Unit 9: Thermodynamics and Electrochemistry

Thermodynamics in AP Chemistry focuses on understanding the energy changes that occur in chemical and physical processes, with an emphasis on predicting whether a process will occur spontaneously under given conditions. This includes examining heat transfer, entropy changes, and the interplay between enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) in determining spontaneity. Students will learn how to quantitatively calculate Gibbs free energy and connect it to equilibrium constants and cell potentials.

Entropy and the Second Law of Thermodynamics

Entropy (\( \Delta S \)) is a measure of the dispersal of energy and the number of possible microstates in a system. Processes that increase entropy generally involve greater molecular disorder, such as phase changes from solid to liquid or liquid to gas, dissolution of ionic solids, or temperature increases that expand particle motion. The AP exam often requires comparing entropy changes qualitatively and calculating them quantitatively from standard molar entropy values.
The Second Law of Thermodynamics states that the total entropy of the universe (\( \Delta S_{\text{universe}} \)) always increases for a spontaneous process. This means that even if the system’s entropy decreases (as in freezing water), the surroundings must experience a greater increase in entropy for the overall process to be spontaneous. Students should focus on the combined system + surroundings perspective to avoid incorrect spontaneity predictions.
Entropy changes can be predicted by examining molecular complexity, phase, and the number of particles in the products versus the reactants. For example, reactions producing more moles of gas tend to have positive \( \Delta S \) values because gases have the highest entropy of all phases. Conversely, when gas molecules are consumed to form fewer particles or condensed phases, entropy typically decreases.
Standard entropy changes (\( \Delta S^\circ \)) for reactions are calculated using the equation \( \Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}} \), with all values taken at standard conditions (298 K, 1 atm, 1 M). Positive \( \Delta S^\circ \) values indicate increased disorder, while negative values indicate increased order in the system. This calculation is critical for linking entropy to Gibbs free energy later in the unit.
Understanding entropy is essential for evaluating spontaneity when combined with enthalpy (\( \Delta H \)) in the Gibbs free energy equation. On the AP exam, students may be asked to justify entropy changes using particle diagrams, chemical formulas, or conceptual reasoning. Mastery of entropy principles ensures accurate predictions of reaction behavior under different conditions.

Factors Affecting Entropy

Phase changes are one of the most significant factors affecting entropy, with gases having the highest entropy, followed by liquids, and then solids. Transitions from a more ordered phase to a less ordered phase (e.g., melting, vaporization, sublimation) lead to large positive \( \Delta S \) values. Conversely, condensation, freezing, or deposition result in large negative \( \Delta S \) values because molecular motion and possible microstates are reduced.
Changes in the number of moles of gas directly influence entropy because gas particles occupy much more volume and have greater positional freedom compared to liquids and solids. If a reaction produces more moles of gas than it consumes, \( \Delta S \) will generally be positive. If fewer moles of gas are produced, \( \Delta S \) will be negative, assuming no other major changes in molecular complexity.
Temperature increases typically lead to positive entropy changes because particles move more vigorously and explore more microstates. At higher temperatures, molecular vibrations, rotations, and translations become more significant, increasing the disorder of the system. This principle explains why heating substances before a phase change can prepare them for a large jump in entropy during the transition.
Molecular complexity and the number of atoms in a molecule also affect entropy, as more complex molecules with more atoms can vibrate and rotate in more ways. For example, \( \text{CO}_2 \) has a higher molar entropy than \( \text{O}_2 \) because of its additional atoms and vibrational modes. On the AP exam, students may be asked to compare entropy values of substances with different structures to predict \( \Delta S \) qualitatively.
Dissolution of ionic compounds often results in increased entropy because the orderly crystal lattice breaks apart and ions disperse into the solvent, increasing the number of microstates. However, this increase may be reduced or even outweighed if strong ion-dipole interactions in the solvent cause extensive ordering of solvent molecules (as in hydration shells). This concept is especially important in connecting thermodynamics to solubility equilibria.

Gibbs Free Energy and Spontaneity

Gibbs free energy (\( \Delta G \)) is the thermodynamic quantity that combines enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) to determine whether a process is spontaneous under constant temperature and pressure. It is calculated using the equation \( \Delta G = \Delta H - T\Delta S \), where \( T \) is in kelvins. A negative \( \Delta G \) indicates a thermodynamically favorable (spontaneous) process, while a positive \( \Delta G \) indicates a nonspontaneous process.
The signs of \( \Delta H \) and \( \Delta S \) together determine spontaneity at different temperatures. When both \( \Delta H \) is negative (exothermic) and \( \Delta S \) is positive (entropy increases), the process is always spontaneous. When both are unfavorable (\( \Delta H \) positive and \( \Delta S \) negative), the process is never spontaneous at any temperature.
In cases where \( \Delta H \) and \( \Delta S \) have the same sign, temperature plays a key role in determining spontaneity. If both are positive, the process is spontaneous only at high temperatures where \( T\Delta S \) outweighs \( \Delta H \). If both are negative, the process is spontaneous only at low temperatures where \( T\Delta S \) does not significantly offset the favorable negative \( \Delta H \).
Standard free energy changes (\( \Delta G^\circ \)) are calculated under standard conditions (298 K, 1 atm, 1 M solutions) using tabulated standard enthalpies of formation (\( \Delta H_f^\circ \)) and standard molar entropies (\( S^\circ \)). On the AP exam, students may need to calculate \( \Delta G^\circ \) from thermodynamic data or from an equilibrium constant using \( \Delta G^\circ = -RT \ln K \).
The concept of spontaneity does not indicate how fast a reaction will occur; it only indicates whether it is thermodynamically favorable. A reaction with a large negative \( \Delta G \) may still proceed very slowly if it has a high activation energy barrier, a key idea that links thermodynamics with kinetics. This is why the unit later discusses thermodynamic vs. kinetic control in greater depth.

Thermodynamic and Kinetic Control

Thermodynamic control occurs when reaction conditions allow the system to reach the most stable (lowest free energy) product distribution, regardless of the time it takes to get there. This typically happens at higher temperatures or over long reaction times, where the system can overcome activation energy barriers and fully equilibrate. The product favored under thermodynamic control is usually more stable but may form more slowly.
Kinetic control occurs when reaction conditions favor the product that forms the fastest, not necessarily the most stable one. This is common at lower temperatures or short reaction times, where the reaction pathway with the lowest activation energy dominates. The kinetically favored product may be less stable and can later convert to the thermodynamic product if conditions change to allow equilibration.
Whether a reaction is under kinetic or thermodynamic control can be predicted by comparing activation energies and final free energies of products. Diagrams for these situations show the difference between reaction pathways: one with a lower activation energy peak (kinetic) and one with a deeper energy well (thermodynamic). On the AP exam, this concept is often tied to changes in temperature or catalysts that selectively affect activation energies.
Real-world applications of control concepts appear in organic synthesis, where chemists deliberately choose conditions to favor one product over another. For example, the formation of different alkene isomers in elimination reactions can be manipulated by adjusting temperature and base strength. These principles also help explain why some industrial processes operate at higher temperatures even if the immediate yield is lower.
In electrochemistry, kinetic limitations explain why some thermodynamically favorable redox reactions proceed very slowly without catalysts. This distinction reinforces that \( \Delta G \) predicts possibility, but activation energy and reaction mechanism determine the rate and which products form first.

Coupled Reactions and Thermodynamic Favorability

Coupled reactions occur when a thermodynamically unfavorable process is driven by a favorable one, making the overall \( \Delta G \) negative. The most common biological example is ATP hydrolysis, which releases a large amount of free energy that can power otherwise nonspontaneous cellular processes. In chemistry, coupling is essential for making certain synthesis reactions possible.
The key principle is that free energy changes for multiple reactions are additive, so if the sum of \( \Delta G \) values is negative, the combined process is spontaneous. This is analogous to Hess’s Law for enthalpy, except it is applied to Gibbs free energy. On the AP exam, this often appears in multi-step reactions where one step is endergonic and the other is strongly exergonic.
Catalysts can facilitate coupling by lowering activation energies and enabling both reactions to proceed in the same medium or at the same time. In industrial chemistry, coupling allows the use of waste energy from one process to drive another, improving efficiency. This concept also links to electrochemistry, where spontaneous redox reactions in a galvanic cell can be harnessed to drive electrolysis in an electrolytic cell.
The success of coupling depends on ensuring that the two processes are physically or mechanistically connected, so the energy released by one can directly perform work on the other. Without such a connection, the energy would dissipate as heat and the unfavorable process would not occur. This means coupling is not just about thermodynamics, but also about engineering the system so that the energy transfer is direct and usable.
Students should remember that coupling does not make the unfavorable reaction favorable on its own; it only works because the combined set of reactions has a net \( \Delta G < 0 \). This distinction is important when analyzing whether a proposed reaction pathway will work in theory versus in practice.

Standard Free Energy Changes (\( \Delta G^\circ \))

Standard free energy change (\( \Delta G^\circ \)) is the change in Gibbs free energy for a reaction under standard conditions: 298 K, 1 atm pressure, and 1 M concentrations for all aqueous species. It serves as a reference point for comparing different reactions under consistent conditions. Values can be calculated using standard enthalpies of formation (\( \Delta H_f^\circ \)) and standard molar entropies (\( S^\circ \)) with the equation \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \).
When \( \Delta G^\circ < 0 \), the reaction is thermodynamically favorable under standard conditions; when \( \Delta G^\circ > 0 \), it is not. However, standard conditions may not reflect actual reaction environments, so real spontaneity can differ if concentrations, temperature, or pressure deviate from standard values. On the AP exam, you may be asked to interpret how changes from standard conditions affect spontaneity.
\( \Delta G^\circ \) can also be calculated from equilibrium constants using the equation \( \Delta G^\circ = -RT \ln K \), where \( R \) is the gas constant (8.314 J/mol·K) and \( K \) is the equilibrium constant at standard temperature. This relationship connects thermodynamics and equilibrium, showing that larger \( K \) values correspond to more negative \( \Delta G^\circ \) and thus stronger thermodynamic favorability.
Because \( \Delta G^\circ \) is temperature-dependent, a reaction that is nonspontaneous at 298 K could become spontaneous at higher or lower temperatures if \( \Delta S \) and \( \Delta H \) values allow it. This reinforces the importance of analyzing the signs and magnitudes of both enthalpy and entropy changes, rather than relying solely on standard free energy tables.
Standard free energy values are especially useful for predicting the feasibility of redox reactions, phase changes, and dissolution processes. They are widely tabulated in data tables provided on the AP Chemistry exam, allowing students to calculate thermodynamic favorability without experimentally measuring energy changes.

Free Energy and Equilibrium

The relationship between Gibbs free energy and equilibrium is expressed by \( \Delta G = \Delta G^\circ + RT \ln Q \), where \( Q \) is the reaction quotient. At equilibrium, \( \Delta G = 0 \) and \( Q = K \), reducing the equation to \( \Delta G^\circ = -RT \ln K \). This shows that the equilibrium constant is directly determined by the standard free energy change of the reaction.
If \( Q < K \), then \( \ln Q \) is negative and \( \Delta G \) becomes negative, meaning the forward reaction is spontaneous until equilibrium is reached. If \( Q > K \), \( \Delta G \) becomes positive, meaning the reverse reaction is spontaneous until equilibrium is reached. This connection allows free energy to predict not just whether a reaction is favorable, but also in which direction it will shift.
When \( \Delta G^\circ \) is large and negative, \( K \) is much greater than 1, indicating a product-favored equilibrium. When \( \Delta G^\circ \) is large and positive, \( K \) is much less than 1, indicating a reactant-favored equilibrium. Moderate \( \Delta G^\circ \) values produce equilibrium constants closer to 1, meaning significant amounts of both reactants and products are present at equilibrium.
Temperature affects both \( \Delta G^\circ \) and \( K \) because of their dependence on \( \Delta H \) and \( \Delta S \). For endothermic reactions with positive \( \Delta S \), raising the temperature increases \( K \); for exothermic reactions with negative \( \Delta S \), raising the temperature decreases \( K \). This is consistent with Le Châtelier’s principle, which predicts how equilibrium shifts in response to temperature changes.
In practice, understanding the link between free energy and equilibrium helps chemists optimize reaction yields, select conditions for desired product ratios, and predict how environmental changes will alter reaction direction. On the AP exam, you should be comfortable moving between \( \Delta G \), \( K \), and \( Q \) to answer both conceptual and calculation-based questions.

Free Energy of Dissolution

The free energy of dissolution refers to the Gibbs free energy change (\( \Delta G_{\text{soln}} \)) when a solute dissolves in a solvent to form a solution. It is determined by the balance between the enthalpy change of dissolution (\( \Delta H_{\text{soln}} \)) and the entropy change (\( \Delta S_{\text{soln}} \)) using the equation \( \Delta G_{\text{soln}} = \Delta H_{\text{soln}} - T\Delta S_{\text{soln}} \). A negative value indicates that dissolution is thermodynamically favorable under the given conditions.
The enthalpy term includes both the energy required to break solute–solute and solvent–solvent interactions and the energy released when solute–solvent interactions form. If the formation of solute–solvent interactions releases more energy than is required to separate solute and solvent particles, \( \Delta H_{\text{soln}} \) will be negative and dissolution will be energetically favorable.
The entropy term is typically positive for dissolutions because the solute particles become more randomly distributed in the solvent, increasing the system’s disorder. However, some dissolutions, such as those involving ionic solids in structured water environments, can have a negative entropy change due to ordering effects like hydration shells.
Solubility depends on the sign and magnitude of both \( \Delta H_{\text{soln}} \) and \( \Delta S_{\text{soln}} \). A dissolution with a positive \( \Delta H_{\text{soln}} \) can still be favorable if \( T\Delta S_{\text{soln}} \) is large enough to make \( \Delta G_{\text{soln}} \) negative. Conversely, an exothermic dissolution can be nonspontaneous if the entropy change is strongly negative.
On the AP exam, you may need to connect \( \Delta G_{\text{soln}} \) to solubility product constants (\( K_{\text{sp}} \)) through the equation \( \Delta G^\circ_{\text{soln}} = -RT\ln K_{\text{sp}} \). This relationship shows that substances with larger \( K_{\text{sp}} \) values have more negative free energies of dissolution and thus higher solubility under standard conditions.

Electrochemistry Fundamentals

Electrochemistry studies the interconversion between chemical energy and electrical energy through redox reactions. In galvanic (voltaic) cells, spontaneous redox reactions generate electric current, while in electrolytic cells, electrical energy is used to drive nonspontaneous chemical changes. Understanding cell design and operation is essential for analyzing reaction spontaneity and predicting cell voltages.
The cell potential (\( E_{\text{cell}} \)) measures the driving force of an electrochemical reaction and is determined by the difference between the reduction potentials of the cathode and anode: \( E_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \). A positive \( E_{\text{cell}} \) corresponds to a spontaneous process, consistent with a negative \( \Delta G \) via the equation \( \Delta G^\circ = -nFE^\circ_{\text{cell}} \), where \( n \) is moles of electrons and \( F \) is Faraday’s constant.
In galvanic cells, oxidation occurs at the anode and reduction at the cathode, with electrons flowing through an external circuit from anode to cathode. The salt bridge or porous barrier maintains electrical neutrality by allowing ion migration, preventing charge buildup that would stop the reaction. The identity of the oxidizing and reducing agents is determined by standard reduction potential values.
Electrolytic cells operate with an external power source that forces electrons to flow in the nonspontaneous direction. These are used for processes such as electroplating, electrolysis of water, and production of pure metals. Although the anode is still the site of oxidation and the cathode the site of reduction, their signs are reversed from galvanic cells because the current is externally driven.
Temperature, concentration, and pressure affect cell potential through the Nernst equation: \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q \). This allows prediction of how nonstandard conditions will change the voltage of a cell, a concept that directly ties electrochemistry to thermodynamics and equilibrium.

Free Energy of Dissolution

The free energy change for dissolution determines whether a solute will dissolve spontaneously under given conditions. It is influenced by both enthalpy changes (heat of solution) and entropy changes (disorder increase when solid particles disperse into solution). The equation \( \Delta G_{\text{dissolution}} = \Delta H_{\text{solution}} - T\Delta S_{\text{solution}} \) applies here just like in other thermodynamic processes.
Even endothermic dissolutions can be spontaneous if they produce a sufficiently large positive entropy change. For example, dissolving sodium chloride in water absorbs heat (\( \Delta H > 0 \)) but is still favorable because the ions disperse, significantly increasing system entropy (\( \Delta S > 0 \)).
If \( \Delta G_{\text{dissolution}} \) is positive, the solute has low solubility at that temperature. Many salts with very low solubility have slightly positive free energy changes, and dissolution proceeds only to a small extent, producing a saturated solution at equilibrium.
The temperature dependence of solubility can be predicted using the signs of \( \Delta H \) and \( \Delta S \). For endothermic dissolutions, increasing temperature generally increases solubility, while for exothermic dissolutions, increasing temperature decreases solubility.
In equilibrium contexts, \( \Delta G \) for dissolution connects directly to the solubility product constant (\( K_{sp} \)) via \( \Delta G^\circ = -RT \ln K_{sp} \). A larger \( K_{sp} \) means more negative \( \Delta G^\circ \) and thus greater solubility under standard conditions.

Electrochemistry Fundamentals

Electrochemistry studies chemical processes that involve electron transfer, linking chemical energy to electrical energy. Oxidation is the loss of electrons, and reduction is the gain of electrons; both always occur together in redox reactions. The substance that is oxidized acts as the reducing agent, while the one reduced acts as the oxidizing agent.
An electrochemical cell uses two half-reactions — one oxidation and one reduction — that occur in separate compartments connected by a conductive pathway. This separation forces electrons to travel through an external circuit, generating an electric current that can do work.
In cell notation, the anode (site of oxidation) is written on the left, and the cathode (site of reduction) is written on the right, with a double vertical line representing the salt bridge. The salt bridge allows ion flow to maintain charge balance without mixing the solutions.
Standard electrode potentials (\( E^\circ \)) are measured under standard conditions (1 M, 1 atm, 25°C) and represent the tendency of a half-reaction to be reduced relative to the standard hydrogen electrode (SHE), which is assigned 0.00 V. Positive \( E^\circ \) values indicate favorable reduction tendencies.
The total cell potential (\( E^\circ_{\text{cell}} \)) is calculated by subtracting the anode potential from the cathode potential: \( E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \). A positive \( E^\circ_{\text{cell}} \) means the cell is spontaneous under standard conditions.

Electrolytic Cells

Electrolytic cells are electrochemical cells that drive nonspontaneous redox reactions using an external energy source, such as a battery or power supply. In contrast to galvanic cells, where chemical energy is converted to electrical energy, electrolytic cells convert electrical energy into stored chemical potential energy.
In electrolytic cells, oxidation still occurs at the anode and reduction at the cathode, but the electrodes’ polarity is reversed compared to galvanic cells: the anode is positive and the cathode is negative because electrons are forced into the cathode by the external power source. This reversal of polarity is a direct result of the imposed electric current.
The applied voltage must be at least equal to the cell’s decomposition potential, which accounts for the thermodynamic requirement to drive the reaction plus any overpotential from kinetic barriers. If the applied voltage is insufficient, no net electrolysis will occur.
Electrolytic cells are used in processes such as electroplating (depositing a thin layer of metal on a surface), electrorefining (purifying metals), and the industrial production of chemicals like chlorine, sodium hydroxide, and hydrogen gas. In each case, the specific electrolyte composition and electrode material are chosen to optimize the desired redox reaction.
Quantitative analysis of electrolytic cells uses Faraday’s laws to determine the mass of material deposited or consumed, requiring knowledge of current, time, the number of electrons transferred per mole, and the molar mass of the substance. This connection between electrical measurements and chemical change makes electrolytic cells a key bridge between physics and chemistry concepts.

Galvanic (Voltaic) Cells

Galvanic cells are electrochemical cells that generate electrical energy from a spontaneous redox reaction (\( E^\circ_{\text{cell}} > 0 \)). They consist of two half-cells connected by a wire and a salt bridge, with oxidation at the anode and reduction at the cathode.
Electrons flow through the external circuit from the anode to the cathode, while ions flow through the salt bridge to maintain charge neutrality. Cations generally migrate toward the cathode, and anions migrate toward the anode.
The voltage measured across the electrodes is the cell potential, which depends on the inherent electrode potentials and the concentrations of ions in solution. Standard cell potential (\( E^\circ_{\text{cell}} \)) assumes 1 M concentrations and 1 atm gases.
Common examples of galvanic cells include the Daniell cell (zinc-copper) and commercial batteries like alkaline cells. The principles governing galvanic cells also apply to fuel cells, where continuous reactant supply maintains constant operation.
The spontaneity of the galvanic cell reaction is directly linked to thermodynamics via \( \Delta G^\circ = -nFE^\circ_{\text{cell}} \), where \( n \) is the moles of electrons transferred and \( F \) is the Faraday constant (96,485 C/mol).

Cell Potentials and the Nernst Equation

The Nernst equation allows calculation of cell potential under nonstandard conditions: \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q \), where \( Q \) is the reaction quotient. This shows how concentration changes affect the driving force of the cell.
At 25°C, the equation simplifies to \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0592}{n} \log Q \). Increasing product concentration or decreasing reactant concentration lowers the cell potential, while the opposite changes increase potential.
The Nernst equation predicts that a galvanic cell eventually reaches equilibrium when \( E_{\text{cell}} = 0 \), which occurs when \( Q = K \). At this point, no net electron flow occurs, and \( \Delta G = 0 \).
Concentration cells are a special case where the cell potential arises solely from a difference in ion concentration between two half-cells. These cells operate until concentrations equalize, at which point the potential becomes zero.
Understanding the Nernst equation is essential for real-world electrochemistry, as most electrochemical systems operate under nonstandard conditions, including biological redox reactions and rechargeable batteries.

Relationship Between Gibbs Free Energy and Cell Potential

The relationship is expressed as \( \Delta G^\circ = -nFE^\circ_{\text{cell}} \), linking thermodynamics and electrochemistry. Here, \( n \) is the number of moles of electrons transferred, \( F \) is Faraday’s constant, and \( E^\circ_{\text{cell}} \) is the standard cell potential.
A positive \( E^\circ_{\text{cell}} \) corresponds to a negative \( \Delta G^\circ \), meaning the cell operates spontaneously in the forward direction. Conversely, a negative \( E^\circ_{\text{cell}} \) means \( \Delta G^\circ \) is positive, and the cell is nonspontaneous without an external power source.
For nonstandard conditions, \( \Delta G = -nFE_{\text{cell}} \) applies. As the cell discharges and concentrations change, \( E_{\text{cell}} \) decreases in magnitude until it reaches zero at equilibrium, where \( \Delta G = 0 \).
This relationship also connects to the equilibrium constant through \( \Delta G^\circ = -RT \ln K \) and \( E^\circ_{\text{cell}} = \frac{RT}{nF} \ln K \). Large positive \( E^\circ_{\text{cell}} \) values correspond to large equilibrium constants, heavily favoring products.
Understanding this equation is critical for predicting cell behavior, designing batteries, and interpreting thermodynamic data in an electrochemical context. It bridges the gap between measurable electrical quantities and underlying energy changes.

Faraday’s Laws of Electrolysis

Faraday’s first law states that the amount of chemical change in an electrolytic process is directly proportional to the total electric charge passed through the system. This means that doubling the current or the time it flows will double the amount of substance produced or consumed at the electrodes.
The second law relates the masses of different substances liberated by the same quantity of electricity to their molar masses and the number of electrons involved in their half-reactions. Substances requiring more electrons per mole will have proportionally lower mass deposited for the same charge.
The relationship can be expressed as \( m = \frac{Q \cdot M}{n \cdot F} \), where \( m \) is the mass produced, \( Q \) is total charge (\( I \times t \)), \( M \) is molar mass, \( n \) is the number of electrons per formula unit, and \( F \) is Faraday’s constant (96,485 C/mol e⁻).
In electrolytic cells, the process is nonspontaneous (\( E_{\text{cell}} < 0 \)) and requires an external power source to drive the reaction. The energy supplied is converted into chemical potential energy stored in the products.
Faraday’s laws are essential for industrial applications such as electroplating, aluminum production from bauxite, and chlorine generation from brine. Calculations using these laws determine the exact current and time required to produce a desired amount of material.