Thermochemistry, Thermodynamics, and Electrochemistry: Study Guide for CHEM 001B Exam 3

Chapter 7: Thermochemistry

7.3 The First Law of Thermodynamics

The First Law of Thermodynamics is a fundamental principle describing energy conservation in chemical systems.

• Definition: The First Law states that energy cannot be created or destroyed, only transferred or transformed.

• Mathematical Expression: $\Delta E = q + w$ where $\Delta E$ is the change in internal energy, $q$ is heat, and $w$ is work.

• Application: In chemical reactions, energy changes are tracked as heat and work exchanged with the surroundings.

• Example: When a gas expands against a piston, it does work on the surroundings.

7.4 Quantifying Heat and Work

Heat and work are the two main ways energy is transferred in chemical processes.

• Heat (q): Energy transferred due to temperature difference.

• Work (w): Energy transferred when an object is moved by a force.

• Equation for Work: $w = -P\Delta V$ (for pressure-volume work in gases)

• Sign Conventions: Heat absorbed by the system ($q > 0$), heat released ($q < 0$); work done by the system ($w < 0$), work done on the system ($w > 0$).

• Example: Compression of a gas increases internal energy.

7.6 Enthalpy

Enthalpy is a state function used to measure heat changes at constant pressure.

• Definition: $H = E + PV$ where $H$ is enthalpy, $E$ is internal energy, $P$ is pressure, $V$ is volume.

• Change in Enthalpy: $\Delta H = \Delta E + P\Delta V$

• Interpretation: $\Delta H$ is the heat exchanged at constant pressure.

• Example: Exothermic reactions have $\Delta H < 0$; endothermic reactions have $\Delta H > 0$.

7.7 Constant-Pressure Calorimetry

Calorimetry is used to measure heat changes in chemical reactions.

• Constant-Pressure Calorimeter: Measures $\Delta H$ for reactions at atmospheric pressure.

• Equation: $q = m c \Delta T$ where $m$ is mass, $c$ is specific heat, $\Delta T$ is temperature change.

• Application: Used for reactions in solution.

• Example: Mixing acid and base in a coffee-cup calorimeter.

7.8 Relationships Involving Enthalpy

Enthalpy changes can be manipulated using Hess's Law and other relationships.

• Hess's Law: The total enthalpy change is the sum of enthalpy changes for individual steps.

• Equation: $\Delta H_{rxn} = \sum \Delta H_{steps}$

• Application: Used to calculate $\Delta H$ for reactions not easily measured directly.

• Example: Formation of CO2 from C and O2 via intermediate steps.

7.9 Enthalpies of Formation

Standard enthalpy of formation is the enthalpy change for forming 1 mole of a compound from its elements.

• Definition: $\Delta H_f^\circ$ is the enthalpy change for formation under standard conditions (1 atm, 25°C).

• Calculation: $\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (products) - \sum n \Delta H_f^\circ (reactants)$

• Example: Formation of water from hydrogen and oxygen.

Chapter 19: Thermodynamics

19.2 Spontaneous and Nonspontaneous Processes

Spontaneity describes whether a process occurs naturally without external intervention.

• Spontaneous Process: Occurs without outside energy input (e.g., ice melting at room temperature).

• Nonspontaneous Process: Requires energy input (e.g., water electrolysis).

• Factors: Entropy, enthalpy, and temperature affect spontaneity.

19.3 Entropy and the Second Law of Thermodynamics

Entropy is a measure of disorder; the Second Law states that the entropy of the universe increases in spontaneous processes.

• Definition: $S$ is entropy; higher $S$ means more disorder.

• Second Law: $\Delta S_{universe} > 0$ for spontaneous processes.

• Example: Dissolving salt in water increases entropy.

19.4 Entropy Changes Associated with State Changes

Phase changes involve significant entropy changes.

• Solid to Liquid: $\Delta S > 0$ (melting increases disorder).

• Liquid to Gas: $\Delta S > 0$ (vaporization increases disorder).

• Equation: $\Delta S = \frac{q_{rev}}{T}$ for reversible processes.

• Example: Boiling water increases entropy.

19.5 Heat Transfer and Changes in the Entropy of the Surroundings

Heat exchange with surroundings affects their entropy.

• Equation: $\Delta S_{surroundings} = -\frac{q_{system}}{T}$

• Interpretation: Exothermic reactions increase surroundings' entropy.

• Example: Combustion releases heat, increasing $S_{surroundings}$.

19.6 Gibbs Free Energy

Gibbs Free Energy determines spontaneity at constant temperature and pressure.

• Definition: $G = H - TS$

• Change in Free Energy: $\Delta G = \Delta H - T\Delta S$

• Interpretation: $\Delta G < 0$ means spontaneous; $\Delta G > 0$ means nonspontaneous.

• Example: Photosynthesis is nonspontaneous ($\Delta G > 0$).

19.7 Entropy Changes in Chemical Reactions

Entropy changes can be calculated for reactions using standard entropy values.

• Equation: $\Delta S_{rxn}^\circ = \sum n S^\circ (products) - \sum n S^\circ (reactants)$

• Application: Used to predict reaction spontaneity.

• Example: Decomposition of hydrogen peroxide.

19.8 Free Energy Changes in Chemical Reactions

Free energy changes indicate whether reactions are spontaneous under standard conditions.

• Equation: $\Delta G_{rxn}^\circ = \sum n \Delta G_f^\circ (products) - \sum n \Delta G_f^\circ (reactants)$

• Application: Used to determine reaction feasibility.

• Example: Combustion of methane.

19.9 Free Energy Changes for Nonstandard States

Free energy can be calculated for reactions under nonstandard conditions.

• Equation: $\Delta G = \Delta G^\circ + RT \ln Q$ where $Q$ is the reaction quotient.

• Application: Used for reactions not at equilibrium or standard state.

• Example: Electrochemical cells with varying concentrations.

19.10 Free Energy and Equilibrium

At equilibrium, free energy change is zero, and relates to the equilibrium constant.

• Equation: $\Delta G^\circ = -RT \ln K$ where $K$ is the equilibrium constant.

• Interpretation: Large $K$ means reaction favors products.

• Example: Acid-base equilibrium.

Chapter 20: Electrochemistry

20.2 Balancing Oxidation-Reduction Equations

Redox reactions involve electron transfer and must be balanced for mass and charge.

• Steps:

  1. Assign oxidation numbers.

  2. Identify oxidation and reduction half-reactions.

  3. Balance atoms and charges.

  4. Combine half-reactions.

• Example: Balancing the reaction between Fe2+ and Cr2O72-.

20.3 Voltaic (or Galvanic) Cells

Voltaic cells generate electrical energy from spontaneous redox reactions.

• Components: Anode (oxidation), cathode (reduction), salt bridge, external circuit.

• Cell Notation: Anode | Anode solution || Cathode solution | Cathode.

• Example: Zn/Cu cell: Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s).

20.4 Standard Electrode Potentials

Standard electrode potentials measure the tendency of a species to be reduced.

• Definition: $E^\circ$ is the standard reduction potential.

• Cell Potential: $E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ$

• Application: Predicts direction of electron flow.

• Example: $E^\circ$ for Cu2+/Cu is +0.34 V.

20.5 Cell Potential, Free Energy, and the Equilibrium Constant

Cell potential is related to free energy and equilibrium.

• Equation: $\Delta G^\circ = -nFE_{cell}^\circ$ where $n$ is moles of electrons, $F$ is Faraday's constant.

• Relationship to Equilibrium: $\Delta G^\circ = -RT \ln K$

• Example: Calculating $K$ for a redox reaction.

20.6 Cell Potential and Concentration

Cell potential changes with ion concentrations; described by the Nernst equation.

• Nernst Equation: $E_{cell} = E_{cell}^\circ - \frac{0.0592}{n} \log Q$ (at 25°C)

• Application: Used for nonstandard conditions.

• Example: Calculating $E_{cell}$ for a cell with unequal ion concentrations.

Concept	Key Equation	Application
First Law of Thermodynamics	$\Delta E = q + w$	Energy conservation in reactions
Enthalpy Change	$\Delta H = \Delta E + P\Delta V$	Heat at constant pressure
Entropy Change	$\Delta S = \frac{q_{rev}}{T}$	Disorder in phase changes
Gibbs Free Energy	$\Delta G = \Delta H - T\Delta S$	Spontaneity of reactions
Cell Potential	$E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ$	Electrochemical cells
Nernst Equation	$E_{cell} = E_{cell}^\circ - \frac{0.0592}{n} \log Q$	Cell potential at nonstandard conditions

Additional info: These notes expand on the listed topics with academic context, definitions, equations, and examples to provide a comprehensive study guide for Exam 3 in CHEM 001B.