Premed · Premed · General Chemistry 1
Lecture 20: Colligative Properties
General Chemistry I
Learning Objectives
By the end of this lecture, students will be able to:
- Define colligative properties and explain why they depend on solute concentration but not solute identity
- Calculate vapor pressure lowering using Raoult's law
- Calculate boiling point elevation and freezing point depression
- Calculate osmotic pressure and explain osmosis
- Apply the van't Hoff factor to account for electrolyte dissociation
- Determine molar mass of a solute from colligative property measurements
Lecture Content
I. What Are Colligative Properties?
Colligative properties are physical properties of solutions that depend on the number of dissolved solute particles but not on their chemical identity. They apply to dilute solutions containing nonvolatile solutes (unless otherwise specified). The four colligative properties are vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. The underlying reason these properties depend only on particle count is that solute particles interfere with the solvent molecules' ability to escape into the gas phase, organize into a crystalline solid, or equalize concentration across a semipermeable membrane.
II. Vapor Pressure Lowering (Raoult's Law)
Adding a nonvolatile solute to a solvent lowers the vapor pressure of the solvent. This relationship is quantified by Raoult's Law: P_solvent = chi_solvent x P_solvent^0, where P_solvent is the vapor pressure above the solution, chi_solvent is the mole fraction of the solvent, and P_solvent^0 is the vapor pressure of the pure solvent. Since chi_solvent is always less than 1 when a solute is present, the solution's vapor pressure is always lower than that of the pure solvent. The magnitude of the lowering is given by delta_P = P_solvent^0 - P_solvent = chi_solute x P_solvent^0. Physically, solute molecules occupy positions at the liquid surface, reducing the number of solvent molecules that can escape into the gas phase.
For solutions containing two volatile components (where both solute and solvent can evaporate), the total vapor pressure is the sum of each component's contribution: P_total = chi_A x P_A^0 + chi_B x P_B^0. This relationship holds for ideal solutions that obey Raoult's law.
III. Boiling Point Elevation
Because a solute lowers the vapor pressure, a higher temperature is required for the solution's vapor pressure to reach atmospheric pressure. Consequently, the boiling point of a solution is higher than that of the pure solvent. The magnitude of this increase is given by delta_T_b = K_b x m x i, where delta_T_b is the boiling point elevation, K_b is the molal boiling point elevation constant (a property of the solvent; for water, K_b = 0.512 C/m), m is the molality of the solution, and i is the van't Hoff factor (the number of particles the solute dissociates into). The new boiling point is T_b = T_b^0 + delta_T_b.
IV. Freezing Point Depression
The freezing point of a solution is lower than that of the pure solvent because solute particles disrupt the formation of the ordered solid lattice, requiring a lower temperature to achieve freezing. The relationship is delta_T_f = K_f x m x i, where delta_T_f is the freezing point depression (defined as a positive value: T_f,pure - T_f,solution), K_f is the molal freezing point depression constant (for water, K_f = 1.86 C/m), m is the molality, and i is the van't Hoff factor. The new freezing point is T_f = T_f^0 - delta_T_f.
Freezing point depression has many practical applications. Road salt (NaCl or CaCl2) lowers the freezing point of water on roads and sidewalks. Antifreeze (ethylene glycol) in automobile radiators prevents the coolant from freezing in winter while also raising its boiling point in summer. And adding salt to an ice bath lowers its temperature, which is essential for making ice cream.
<image>A phase diagram overlay showing how a nonvolatile solute affects the phase boundaries of water. The original pure water phase diagram is shown with solid lines (vapor pressure curve, freezing/melting line). The solution phase diagram is overlaid with dashed lines. Key differences highlighted: (1) The vapor pressure curve of the solution is lower than that of pure water at every temperature (labeled "Vapor pressure lowering"). (2) The intersection of the solution vapor pressure curve with the 1 atm line occurs at a higher temperature (labeled "Boiling point elevation, delta_T_b"). (3) The freezing point of the solution is shifted to a lower temperature (labeled "Freezing point depression, delta_T_f"). The triple point of the solution is also shifted to lower T and lower P. Numerical values for water's K_b and K_f are noted.</image>
V. The van't Hoff Factor (i)
The van't Hoff factor accounts for the fact that some solutes dissociate into multiple particles in solution. For nonelectrolytes that do not dissociate (such as glucose, sucrose, ethylene glycol, and urea), i = 1. For strong electrolytes that dissociate completely, the theoretical van't Hoff factor equals the number of ions produced: NaCl yields Na+ and Cl- (i = 2), CaCl2 yields Ca^2+ and 2 Cl- (i = 3), and FeCl3 yields Fe^3+ and 3 Cl- (i = 4).
In practice, measured i values for electrolytes are slightly less than the theoretical values because of ion pairing -- the transient association of a cation and anion in solution that effectively reduces the particle count. For NaCl, the theoretical i is 2, but the measured value in dilute solution is approximately 1.87. More concentrated solutions exhibit more ion pairing and consequently lower effective i values. For routine calculations involving dilute solutions, the theoretical i value is typically used.
VI. Osmotic Pressure
Osmosis is the net flow of solvent molecules through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. The membrane permits solvent passage but blocks solute particles. Osmotic pressure (pi) is the pressure that must be applied to the solution side to halt osmosis, given by pi = iMRT, where i is the van't Hoff factor, M is the molarity, R = 0.08206 Latm/(molK), and T is the temperature in Kelvin.
Osmotic pressure is remarkably large even for dilute solutions, making it the most sensitive of the colligative properties. A 0.10 M NaCl solution, for example, exerts an osmotic pressure of approximately 4.9 atm. Applications are widespread: in cell biology, osmotic pressure governs the behavior of cells in different solution environments; in water purification, reverse osmosis applies pressure exceeding pi to force water through a membrane while retaining dissolved solutes; and in medicine, intravenous fluids must be isotonic with blood (approximately 0.9% NaCl, or about 0.30 osmol/L) to prevent damage to blood cells.
VII. Tonicity and Biological Applications
An isotonic solution has the same osmotic pressure as the cell interior, so there is no net water movement and the cell maintains its normal volume. Normal saline (0.9% NaCl) and 5% dextrose are isotonic with human blood. A hypotonic solution has lower osmotic pressure than the cell interior, causing water to flow into the cell. The cell swells and may burst (lyse); placing red blood cells in pure water causes hemolysis. A hypertonic solution has higher osmotic pressure than the cell interior, drawing water out of the cell and causing it to shrink (crenation). Concentrated salt solutions cause crenation of red blood cells.
<image>A three-panel diagram showing the effect of solution tonicity on red blood cells. Panel A (Isotonic -- 0.9% NaCl): a red blood cell with its normal biconcave disc shape; arrows show equal water flow in and out. Label: "No net water movement." Panel B (Hypotonic -- 0.2% NaCl): a swollen, spherical red blood cell; larger arrows point inward showing net water entry. Label: "Water enters cell; cell swells (may lyse)." Panel C (Hypertonic -- 3% NaCl): a shrunken, spiky (crenated) red blood cell; larger arrows point outward showing net water loss. Label: "Water leaves cell; cell shrinks (crenation)." Below all three panels, beakers are shown with the relative solute concentrations inside and outside each cell indicated by dot density.</image>
VIII. Determining Molar Mass from Colligative Properties
Colligative properties provide a practical method for determining the molar mass of an unknown solute. From freezing point depression, measure delta_T_f, calculate the molality as m = delta_T_f / (K_f x i), use molality and the mass of solvent to find moles of solute, and finally divide the mass of solute by its moles to obtain the molar mass. Osmotic pressure measurements offer even greater sensitivity, making them ideal for large molecules such as proteins and polymers. From osmotic pressure, calculate molarity as M = pi / (iRT), use molarity and solution volume to find moles, and then determine molar mass from mass and moles.
IX. Ideal vs. Nonideal Solutions
An ideal solution obeys Raoult's law exactly, with delta_H_soln = 0 and no volume change upon mixing. This occurs when solute-solvent interactions are essentially identical in strength to the solute-solute and solvent-solvent interactions being replaced. A mixture of benzene and toluene, which are structurally very similar, approximates ideal behavior.
Real solutions often deviate from Raoult's law. Positive deviation occurs when solute-solvent interactions are weaker than the pure-component interactions. The vapor pressure is higher than Raoult's law predicts, and dissolution is endothermic (delta_H_soln > 0). Ethanol mixed with hexane is an example. Negative deviation occurs when solute-solvent interactions are stronger than the pure-component interactions. The vapor pressure is lower than predicted, and dissolution is exothermic (delta_H_soln < 0). Acetone mixed with chloroform exemplifies this, as a favorable dipole-dipole interaction forms between the C=O group of acetone and the H-CCl3 group of chloroform.
X. Colloids
A colloid is a mixture with particle sizes intermediate between a true solution and a suspension, typically in the range of 1 to 1000 nm. Colloidal particles are large enough to scatter light, producing the Tyndall effect (the visible beam of light through fog or dust), but small enough to remain suspended indefinitely without settling. Common types include aerosols (fog), emulsions (milk), sols (paint), and gels (gelatin). Colloids are stabilized by surface charges or surfactants that prevent the particles from aggregating. They are biologically significant: blood is a colloid, and cell membranes involve colloidal-scale structures.
