Thermodynamics and Electrochemistry · ⁨Nhiệt động lực học và Điện hóa⁩

Learning Objective 9.1.A: Identify the sign and relative magnitude of the entropy change associated with chemical or physical processes.

• 9.1.A.1 Entropy increases when matter becomes more dispersed. For example, the phase change from solid to liquid or from liquid to gas results in a dispersal of matter as the individual particles become freer to move and generally occupy a larger volume. Similarly, for a gas, the entropy increases when there is an increase in volume (at constant temperature), and the gas molecules are able to move within a larger space. For reactions involving gas-phase reactants or products, the entropy generally increases when the total number of moles of gas-phase products is greater than the total number of moles of gas-phase reactants.
• 9.1.A.2 Entropy increases when energy is dispersed. According to kinetic molecular theory (KMT), the distribution of kinetic energy among the particles of a gas broadens as the temperature increases. As a result, the entropy of the system increases with an increase in temperature.

Learning Objective 9.2.A: Calculate the standard entropy change for a chemical or physical process based on the absolute entropies (standard molar entropies) of the species involved in the process.

• 9.2.A.1 The entropy change for a process can be calculated from the absolute entropies of the species involved before and after the process occurs.
  • Equation: $\Delta S^{\circ}_{reaction} = \Sigma S^{\circ}_{products} - \Sigma S^{\circ}_{reactants}$

Learning Objective 9.3.A: Explain whether a physical or chemical process is thermodynamically favored based on an evaluation of $\Delta G^{\circ}$.

• 9.3.A.1 The Gibbs free energy change for a chemical process in which all the reactants and products are present in a standard state (as pure substances, as solutions of 1.0 M concentration, or as gases at a pressure of 1.0 atm (or 1.0 bar)) is given the symbol $\Delta G^{\circ}$.

• 9.3.A.2 The standard Gibbs free energy change for a chemical or physical process is a measure of thermodynamic favorability. Historically, the term "spontaneous" has been used to describe processes for which $\Delta G^{\circ} < 0$. The phrase "thermodynamically favored" is preferred instead so that common misunderstandings (equating "spontaneous" with "suddenly" or "without cause") can be avoided. When $\Delta G^{\circ} < 0$ for the process, it is said to be thermodynamically favored.

• 9.3.A.3 The standard Gibbs free energy change for a physical or chemical process may also be determined from the standard Gibbs free energy of formation of the reactants and products.

  • Equation: $\Delta G^{\circ}_{reaction} = \Sigma \Delta G^{\circ}_{f\ products} - \Sigma \Delta G^{\circ}_{f\ reactants}$

• 9.3.A.4 In some cases, it is necessary to consider both enthalpy and entropy to determine if a process will be thermodynamically favored. The freezing of water and the dissolution of sodium nitrate are examples of such phenomena.

• 9.3.A.5 Knowing the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for a process at a given temperature allows $\Delta G^{\circ}$ to be calculated directly.

  • Equation: $\Delta G^{\circ} = \Delta H^{\circ} - T\,\Delta S^{\circ}$

• 9.3.A.6 In general, the temperature conditions for a process to be thermodynamically favored ($\Delta G^{\circ} < 0$) can be predicted from the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ as shown in the table below:

  $\Delta H^{\circ}$	$\Delta S^{\circ}$	Symbols	$\Delta G^{\circ} < 0$, favored at:
  $< 0$	$> 0$	$<\ >$	all $T$
  $> 0$	$< 0$	$>\ <$	no $T$
  $> 0$	$> 0$	$>\ >$	high $T$
  $< 0$	$< 0$	$<\ <$	low $T$

  In cases where $\Delta H^{\circ} < 0$ and $\Delta S^{\circ} > 0$, no calculation of $\Delta G^{\circ}$ is necessary to determine that the process is thermodynamically favored ($\Delta G^{\circ} < 0$). In cases where $\Delta H^{\circ} > 0$ and $\Delta S^{\circ} < 0$, no calculation of $\Delta G^{\circ}$ is necessary to determine that the process is thermodynamically unfavored ($\Delta G^{\circ} > 0$).

Learning Objective 9.4.A: Explain, in terms of kinetics, why a thermodynamically favored reaction might not occur at a measurable rate.

• 9.4.A.1 Many processes that are thermodynamically favored do not occur to any measurable extent, or they occur at extremely slow rates.
• 9.4.A.2 Processes that are thermodynamically favored, but do not proceed at a measurable rate, are under "kinetic control." High activation energy is a common reason for a process to be under kinetic control. The fact that a process does not proceed at a noticeable rate does not mean that the chemical system is at equilibrium. If a process is known to be thermodynamically favored, and yet does not occur at a measurable rate, it is reasonable to conclude that the process is under kinetic control.

Learning Objective 9.5.A: Explain whether a process is thermodynamically favored using the relationships between $K$, $\Delta G^{\circ}$, and $T$.

• 9.5.A.1 The phrase "thermodynamically favored" ($\Delta G^{\circ} < 0$) means that the products are favored at equilibrium ($K > 1$) under standard conditions.
• 9.5.A.2 The equilibrium constant is related to free energy by the equations
  • Equation: $K = e^{-\Delta G^{\circ}/RT}$
  • Equation: $\Delta G^{\circ} = -RT \ln K$
• 9.5.A.3 Connections between $K$ and $\Delta G^{\circ}$ can be made qualitatively through estimation. When $\Delta G^{\circ}$ is near zero, the equilibrium constant will be close to 1. When $\Delta G^{\circ}$ is much larger or much smaller than $RT$, the value of $K$ deviates strongly from 1.
• 9.5.A.4 Processes with $\Delta G^{\circ} < 0$ favor products (i.e., $K > 1$) and those with $\Delta G^{\circ} > 0$ favor reactants (i.e., $K < 1$).

Learning Objective 9.6.A: Explain the relationship between the solubility of a salt and changes in the enthalpy and entropy that occur in the dissolution process.

• 9.6.A.1 The free energy change ($\Delta G^{\circ}$) for dissolution of a substance reflects a number of factors: the breaking of the intermolecular interactions that hold the solid together, the reorganization of the solvent around the dissolved species, and the interaction of the dissolved species with the solvent. It is possible to estimate the sign and relative magnitude of the enthalpic and entropic contributions to each of these factors. However, making predictions for the total change in free energy of dissolution can be challenging due to the cancellations among the free energies associated with the three factors cited.

Learning Objective 9.7.A: Explain the relationship between external sources of energy or coupled reactions and their ability to drive thermodynamically unfavorable processes.

• 9.7.A.1 An external source of energy can be used to make a thermodynamically unfavorable process occur. Examples include:
  • 9.7.A.1.i Electrical energy to drive an electrolytic cell or charge a battery.
  • 9.7.A.1.ii Light to drive the overall conversion of carbon dioxide to glucose in photosynthesis.
• 9.7.A.2 A desired product can be formed by coupling a thermodynamically unfavorable reaction that produces that product to a favorable reaction (e.g., the conversion of $ATP$ to $ADP$ in biological systems). In the coupled system, the individual reactions share one or more common intermediates. The sum of the individual reactions produces an overall reaction that achieves the desired outcome and has $\Delta G^{\circ} < 0$.

Learning Objective 9.8.A: Explain the relationship between the physical components of an electrochemical cell and the overall operational principles of the cell.

• 9.8.A.1 Each component of an electrochemical cell (electrodes, solutions in the half-cells, salt bridge, voltage/current measuring device) plays a specific role in the overall functioning of the cell. The operational characteristics of the cell (galvanic vs. electrolytic, direction of electron flow, reactions occurring in each half-cell, change in electrode mass, evolution of a gas at an electrode, ion flow through the salt bridge) can be described at both the macroscopic and particulate levels.
• 9.8.A.2 Galvanic, sometimes called voltaic, cells involve a thermodynamically favored reaction, whereas electrolytic cells involve a thermodynamically unfavored reaction. Visual representations of galvanic and electrolytic cells are tools of analysis to identify where half-reactions occur and in what direction current flows.
• 9.8.A.3 For all electrochemical cells, oxidation occurs at the anode and reduction occurs at the cathode.
  • Exclusion statement: Labeling an electrode as positive or negative will not be assessed on the AP Exam.

Learning Objective 9.9.A: Explain whether an electrochemical cell is thermodynamically favored, based on its standard cell potential and the constituent half-reactions within the cell.

• 9.9.A.1 Electrochemistry encompasses the study of redox reactions that occur within electrochemical cells. The reactions are either thermodynamically favored (resulting in a positive voltage) or thermodynamically unfavored (resulting in a negative voltage and requiring an externally applied potential for the reaction to proceed).
• 9.9.A.2 The standard cell potential of electrochemical cells can be calculated by identifying the oxidation and reduction half-reactions and their respective standard reduction potentials.
• 9.9.A.3 $\Delta G^{\circ}$ (standard Gibbs free energy change) is proportional to the negative of the cell potential for the redox reaction from which it is constructed. Thus, a cell with a positive $E^{\circ}$ involves a thermodynamically favored reaction, and a cell with a negative $E^{\circ}$ involves a thermodynamically unfavored reaction.
  • Equation: $\Delta G^{\circ} = -nFE^{\circ}$

Learning Objective 9.10.A: Explain the relationship between deviations from standard cell conditions and changes in the cell potential.

• 9.10.A.1 In a real system under nonstandard conditions, the cell potential will vary depending on the concentrations of the active species. The cell potential is a driving force toward equilibrium; the farther the reaction is from equilibrium, the greater the magnitude of the cell potential.

• 9.10.A.2 Equilibrium arguments such as Le Châtelier's principle do not apply to electrochemical systems, because the systems are not in equilibrium.

• 9.10.A.3 The standard cell potential $E^{\circ}$ corresponds to the standard conditions of $Q = 1$. As the system approaches equilibrium, the magnitude (i.e., absolute value) of the cell potential decreases, reaching zero at equilibrium (when $Q = K$). Deviations from standard conditions that take the cell further from equilibrium than $Q = 1$ will increase the magnitude of the cell potential relative to $E^{\circ}$. Deviations from standard conditions that take the cell closer to equilibrium than $Q = 1$ will decrease the magnitude of the cell potential relative to $E^{\circ}$. In concentration cells, the direction of spontaneous electron flow can be determined by considering the direction needed to reach equilibrium.

• 9.10.A.4 Algorithmic calculations using the Nernst equation are insufficient to demonstrate an understanding of electrochemical cells under nonstandard conditions. However, students should qualitatively understand the effects of concentration on cell potential and use conceptual reasoning, including the qualitative use of the Nernst equation:

  • Equation: $E = E^{\circ} - (RT/nF) \ln Q$

  to solve problems.

Learning Objective 9.11.A: Calculate the amount of charge flow based on changes in the amounts of reactants and products in an electrochemical cell.

• 9.11.A.1 Faraday's laws can be used to determine the stoichiometry of the redox reaction occurring in an electrochemical cell with respect to the following:
  • 9.11.A.1.i Number of electrons transferred
  • 9.11.A.1.ii Mass of material deposited on or removed from an electrode (as in electroplating)
  • 9.11.A.1.iii Current
  • 9.11.A.1.iv Time elapsed
  • 9.11.A.1.v Charge of ionic species
  • Equation: $I = q/t$