Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Physical Chemistry → Electrochemistry ↓


Conductivity and mobility


Electrochemistry extends its relevance to many fields, including physical chemistry, materials science, and chemical engineering. A detailed understanding of conductivity and mobility forms the backbone of electrochemical applications ranging from battery technologies to biological systems. In this exposition, we will explore the fundamental concepts of ionic conductivity and mobility, the associated mathematical formulas, illustrative examples, and their real-world applications.

Understanding conductivity

Conductivity, in a broad sense, refers to the ability of a substance to conduct an electric current. In electrochemistry, we particularly focus on ionic conductivity, which deals with the movement of charged particles, typically ions, through a medium. Conductivity ((sigma)) is defined as the inverse of resistivity ((rho)). Therefore, it can be mathematically represented as:

(sigma = frac{1}{rho})

In this context, resistivity is the intrinsic property of a medium that impedes the flow of electric current.

Mathematical formulation of conductivity

Conductivity is affected by both the concentration of the charged species and their mobility. The simplest representation for the conductivity of an electrolyte solution is given by Kohlrausch's law for an electrolyte:

(sigma = c cdot |z| cdot F cdot (u_+ + u_-))

Where:

  • c = concentration of ions (mol/L)
  • |z| = absolute value of charge of the ions
  • F = Faraday constant (96500 C/mol)
  • u_+, u_-) = ion mobility of cations and anions respectively (m2/V s)

Discovery of ionic mobility

Ionic mobility (u) refers to how quickly an ion moves in a solution under an electric field. It is a measure of the velocity acquired by an ion per unit electric field. Mobility represents the response of ions to the applied electric field:

(u = frac{v}{E})

Where:

  • v = drift velocity of the ion (m/s)
  • E = electric field strength (V/m)

Factors affecting ionic mobility

  • Ion size: Larger ions have lower mobility because they experience a greater pull from the solvent. For example, compare the mobility of Na + and K +. Typically, K + will have a slightly lower mobility because it is slightly larger than Na +.
  • Solvent viscosity: A solvent with high viscosity offers greater resistance to the movement of ions, reducing their mobility.
  • Temperature: Generally, increase in temperature increases the mobility of ions because it decreases the viscosity of the solvent.
  • Strength of electric field: Strong electric field increases the forces acting on the ions, thereby increasing their velocity.

Relation of conductivity and mobility

Conductivity and mobility are interrelated through the concentration of ions. Higher mobility means higher contribution to conductivity because ions in faster motion significantly enhance the conduction process. Individual ionic mobilities contribute to the total conductivity:

(sigma = sum_{i}^{} c_i cdot |z_i| cdot F cdot u_i)

Here, c_i denotes the concentration of ion i, z_i denotes its charge and u_i denotes its mobility.

Example calculation

Consider an aqueous solution of sodium chloride (NaCl). The concentration of the solution is 0.1 mol/L. The ionic mobilities are calculated u_{Na^+} = 5.19 times 10^{-8} text{ m}^2/text{V}cdottext{s} and u_{Cl^-} = 7.91 times 10^{-8} text{ m}^2/text{V}cdottext{s} using the formula:

(sigma = c cdot F cdot (u_{Na^+} + u_{Cl^-}) = 0.1 cdot 96500 cdot (5.19 times 10^{-8} + 7.91 times 10^{-8}))

The above calculation gives the conductivity (sigma approx 1.26 , text{S/m}), which shows strong current carrying capacity.

Applications in real-world scenarios

Understanding and controlling conductivity and mobility in electrochemical systems has many applications, including:

Batteries

In battery technology, the conductivity of the electrolyte is a key factor determining the efficiency and power output of the battery. The non-aqueous electrolytes used in lithium-ion batteries are specifically chosen for their high ionic mobility, which allows efficient operation even at low temperatures.

Fuel cells

Fuel cells rely heavily on ionic conduction through membranes which makes considerations of both conductivity and ionic mobility important. For example, proton exchange membrane (PEM) fuel cells focus specifically on proton mobility within the membrane to ensure efficient water management and energy conversion.

Biological systems

Ionic mobility and conductivity are also fundamental in a variety of biological processes, including nerve impulse transmission and muscle contraction, which depend on the rapid movement of ions such as sodium (Na +), potassium (K +), and calcium (Ca 2+).

Visualization of conductivity and mobility

To make this concept clear, consider a simple example:

Ions moving in an electric field

In the diagram above, the circles represent ions moving through the medium. The speed of the ions (conductivity) and their instantaneous response to the electric field (mobility) are represented conceptually by directional arrows.

Conclusion

The complex dance of ions under the influence of an electric field – embodied by conductivity and mobility – plays a key role in many applications crucial to modern technology and natural processes. A thorough understanding of these parameters serves as a basis for designing and optimizing electrochemical devices and systems across a wide range of industries. As we continue to explore new materials and innovative applications, the concepts of ionic mobility and conductivity will remain at the forefront of technological advancement.


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