as ethylene glycol to water lowers the freezing point of the solution, allowing it to remain liquid at temperatures below 0°C
• This property is utilized in automotive antifreeze to prevent engine coolant from freezing in cold weather
• Example: A 50/50 mixture of ethylene glycol and water has a freezing point of approximately -37 °C, making it suitable for use in most winter conditions

Desalination

• Reverse osmosis is a process that uses a semi-permeable membrane to remove solutes (such as salt ions) from water
• By applying pressure greater than the osmotic pressure of the solution, pure water is forced through the membrane, leaving behind the solutes
• This technique is used in desalination plants to produce potable water from seawater or brackish water
• Example: The osmotic pressure of seawater (3.5% salt) is approximately 27 atm. To desalinate seawater using reverse osmosis, a pressure greater than 27 atm must be applied to the seawater side of the membrane

Osmotic drug delivery

• Osmotic pumps are used in controlled-release drug delivery systems
• The pump consists of a semi-permeable membrane containing a drug solution. As water flows into the pump due to osmosis, the drug solution is slowly released through a small orifice at a controlled rate, providing a constant and prolonged drug delivery
• Example: The OROS (Osmotic-controlled Release Oral delivery System) technology is used in various medications, such as Concerta (methylphenidate) for ADHD treatment, to provide a consistent drug release over an extended period

Solute properties and colligative properties

Molecular weight

• Colligative properties depend on the concentration of solute particles, not their identity. Therefore, solutes with lower molecular weights will have a greater effect on colligative properties at the same mass concentration, as they contribute more particles per unit mass
• Example: A 1 molal solution of glucose (MW = 180 g/mol) will have a greater effect on colligative properties than a 1 molal solution of sucrose (MW = 342 g/mol) because glucose produces more particles per unit mass

Van 't Hoff factor (i)

• The van 't Hoff factor accounts for the dissociation of ionic compounds or the association of solute molecules in solution. It represents the ratio of the actual concentration of particles in solution to the concentration of the solute
• For non-electrolytes, i = 1, as these solutes do not dissociate in solution
• For electrolytes that completely dissociate, i equals the number of ions produced per formula unit. For example, NaCl has i = 2, while CaCl2 has i = 3
• For electrolytes that partially dissociate or solutes that associate in solution, i can be a non-integer value between 1 and the number of ions per formula unit
• The magnitude of colligative properties is directly proportional to the van 't Hoff factor, as a higher i value indicates a greater concentration of solute particles in solution
• Example: A 1 molal solution of NaCl will have approximately twice the effect on colligative properties as a 1 molal solution of glucose because NaCl dissociates into two ions (i ≈ 2), while glucose does not dissociate (i = 1)

Osmosis and osmotic pressure

Concept of osmosis

• Osmosis is the net movement of solvent molecules across a semi-permeable membrane from a region of high solvent concentration (low solute concentration) to a region of low solvent concentration (high solute concentration)
• The driving force for osmosis is the difference in chemical potential of the solvent across the membrane, which is related to the concentration difference of the solute
• Example: When a cell is placed in a hypotonic solution (lower solute concentration than the cell's cytoplasm), water will move into the cell through osmosis, causing the cell to swell and potentially burst

Osmotic pressure

• Osmotic pressure is the pressure that must be applied to the solution side of the membrane to prevent the net flow of solvent molecules across the membrane
• The osmotic pressure of a solution is a colligative property, as it depends on the concentration of solute particles and not their identity
• In a system with two solutions separated by a semi-permeable membrane, osmosis will occur until the osmotic pressures on both sides of the membrane are equal, at which point the system reaches osmotic equilibrium
• Example: When a cell is placed in an isotonic solution (equal solute concentration to the cell's cytoplasm), no net movement of water occurs because the osmotic pressure is balanced on both sides of the cell membrane

Relationship between osmosis and osmotic pressure

• The osmotic pressure of a solution is a measure of the solution's tendency to draw in water through osmosis
• Higher osmotic pressures indicate a greater driving force for osmosis and a higher solute concentration in the solution
• Example: In a hypertonic solution (higher solute concentration than the cell's cytoplasm), the osmotic pressure of the solution is greater than that of the cell, causing water to move out of the cell through osmosis, leading to cell shrinkage (crenation)