Thermodynamics, Electrochemistry, and Nuclear Chemistry Study Notes

Thermodynamics (Ch. 18)

18.1 Predicting the Sign of Entropy (S) Change

Entropy (S) is a measure of the disorder or randomness of a system. The sign of entropy change can be predicted based on the physical and chemical changes occurring in a system.

• Entropy increases when:

  • Solids change to liquids or gases

  • Liquids change to gases

  • Solids dissolve

  • More moles of gas are formed in a reaction

• Entropy decreases when gases condense, dissolve, or when fewer moles of gas are produced.

Example: The reaction $2H_2O(l) \rightarrow 2H_2(g) + O_2(g)$ increases entropy because liquid water forms gaseous products.

18.2 Entropy Change for Phase Changes

Phase changes involve significant changes in entropy.

• Formula: $\Delta S = \frac{q_{rev}}{T}$

• At the phase transition temperature, $q_{rev}$ is the heat absorbed or released reversibly.

Example: Melting ice at 0°C increases entropy as solid changes to liquid.

18.3 Entropy Change of Surroundings

The entropy change of the surroundings is related to the heat exchanged by the system and the temperature of the surroundings.

• Formula: $\Delta S_{surr} = -\frac{\Delta H_{sys}}{T}$

• Exothermic reactions ($\Delta H_{sys} < 0$) increase the entropy of the surroundings.

Example: Combustion reactions release heat, increasing $S_{surr}$.

18.4 Gibbs Free Energy & Spontaneity

Gibbs free energy (G) predicts the spontaneity of a process at constant temperature and pressure.

• Formula: $\Delta G = \Delta H - T\Delta S$

• If $\Delta G < 0$, the process is spontaneous.

• If $\Delta G > 0$, the process is nonspontaneous.

Example: The melting of ice at temperatures above 0°C is spontaneous because $\Delta G < 0$.

18.5 Standard Entropy Change ($\Delta S^\circ$)

The standard entropy change for a reaction is calculated using standard molar entropies.

• Formula: $\Delta S^\circ_{rxn} = \sum nS^\circ_{products} - \sum nS^\circ_{reactants}$

Example: Calculate $\Delta S^\circ$ for $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$ using tabulated $S^\circ$ values.

18.6 $\Delta G^\circ$ from $\Delta G^\circ_f$

Standard free energy change can be calculated from standard free energies of formation.

• Formula: $\Delta G^\circ_{rxn} = \sum n\Delta G^\circ_f (products) - \sum n\Delta G^\circ_f (reactants)$

18.7 $\Delta G^\circ$ from $\Delta H^\circ$ and $\Delta S^\circ$

Gibbs free energy can also be calculated using enthalpy and entropy changes.

• Formula: $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

18.8 Stepwise Reaction $\Delta G^\circ$

For reactions occurring in steps, the overall $\Delta G^\circ$ is the sum of the $\Delta G^\circ$ values for each step.

• Add $\Delta G^\circ$ values for individual steps.

18.9 $\Delta G$ Under Nonstandard Conditions

Gibbs free energy under nonstandard conditions is related to the reaction quotient $Q$.

• Formula: $\Delta G = \Delta G^\circ + RT\ln Q$

• $R$ = 8.314 \(J\,mol^{-1}\,K^{-1}\)

18.10 Relate K and $\Delta G^\circ$

The equilibrium constant $K$ is related to the standard free energy change.

• Formula: $\Delta G^\circ = -RT\ln K$

Electrochemistry (Ch. 19)

19.1 Balance Redox in Acid (Half-Reactions)

Redox reactions can be balanced using the half-reaction method, especially in acidic solution.

1. Split into half-reactions.

2. Balance all elements except H and O.

3. Balance O by adding $H_2O$.

4. Balance H by adding $H^+$.

5. Balance charge by adding electrons ($e^-$).

6. Multiply half-reactions to equalize electrons, then add together.

19.2 Balance Redox in Base

To balance redox reactions in basic solution, first balance as in acid, then neutralize $H^+$ with $OH^-$ to form $H_2O$.

• Add $OH^-$ to both sides for each $H^+$ present.

19.3 Standard Cell Potentials ($E^\circ_{cell}$)

The standard cell potential is calculated from the standard reduction potentials of the half-cells.

• Formula: $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$

• Electrons flow from anode to cathode.

19.4 Predict Spontaneity & Sketch Cell

• If $E^\circ_{cell} > 0$, the cell reaction is spontaneous.

• Label anode (oxidation) and cathode (reduction) in cell diagrams.

19.5 Relate $\Delta G^\circ$ and $E^\circ_{cell}$

• Formula: $\Delta G^\circ = -nFE^\circ_{cell}$

• $n$ = number of moles of electrons transferred

• $F$ = Faraday's constant ($96,485\ C\,mol^{-1}$)

19.6 Nernst Equation

• Formula: $E = E^\circ - \frac{0.0592}{n} \log Q$

• Relates cell potential to nonstandard conditions.

19.7 Cell Potential Nonstandard (Nernst)

• Formula: $E = E^\circ - \frac{0.0592}{n} \log Q$

19.8 Predict Electrolysis Products

• Compare reduction and oxidation potentials to predict which species will be reduced or oxidized at the electrodes.

• Consider overpotentials and concentration effects.

19.9 Stoichiometry of Electrolytic Cells

• Formula: $q = I \times t$

• Use $q$ (charge in coulombs) to find moles of electrons, then relate to moles of product formed.

Nuclear Chemistry (Ch. 20)

20.1 Alpha Decay

Alpha decay involves the emission of an alpha particle ($^4_2He$ nucleus) from a radioactive nucleus.

• General equation: $^A_ZX \rightarrow ^{A-4}_{Z-2}Y + ^4_2He$

20.2 Beta Decay, Positron, Electron Capture

• Beta decay: $^A_ZX \rightarrow ^A_{Z+1}Y + ^0_{-1}e$

• Positron emission: $^A_ZX \rightarrow ^A_{Z-1}Y + ^0_{+1}e$

• Electron capture: $^A_ZX + ^0_{-1}e \rightarrow ^A_{Z-1}Y$

20.3 Predict Type of Decay

• Neutron-rich nuclei: likely to undergo beta decay.

• Neutron-poor nuclei: likely to undergo positron emission or electron capture.

20.4 Radioactive Decay Kinetics

• Radioactive decay follows first-order kinetics.

• Formula: $N = N_0 e^{-kt}$

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

20.5 Radiocarbon Dating

• Used to date ancient organic materials using $^{14}C$ decay.

20.6 U/Pb Dating

• Compares ratios of $^{206}Pb$ and $^{207}Pb$ to $^{238}U$ and $^{235}U$ for dating rocks.

20.7 Mass Defect & Binding Energy

• Mass defect ($\Delta m$) is the difference between the mass of a nucleus and the sum of its nucleons.

• Binding energy is calculated using $E = \Delta m c^2$.

Example: Calculate the binding energy for $^4He$ using its mass defect.