Provided Equations and Constants

Essential Equations for General Chemistry

This section lists fundamental equations and constants commonly used in General Chemistry, including thermodynamics, kinetics, equilibrium, and electrochemistry.

• Clausius-Clapeyron Equation:

• Gibbs Free Energy:

• Arrhenius Equation:

• Equilibrium Constant: (for balanced reaction)

• Henderson-Hasselbalch Equation:

• Nernst Equation:

• First Law of Thermodynamics:

• Rate Law (General):

• Zero, First, Second Order Integrated Rate Laws:

  • Zero:

  • First:

  • Second:

Additional info: These equations are foundational for solving quantitative chemistry problems involving gases, solutions, kinetics, equilibrium, and thermodynamics.

Intermolecular Forces

Types and Identification of Intermolecular Forces

• Dispersion (London) Forces: Present in all molecules, especially nonpolar ones (e.g., CH4).

• Dipole-Dipole Forces: Occur between polar molecules (e.g., HCl, NH3).

• Hydrogen Bonding: Strong dipole-dipole interaction when H is bonded to N, O, or F (e.g., H2O, NH3).

• Ion-Ion Forces: Occur between ionic compounds (e.g., NaNO3).

Example: H2O exhibits hydrogen bonding, making it have higher boiling point than similar-sized molecules.

Phase Transitions

Understanding Phase Diagrams and Transitions

• Phase Diagram: Graphical representation of pressure (P) vs. temperature (T) showing regions of solid, liquid, and gas.

• Phase Transition: Change from one state of matter to another (e.g., melting, boiling, sublimation).

• Key Points: Moving from one region to another (e.g., A to C) corresponds to a specific phase change.

Example: Moving from solid to gas directly is called sublimation.

Colligative Properties

Boiling Point Elevation and Freezing Point Depression

• Colligative Properties: Depend on the number of solute particles, not their identity.

• Boiling Point Elevation:

• Freezing Point Depression:

• Van't Hoff Factor (i): Number of particles the solute dissociates into.

Example: 1.0 m NaCl (i = 2) will have a higher boiling point than 0.5 m KCl (i = 2), but the lowest boiling point will be the solution with the fewest particles.

Kinetics – Rate Laws

Writing Rate Laws for Elementary Reactions

• Elementary Reaction: Rate law can be written directly from the stoichiometry.

• General Form: For products,

Example: For ,

Kinetics – Mechanisms

Reaction Mechanisms and Rate-Determining Step

• Mechanism: Sequence of elementary steps that make up the overall reaction.

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

• Writing Rate Law: Express in terms of initial reactants; intermediates must be substituted out using pre-equilibrium or steady-state approximation.

Example: For a mechanism with a slow step involving CHCl3 and Cl, the rate law is .

Kinetics – Reaction Barriers

Energy Profiles and Activation Energy

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

• Reaction Coordinate Diagram: Shows energy changes during a reaction; catalyzed reactions have lower .

• Exothermic vs. Endothermic: Exothermic reactions release energy; endothermic absorb energy.

Example: The solid curve in an energy diagram is typically the uncatalyzed reaction; the dashed curve is the catalyzed reaction.

Equilibrium Constant Expressions

Writing and Expressions

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

• General Form: For ,

Example: For ,

Le Chatelier's Principle

Predicting Shifts in Equilibrium

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

• Factors Affecting Equilibrium: Concentration, pressure/volume, temperature, and catalysts.

• Endothermic vs. Exothermic: Increasing temperature favors endothermic direction; decreasing favors exothermic.

Example: Adding more reactant shifts equilibrium to the right (toward products).

Bronsted-Lowry Acids and Bases

Identifying Conjugate Acid-Base Pairs

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

• Bronsted-Lowry Base: Proton acceptor.

• Conjugate Base: Species formed when an acid loses a proton.

Titration Curves

Acid-Base Titration and Equivalence Point

• Titration Curve: Plot of pH vs. volume of titrant added.

• Equivalence Point: Point where moles of acid equal moles of base.

• Weak Acid/Strong Base: Curve shows buffer region, sharp rise at equivalence.

Example: Titration of acetic acid with NaOH shows a buffer region before equivalence point.

Balancing Redox Reactions

Steps for Balancing Redox Equations

• Assign oxidation numbers to all elements.

• Write half-reactions for oxidation and reduction.

• Balance atoms and charges (add H2O, H+, OH- as needed).

• Combine half-reactions and balance electrons.

Example: (balance using half-reactions).

Heat and Phase Transitions

Calculating Energy for Heating and Phase Changes

• q = mcΔT: Energy to change temperature within a phase.

• q = nΔH: Energy for phase change (fusion, vaporization).

• Sum energy for each step (heating, melting, vaporizing, etc.).

Example: To heat ice from -10°C to 90°C, calculate energy for warming ice, melting, warming water, vaporizing, etc.

Freezing/Melting Point Changes

Calculating Molality and Boiling Point Elevation

• Freezing Point Depression:

• Boiling Point Elevation:

• Molality (m): Moles of solute per kg of solvent.

Example: If a solution freezes at -1.2°C, use to find molality.

Determining Rate Laws

Using Experimental Data to Find Rate Law and Rate Constant

• Compare initial rates as concentrations change to determine reaction order with respect to each reactant.

• Plug values into rate law to solve for rate constant .

Example: Doubling [A] doubles the rate, so first order in A; halving [B] halves the rate, so first order in B.

Arrhenius Equation

Temperature Dependence of Reaction Rates

• Arrhenius Equation:

• Linear Form:

• Activation Energy (): Determined from slope of vs. plot.

Example: Slope of K gives .

Equilibrium Problems

Calculating Equilibrium Concentrations

• Set up ICE table (Initial, Change, Equilibrium).

• Use to solve for unknown concentrations at equilibrium.

Example: For , very little product forms; equilibrium lies far to the left.

Acid/Base pH Problems

Calculating pH of Weak Acid Solutions

• Set up equilibrium expression for weak acid dissociation.

• Use to solve for [H+], then .

Example: For 0.1 M HF, , solve for [H+].

Henderson-Hasselbalch Equation

Buffer Solutions and pH Calculation

• Buffer: Solution of weak acid and its conjugate base resists pH changes.

• Equation:

• Adding strong base converts some acid to conjugate base; recalculate concentrations and pH.

Example: Mixing CH3COOH and NaCH3COO forms an acetic acid/acetate buffer.

Solubility Products

Calculating Molar Solubility Using

• Solubility Product (): for AgCl.

• In presence of common ion (e.g., NaCl), solubility decreases due to common ion effect.

Example: Calculate for AgCl in pure water and in 0.05 M NaCl.

ΔH, ΔS, and ΔG

Thermodynamic Quantities and Their Calculation

• ΔH (Enthalpy): Heat change at constant pressure.

• ΔS (Entropy): Measure of disorder.

• ΔG (Gibbs Free Energy): Determines spontaneity:

• Use standard values to calculate for reactions.

Example: For , use tabulated values to find .

Nernst Equation

Electrochemical Cells and Cell Potentials

• Nernst Equation:

• Q: Reaction quotient; is number of electrons transferred.

• Use concentrations and standard potentials to calculate .

Example: For a cell with Cu and Sn electrodes, calculate at nonstandard conditions.

Harder Nernst Equation Applications

Calculating Equilibrium Constants from Cell Potentials

• At equilibrium, and .

• Use to solve for :

Example: For , use standard reduction potentials to find .