PHD
  1. Inorganic chemistry  1.1. Coordination chemistry  1.1.1. Ligand field theory  1.1.2. Crystal field theory  1.1.3. Molecular Orbital Theory for Coordination Compounds  1.1.4. Stability of Coordination Compounds  1.1.5. Electronic spectra of coordination compounds  1.1.6. Isomerism in Coordination Compounds  1.1.7. Kinetics and mechanism of coordination reactions  1.2. Organometallic Chemistry  1.2.1. Metal Carbonyls  1.2.2. Metal alkyl and aryl  1.2.3. Fischer and Schrock carbonaceans  1.2.4. Oxidative Addition and Reductive Elimination  1.2.5. Metal Hydrides  1.2.6. Catalysis by organometallic compounds  1.2.7. Metallocenes and Sandwich Complexes  1.2.8. CH activation  1.3. Solid state chemistry  1.3.1. Crystal structures and lattices  1.3.2. Band theory and electrical properties  1.3.3. Defects in the crystal  1.3.4. Synthesis of solid state materials  1.3.5. Magnetic and optical properties of solids  1.3.6. Superconductivity  1.3.7. Solid state ionics  1.4. Bio-inorganic chemistry  1.4.1. Metalloproteins and enzymes  1.4.2. Metal ion transport and storage  1.4.3. The role of metals in medicine  1.4.4. Bioinspired catalysis  1.4.5. Metal–DNA interactions  1.4.6. Metal Complexes in Medical Science  1.5. Lanthanides and Actinides  1.5.1. Electronic configuration and oxidation states in lanthanides and actinides  1.5.2. Spectral and Magnetic Properties in Lanthanides and Actinides  1.5.3. Separation and Extraction of Lanthanides and Actinides  1.5.4. Coordination chemistry of f-block elements  1.6. Main Group Chemistry  1.6.1. Chemistry of boron compounds  1.6.2. Chemistry of Silicon and Germanium Compounds  1.6.3. Chemistry of Phosphorus and Sulfur Compounds  1.6.4. Organosilicon chemistry  1.6.5. Noble Gas Chemistry
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition and substitution reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic Reactions  2.1.7. Photochemical reactions  2.2. Stereoscopic  2.2.1. Chirality and optical activity  2.2.2. Structural analysis  2.2.3. Stereoelectronic effects  2.2.4. Asymmetric synthesis  2.2.5. Dynamic Stereochemistry  2.3. Organometallic Chemistry in Organic Synthesis  2.3.1. Organolithium and organomagnesium reagents  2.3.2. Transition metal catalyzed coupling reactions  2.3.3. Palladium-catalyzed reactions  2.3.4. Olefin Metathesis  2.3.5. Gold and silver catalysis  2.4. Natural products chemistry  2.4.1. Alkaloids and terpenoids  2.4.2. Steroids and Flavonoids  2.4.3. Total synthesis of natural products  2.4.4. Biosynthesis of natural products  2.5. Supramolecular Chemistry  2.5.1. Host-Guest Chemistry  2.5.2. Self-assembly and molecular recognition  2.5.3. Supramolecular Catalysis  2.5.4. Molecular Machines
  3. Physical Chemistry  3.1. Thermodynamics  3.1.1. Laws of Thermodynamics  3.1.2. Chemical Potential and Equilibrium  3.1.3. Statistical thermodynamics  3.1.4. Non-equilibrium thermodynamics  3.2. Quantum Chemistry  3.2.1. Schrödinger equation and its applications  3.2.2. Molecular orbital theory  3.2.3. Density functional theory  3.2.4. Post-Hartree–Fock methods  3.3. Chemical kinetics  3.3.1. Reaction rate theory  3.3.2. Mechanism and rate laws  3.3.3. Catalysis and enzyme kinetics  3.3.4. Reaction dynamics  3.4. Spectroscopy and molecular structure  3.4.1. Infrared Spectroscopy  3.4.2. UV-visible spectroscopy  3.4.3. Nuclear Magnetic Resonance Spectroscopy  3.4.4. Mass Spectrometry  3.4.5. Raman Spectroscopy  3.5. Surface and Colloid Chemistry  3.5.1. Absorption and Catalysis  3.5.2. Surfactants and micelles  3.5.3. Colloidal Stability  3.5.4. Nanomaterials and Interfaces
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.1.4. Ion Chromatography  4.2. Electroanalytical techniques  4.2.1. Voltammetry and Polarography  4.2.2. Conductometry and potentiometry  4.2.3. Colometry  4.3. Spectroscopic Methods  4.3.1. Atomic absorption spectroscopy  4.3.2. Fluorescence Spectroscopy  4.3.3. X-ray diffraction  4.3.4. Electron paramagnetic resonance spectroscopy  4.4. Chemometrics  4.4.1. Data processing and statistical methods  4.4.2. Multidisciplinary analysis  4.4.3. Machine Learning in Analytical Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.2. Quantum chemistry methods  5.3. Computational drug design  5.4. Machine Learning in Chemistry  5.5. Ab initio molecular dynamics
  6. Biophysics and Medicinal Chemistry  6.1. Drug discovery and design  6.2. Enzyme kinetics and inhibition  6.3. Chemical biology approach  6.4. Protein-ligand interactions  6.5. Bioorthogonal chemistry
  7. Materials chemistry  7.1. Polymer chemistry  7.1.1. Polymerization mechanism  7.1.2. Functional Polymers  7.1.3. Biodegradable Polymer  7.1.4. Conducting and semiconducting polymers  7.2. Nano Chemistry  7.2.1. Nanoparticles and nanostructures  7.2.2. Carbon-based nanomaterials  7.2.3. Quantum dots  7.3. Energy and Environmental Chemistry  7.3.1. Battery and Fuel Cell Chemistry  7.3.2. Green chemistry and sustainable materials  7.3.3. Photocatalysis

PHD → Physical Chemistry → Thermodynamics ↓


Chemical Potential and Equilibrium


Chemical potential and equilibrium are important concepts in thermodynamics, particularly in the field of physical chemistry. These concepts play a vital role in understanding how reactions occur, how substances behave under different conditions, and how the overall energy exchange occurs in chemical systems. Let us look at these topics in detail.

Understanding chemical potential

The term "chemical potential" refers to the change in the Gibbs free energy of a system when an additional amount of a substance is added to it at constant temperature and pressure. Essentially, it is a measure of the tendency of particles to move from one phase or chemical state to another. It is an intensive property, meaning that it does not depend on the amount of substance.

Mathematically, the chemical potential, denoted by μ, for component i in a system can be expressed as:

μ i = (∂G/∂n i) T,P,n j ≠i

where G is the Gibbs free energy, n i is the number of moles of component i, and the partial derivative is taken at constant temperature, pressure, and moles of the other components.

The chemical potential indicates how the energy of a system changes as the amount of substance changes, giving information about the driving forces of reactions and phase transitions.

Visual example of chemical potential

phase 1 phase 2 μ₁ μ₂

In this illustration, we have two phases: light blue for phase 1 and light coral for phase 2, which are separated by a line. The chemical potential μ₁ for phase 1, and μ₂ for phase 2, can help us understand which direction the substance will naturally move in to achieve equilibrium.

Understanding chemical equilibrium

Chemical equilibrium occurs when a chemical reaction and its opposite reaction proceed at the same rate. At this point, the concentrations of reactants and products remain constant over time, reflecting a state of dynamic equilibrium.

The state of chemical equilibrium can be described by the equality of the chemical potentials of the reactants and products. This concept can be extended to any reaction:

AA + BB ⇌ CC + DD

on balance:

μ A + μ B = μ C + μ D

This balance of chemical potentials ensures that the forward and reverse reactions occur at the same rate.

Visual example of chemical equilibrium

Reactants Products

In this visual example, the yellow circle represents the reactants, and the green circle represents the products. The double-headed arrow shows the dynamic nature of the equilibrium state where transitions from reactants to products and back occur at the same rate.

Role of Gibbs free energy

Gibbs free energy (G) is an important concept in understanding chemical potential and equilibrium. It is defined as:

G = H – TS

where H is enthalpy, T is temperature, and S is entropy. The change in Gibbs free energy for a process, ΔG, determines the spontaneity of the process:

  • If ΔG < 0, then the process is spontaneous.
  • If ΔG = 0, then the system is at equilibrium.
  • If ΔG > 0, then the process will occur spontaneously.

At equilibrium, the change in Gibbs free energy, ΔG, is zero, meaning there is no net change to the system.

Text Example of Gibbs free energy application

Consider the response:

N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g)

Here, the Gibbs free energy change can be obtained using the chemical potentials of nitrogen, hydrogen, and ammonia:

ΔG = 2μ NH₃ - (μ N₂ + 3μ H₂)

At equilibrium, ΔG = 0, which means:

2μ NH₃ = μ N₂ + 3μ H₂

Le Chatelier's principle and equilibrium

Le Chatelier's principle is an important part of understanding chemical equilibrium. It states that if an external stress is applied to a system at equilibrium, the system adjusts itself to minimize that stress and achieve equilibrium.

Examples of stress include changes in concentration, pressure, and temperature:

  • Increasing the concentration of the reactants will shift the equilibrium and more products will be formed.
  • Increasing the pressure will shift the equilibrium towards the side where there are fewer moles of gas.
  • An increase in temperature will shift the equilibrium depending on the endothermic or exothermic nature of the reaction.

Textual Example of Le Chatelier's principle

Consider the exothermic reaction:

N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g)

If the temperature is increased, the equilibrium will shift to the left in favor of the reactants, because the reaction is exothermic, and the heat released will offset the additional temperature.

Applications in real-world scenarios

An understanding of chemical potentials and equilibria is fundamental to many applications, ranging from industrial synthesis processes to biological systems.

Text Example of Industrial Application

In the Haber process for ammonia production:

N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g)

Controlling temperature and pressure based on equilibrium principles results in maximum yield of ammonia, which is important for fertilizer production.

Text Example of Biological Application

In biological systems, the chemical potential of ions across membranes determines muscle contractions, nerve impulses, and other vital processes, emphasizing the role of balance in the molecular machinery of life.

Conclusion

Chemical potential and equilibrium are powerful concepts in physical chemistry, covering reaction kinetics, phase transitions, and the effects of external conditions. These principles are not only foundational in academic studies but are also vital in industrial and biological processes. Understanding and using these principles allows chemists to effectively predict and manipulate chemical reactions, leading to advances in technology and a better understanding of natural phenomena.


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Chemical Potential and Equilibrium

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