General Chemistry Study Guide: Chemical Kinetics, Chemical Equilibrium, and Acids & Bases (Chapters 15–17)

Chapter 15: Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the rates at which chemical reactions occur and the factors that affect these rates. Understanding kinetics allows chemists to control reactions and optimize conditions for desired outcomes.

• Reaction Rate: The change in concentration of a reactant or product per unit time.

• Factors Affecting Rate: Concentration, temperature, surface area, catalysts, and the nature of reactants.

• Example: Increasing temperature generally increases reaction rate due to higher kinetic energy of molecules.

Expressing and Calculating Reaction Rates

• Average Rate: Calculated over a time interval using initial and final concentrations.

• Instantaneous Rate: The rate at a specific moment, determined from the slope of a concentration vs. time graph.

• Rate Law: An equation that relates the rate of a reaction to the concentration of reactants, typically in the form $\text{rate} = k[A]^m[B]^n$.

• Rate Constant (k): A proportionality constant specific to a reaction at a given temperature; units depend on the overall reaction order.

• Example: For a first-order reaction, $\text{rate} = k[A]$.

Determining Rate Laws and Rate Constants

• Experimental Determination: Rate laws are determined by measuring how the rate changes as reactant concentrations change.

• Calculating k: Use experimental data and the rate law to solve for the rate constant.

Integrated Rate Laws

Integrated rate laws relate concentrations of reactants to time for different reaction orders.

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

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

• Zero-Order: $[A]_t - [A]_0 = -kt$

• Applications:

  • Find concentration at any time.

  • Calculate time for a given fraction to react.

  • Determine time to reach a certain concentration.

Half-Life and Reaction Order

• Half-Life (t1/2): Time required for half the reactant to be consumed.

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

• Relationship: For first-order reactions, half-life is independent of initial concentration.

Activation Energy and Temperature Dependence

• Activation Energy (Ea): Minimum energy required for a reaction to occur.

• Arrhenius Equation: $k = A e^{-E_a/(RT)}$

• Temperature Effect: Higher temperature increases k, thus increasing rate.

Reaction Mechanisms and Molecularity

• Elementary Step: A single step in a reaction mechanism.

• Rate-Determining Step: The slowest step, which controls the overall rate.

• Intermediate: A species produced and consumed during the mechanism.

• Collision Model: Reactions occur when molecules collide with sufficient energy and proper orientation.

Catalysis

• Catalyst: Substance that increases reaction rate without being consumed.

• Homogeneous Catalyst: Catalyst in the same phase as reactants.

• Heterogeneous Catalyst: Catalyst in a different phase than reactants.

• Recognition: Catalysts appear in the mechanism but not in the overall reaction equation.

Chapter 16: Chemical Equilibrium

Introduction to Chemical Equilibrium

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

• Dynamic Equilibrium: Both forward and reverse reactions continue at equal rates.

Equilibrium Expressions

• Equilibrium Constant (K): Ratio of product concentrations to reactant concentrations, each raised to the power of their coefficients.

• For Concentrations (Kc): $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• For Partial Pressures (Kp): $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$

• Heterogeneous Equilibria: Pure solids and liquids are omitted from the equilibrium expression.

Calculating and Interpreting Equilibrium Constants

• Evaluating K: Use equilibrium concentrations or pressures to calculate K.

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

• Magnitude of K: Large K means products favored; small K means reactants favored.

Reaction Quotient (Q) and Predicting Direction

• Reaction Quotient (Q): Calculated like K but with initial concentrations.

• Comparing Q and K:

  • If Q < K, reaction proceeds forward.

  • If Q > K, reaction proceeds in reverse.

  • If Q = K, system is at equilibrium.

Le Chatelier’s Principle

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

• Factors: Changes in concentration, pressure, volume, or temperature.

• Example: Increasing reactant concentration shifts equilibrium toward products.

Effect of Catalysts on Equilibrium

• Catalyst: Speeds up attainment of equilibrium but does not affect the position of equilibrium or the value of K.

Chapter 17: Acids and Bases

Properties and Definitions

• Acidic Solutions: Taste sour, turn litmus red, conduct electricity; contain excess H+ (or H3O+).

• Basic Solutions: Taste bitter, feel slippery, turn litmus blue; contain excess OH-.

Bronsted-Lowry Theory

• Bronsted-Lowry Acid: Proton (H+) donor.

• Bronsted-Lowry Base: Proton acceptor.

• Conjugate Acid-Base Pairs: Two species that differ by one proton.

• Example: In $\mathrm{NH_3} + \mathrm{H_2O} \rightleftharpoons \mathrm{NH_4^+} + \mathrm{OH^-}$, NH3 is the base, NH4+ is its conjugate acid.

Autoionization of Water and pH

• Autoionization: $2\mathrm{H_2O} \rightleftharpoons \mathrm{H_3O^+} + \mathrm{OH^-}$

• Ion-Product Constant: $K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}$ at 25°C

• pH Definition: $\mathrm{pH} = -\log[\mathrm{H^+}]$

• pOH: $\mathrm{pOH} = -\log[\mathrm{OH^-}]$

• Relationship: $\mathrm{pH} + \mathrm{pOH} = 14$

Strong and Weak Acids/Bases

• Strong Acids: Completely ionize in water (e.g., HCl, HNO3, H2SO4).

• Strong Bases: Completely ionize (e.g., NaOH, KOH).

• Weak Acids/Bases: Partially ionize; characterized by equilibrium constants Ka (acid) and Kb (base).

• Calculating pH: For strong acids/bases, use initial concentration; for weak, use ICE tables and Ka or Kb.

Calculations Involving Acids and Bases

• Finding pH from [H+]: $\mathrm{pH} = -\log[\mathrm{H^+}]$

• Finding [H+] from pH: $[\mathrm{H^+}] = 10^{-\mathrm{pH}}$

• Percent Ionization: $\text{Percent Ionization} = \frac{[\mathrm{H^+}]_{eq}}{[\text{Acid}]_{initial}} \times 100\%$

• Relationship between Ka and Kb: $K_a \times K_b = K_w$

Polyprotic Acids

• Definition: Acids that can donate more than one proton (e.g., H2SO4).

• Successive Ionizations: Each step has its own Ka, with Ka1 > Ka2.

Acid-Base Properties of Salts

• Salt Solutions: May be acidic, basic, or neutral depending on the ions produced upon dissolution.

• Prediction: Analyze the parent acid and base to determine the nature of the solution.

Acid Strength and Molecular Structure

• Bond Polarity: More polar H–X bonds favor acidity.

• Bond Strength: Weaker H–X bonds favor acidity.

Lewis Acid-Base Theory

• Lewis Acid: Electron pair acceptor.

• Lewis Base: Electron pair donor.

• Example: BF3 (acid) + NH3 (base) → F3B–NH3

Table: Comparison of Acid-Base Theories

Theory	Acid	Base
Arrhenius	Produces H+ in water	Produces OH- in water
Bronsted-Lowry	Proton donor	Proton acceptor
Lewis	Electron pair acceptor	Electron pair donor

Additional info: For all calculations, use ICE (Initial, Change, Equilibrium) tables for weak acids/bases, and remember to check assumptions for small x in equilibrium problems. For kinetics, always check units of k and ensure correct application of integrated rate laws for the reaction order.