General Chemistry II: Chemical Kinetics, Equilibrium, and Solutions – Exam Study Guide

Chemical Kinetics

Reaction Rates and Rate Laws

Chemical kinetics is the study of the speed at which chemical reactions occur and the factors that affect these rates.

• Reaction Rate: The change in concentration of a reactant or product per unit time, typically expressed as molarity per second (M/s).

• Rate Law: An equation that relates the reaction rate to the concentrations of reactants, often in the form $\text{rate} = k[A]^m[B]^n$ where $k$ is the rate constant and $m$, $n$ are the reaction orders.

• Order of Reaction: The power to which the concentration of a reactant is raised in the rate law. The overall order is the sum of the exponents.

• Determining Rate Laws: Experimentally, by measuring how the rate changes as reactant concentrations are varied.

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

Example: For a first-order reaction, $\text{rate} = k[A]$, the integrated rate law is $\ln[A]_t = -kt + \ln[A]_0$.

Reaction Mechanisms and Intermediates

Complex reactions may occur in multiple steps, each with its own rate law. The slowest step determines the overall rate (rate-determining step).

• Intermediate: A species formed in one step and consumed in another; does not appear in the overall reaction.

• Catalyst: A substance that increases the reaction rate without being consumed.

Example: For the mechanism: Step 1: $2NO_2 \rightarrow NO_3 + NO$ (slow) Step 2: $NO_3 + CO \rightarrow NO_2 + CO_2$ (fast) The overall reaction is $NO_2 + CO \rightarrow NO + CO_2$.

Activation Energy and Reaction Profiles

The activation energy ($E_a$) is the minimum energy required for a reaction to proceed. Reaction profiles show the energy changes during a reaction.

• Endothermic Reaction: Absorbs heat; products have higher energy than reactants.

• Exothermic Reaction: Releases heat; products have lower energy than reactants.

Equation: Arrhenius Equation: $k = Ae^{-E_a/RT}$

Chemical Equilibrium

Dynamic Equilibrium

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

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

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

Solutions and Colligative Properties

Concentration Units

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Molality (m): $m = \frac{\text{moles of solute}}{\text{kg of solvent}}$

• Parts per million (ppm): $\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$

Colligative Properties

Properties that depend on the number of solute particles, not their identity.

• Boiling Point Elevation: $\Delta T_b = iK_b m$

• Freezing Point Depression: $\Delta T_f = iK_f m$

• Vapor Pressure Lowering: $P_{solution} = X_{solvent} P^0_{solvent}$

• Osmotic Pressure: $\Pi = MRT$

Example: A solution of glucose in water lowers the freezing point; calculate using $\Delta T_f = iK_f m$.

Henry's Law

The solubility of a gas in a liquid is proportional to the pressure of the gas above the liquid.

• Equation: $C = kP$ where $C$ is the concentration, $k$ is Henry's law constant, and $P$ is the pressure.

Nuclear Chemistry

Radioactive Decay and Half-Life

Radioactive decay follows first-order kinetics. The half-life ($t_{1/2}$) is the time required for half of a radioactive sample to decay.

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

Thermochemistry

Enthalpy Changes

Thermochemistry deals with the heat changes in chemical reactions.

• Lattice Energy: The energy required to separate one mole of an ionic solid into gaseous ions.

• Heat of Solution: The enthalpy change when a solute dissolves in a solvent.

Tables

Sample Table: Initial Concentrations and Rates

Experiment #	[A] (M)	[B] (M)	Initial Rate (M/s)
1	0.100	0.100	0.020
2	0.200	0.100	0.040
3	0.100	0.200	0.040

Main Purpose: To determine the order of reaction with respect to each reactant by comparing how the rate changes as concentrations are varied.

Useful Equations

• $k = \frac{0.693}{t_{1/2}}$

• $\Delta T_f = iK_f m$

• $\Delta T_b = iK_b m$

• $\Pi = MRT$

• $P_{solution} = X_{solvent} P^0_{solvent}$

• $\ln[A]_t = -kt + \ln[A]_0$

• $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$

• $\Delta H_{solution} = \Delta H_{lattice} + \Delta H_{hydration}$

Additional info: This guide covers key concepts from chemical kinetics, equilibrium, solutions, thermochemistry, and nuclear chemistry, as reflected in the exam questions. It is suitable for students preparing for a General Chemistry II exam.