Solutions and Colligative Properties (General Chemistry Chapter 14, Part 2)

Solutions: Concentration Units and Colligative Properties

Concentration Units

Understanding how to express the concentration of solutions is fundamental in chemistry. Several units are used, each with specific applications and advantages.

• Molarity (M): Defined as the number of moles of solute per liter of solution. Formula: $M = \frac{\text{moles of solute}}{\text{volume of solution in L}}$ Key Points:

  • Solute must be added before filling the flask to the mark to ensure accurate concentration.

  • Molarity is temperature-dependent because solution volume changes with temperature.

  • Standard solutions are often labeled with their preparation temperature (e.g., 25°C).

• Molality (m): Defined as the number of moles of solute per kilogram of solvent. Formula: $m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$ Key Points:

  • Molality is temperature-independent, making it useful for studies involving temperature changes.

• Mole Fraction (x): The ratio of moles of a component to the total moles in the solution. Formula: $x_A = \frac{\text{moles of component A}}{\text{total moles in solution}}$

• Parts by Mass (ppm, ppb): Used for very dilute solutions. Formula: $\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$ $\text{ppb} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9$

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles, not their chemical identity.

• Definition: Properties that depend only on the quantity of particles in solution.

• Examples: Vapor pressure lowering, boiling point elevation, freezing point depression, osmotic pressure.

Vapor Pressure and Raoult's Law

Adding a solute to a solvent affects the vapor pressure of the solution.

• Vapor Pressure: The pressure exerted by a vapor in equilibrium with its solid or liquid phase.

• Vapor Pressure of Solution ($P_{\text{soln}}$): The pressure of the solvent in the vapor phase when equilibrium is reached.

• Raoult's Law: Describes the vapor pressure of an ideal solution. Formula: $P_{\text{soln}} = X_{\text{solvent}} P^\circ_{\text{solvent}}$ where $P^\circ_{\text{solvent}}$ is the vapor pressure of the pure solvent and $X_{\text{solvent}}$ is its mole fraction in the solution.

Boiling Point Elevation and Freezing Point Depression

Adding a solute to a solvent changes its boiling and freezing points.

• Boiling Point Elevation: The boiling point of a solution is higher than that of the pure solvent. Formula: $\Delta T_b = m K_b$ where $m$ is molality and $K_b$ is the ebullioscopic constant.

• Freezing Point Depression: The freezing point of a solution is lower than that of the pure solvent. Formula: $\Delta T_f = m K_f$ where $K_f$ is the cryoscopic constant.

Osmosis and Osmotic Pressure

Osmosis is the movement of solvent molecules through a semipermeable membrane from a region of lower solute concentration to higher concentration.

• Osmotic Pressure ($\Pi$): The pressure required to stop osmosis. Formula: $\Pi = MRT$ where $M$ is molarity, $R$ is the ideal gas constant ($8.3145\ \text{J}\ \text{K}^{-1}\ \text{mol}^{-1}$ or $0.08206\ \text{L atm}\ \text{K}^{-1}\ \text{mol}^{-1}$), and $T$ is temperature in Kelvin.

van't Hoff Factor, i

The van't Hoff factor ($i$) accounts for the number of particles produced when a solute dissolves, especially for ionic compounds.

• For ionic solutes: $i$ is the number of ions formed per formula unit.

• Example: $\text{NaCl}_{(aq)} \rightarrow \text{Na}^+_{(aq)} + \text{Cl}^-_{(aq)}$, so $i \approx 2$.

• Adjusted Formulas: $\Delta T_f = imK_f$ $\Delta T_b = imK_b$ Note: Due to ion pairing, the measured $i$ may be slightly less than the theoretical value.

Key Terminology

• Colligative property

• Raoult's law

• Vapor pressure lowering

• Ideal solution

• Freezing point depression

• Boiling point elevation

• Osmosis

• Semipermeable membrane

• Osmotic pressure

• van't Hoff factor, i

• Colloid

• Colloidal dispersion

• Tyndall effect

Example Table: Comparison of Concentration Units

Unit	Definition	Temperature Dependence	Typical Use
Molarity (M)	mol solute / L solution	Dependent	General laboratory solutions
Molality (m)	mol solute / kg solvent	Independent	Colligative property calculations
Mole Fraction (x)	mol component / total mol	Independent	Vapor pressure, Raoult's law
ppm, ppb	mass solute / mass solution × 106 or 109	Independent	Trace analysis

Example Application

• Calculating boiling point elevation: A solution is prepared by dissolving 1 mol of NaCl in 1 kg of water. The boiling point elevation is calculated using $\Delta T_b = imK_b$, where $i = 2$ for NaCl.

• Osmotic pressure in biological systems: Red blood cells in hypertonic solutions shrink due to water loss, while in hypotonic solutions they swell and may burst.

Additional info: These notes cover the essential concepts from General Chemistry Chapter 14, focusing on solution concentration units and colligative properties, as well as their practical and theoretical implications.