General Chemistry Study Notes: Colligative Properties, Chemical Kinetics, and Chemical Equilibrium

Chapter 14: Colligative Properties

Overview of Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles present, not their identity. These properties are crucial in understanding how solutes affect the behavior of solvents.

• Vapor Pressure Lowering: Described by Raoult's Law, which states that the vapor pressure of a solution is lower than that of the pure solvent.

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

• Freezing Point Lowering: The freezing point of a solution is lower than that of the pure solvent. The change is given by: $\Delta T_f = K_f m$ where $K_f$ is the cryoscopic constant and $m$ is the molality.

• Osmotic Pressure: The pressure required to stop osmosis, given by: $\Pi = MRT$ where $M$ is molarity, $R$ is the gas constant, and $T$ is temperature in Kelvin.

Calculating Molar Mass from Colligative Properties

Colligative properties can be used to determine the molar mass of an unknown solute by measuring changes in boiling point, freezing point, or osmotic pressure.

• Example: If a solute lowers the freezing point of water by a known amount, its molar mass can be calculated using the formula for freezing point depression.

Colligative Properties of Electrolyte Solutions

Electrolytes dissociate into ions, increasing the number of particles in solution and thus amplifying colligative effects. The van’t Hoff factor ($i$) accounts for this effect.

• van’t Hoff Factor ($i$): The number of particles into which a solute dissociates in solution.

• Modified Equations: For electrolytes, multiply $m$ by $i$ in colligative property equations.

• Example: NaCl dissociates into two ions, so $i = 2$.

Chapter 15: Chemical Kinetics

Chemical Reaction Rates

Chemical kinetics studies the speed of chemical reactions and the factors that affect them. The rate of a reaction is determined by measuring the change in concentration of reactants or products over time.

• Rate Expression: Derived from balanced chemical equations and experimental data.

• Example: For $A \rightarrow B$, rate = $-\frac{d[A]}{dt}$.

Factors Affecting Reaction Rates

• Concentration: Higher concentration usually increases reaction rate.

• Temperature: Higher temperature increases kinetic energy and reaction rate.

• Catalysts: Lower activation energy, increasing reaction rate.

• Surface Area: Greater surface area increases rate for heterogeneous reactions.

Differential and Integrated Rate Laws

• Differential Rate Law: Shows how rate depends on concentration.

• Integrated Rate Law: Relates concentration to time for zero, first, and second order reactions.

• Zero Order: $[A] = [A]_0 - kt$

• First Order: $\ln [A] = \ln [A]_0 - kt$

• Second Order: $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$

Half-Life and Rate Constants

• Half-Life ($t_{1/2}$): Time required for half the reactant to be consumed.

• First Order Half-Life: $t_{1/2} = \frac{0.693}{k}$

Arrhenius Equation

• Arrhenius Equation: Relates rate constant to temperature and activation energy. $k = A e^{-E_a/(RT)}$ where $A$ is the frequency factor, $E_a$ is activation energy, $R$ is the gas constant, and $T$ is temperature.

Reaction Mechanisms and Energy Diagrams

• Reaction Mechanism: Sequence of elementary steps that make up a reaction.

• Energy Diagram: Shows energy changes during a reaction, including activation energy and intermediates.

• Catalysts: Lower activation energy, providing an alternative pathway.

Chapter 16: Chemical Equilibrium

Equilibrium Expressions

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, and concentrations of reactants and products remain constant.

• Equilibrium Constant ($K$): For a general reaction $aA + bB \rightleftharpoons cC + dD$: $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Writing Equilibrium Expressions: Only include gases and aqueous species; solids and liquids are omitted.

Predicting Changes: Le Châtelier’s Principle

• Le Châtelier’s Principle: If a system at equilibrium is disturbed, it will shift to counteract the disturbance.

• Disturbances: Changes in concentration, pressure, or temperature.

• Example: Adding more reactant shifts equilibrium toward products.

Equilibrium Constants: $K_c$ and $K_p$

• $K_c$: Equilibrium constant in terms of concentration (mol/L).

• $K_p$: Equilibrium constant in terms of partial pressure (atm).

• Relationship: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.

Equilibrium for Solids and Liquids

• Solids and Liquids: Their concentrations are constant and not included in equilibrium expressions.

Calculating Equilibrium Constants from Experimental Data

• Experimental Measurement: Use measured concentrations at equilibrium to calculate $K$.

• Example: If at equilibrium, $[A] = 0.2$ M, $[B] = 0.3$ M, $[C] = 0.4$ M, then $K = \frac{[C]}{[A][B]}$.