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# IRan Education & Research NETwork (IRERNET) mad sg .com

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1. Debye–Hückel theory

2. Agenda • Biography • Introduction • The model of DH Theory • Mathematical development • Extended Debye-Hückel Equation

3. Biography

4. Introduction • In the early 1900s, Several physical chemists, including NielsBjerrum and William Sutherland, assumed that strong electrolytes are completely dissociated in solution. • Based on this assumption, Milner calculated osmotic coefficients, a quantity related to the activity coefficient. • Debye and Hückel developed a mathematical route to treat equilibrium properties of electrolytes. TheDebye–Hückel theory is a theoretical explanation for departures from ideality in electrolytes solutions.

5. Introduction • Ideal Solution: • Measurement quantity are proportional to the concentration of the solute. • Real Solution: • Measurement quantity are proportional to the activation of the solute. The Debye-Hückel limiting lawenables to determine the activity coefficient of an ion in a dilute solution of known ionic strength. A Measurement quantity B C mole fraction

6. The model of DH Theory principal assumption is that departure from ideality is due to electrostatic interactions between ions, mediated by Coulomb's law: It is also assumed that: • The dissolved electrolyte is completely dissociated. • Ions are spherical and are not polarized by the surrounding electric field. • The solvent plays no role other than providing a medium of constant relative permittivity. • There is no electrostriction. • Central ion is surrounded by a spherically symmetric cloud of opposite ions.

7. Mathematical development D&H use the Helmholtz and Gibbs free entropies to express the effect of electrostatic forces in an electrolyte solution. • i: is a species s: is the number of different particle types in solution • Ni: is the number of particles of species i • : is the particle specific Gibbs free entropy of species i • kB: is Boltzmann's constant • : is the mole fraction of species i Ue = ?

8. Mathematical development Step1: Poisson equation r & Step2: Boltzmann distribution

9. Mathematical development With using first order Taylor series approximation for the exponential function: for The Poisson-Boltzmann equation is transformed to: &

10. Mathematical development The equation has the following general solution: D&H say that the total potential inside the sphere is Bi is a constant that represents potential added by the ionic atmosphere and be caused non-ideal behavior.

11. Mathematical development The definition of the Gibbs free entropy is: paper Debye in 1924reformulated his original paper with Hückel (1923), which dealtwith osmotic coefficient. This equation (Debye-Hückel limiting law) is one studies in modern physical chemistry textbooks.

12. Extended Debye-Hückel Equation The assumptions can be challenged: • Complete dissociation: Ion association may take place, particularly with ions of higher charge. • Weak electrolytes: A weak electrolyte is not fully dissociated. • Ions are spherical and are not polarized: Many ions such as the nitrate ion NO3- are manifestly not spherical and Polyatomic ions are also polarizable. • Role of the solvent: The solvent is not a structureless medium. The water molecules in aqueous solution are both dipolar and polarizable. One such Extended Debye-Hückel Equation is:

13. Eponyms of Debye • Debye shielding – In plasmas, semiconductors and electrolytes, the process by which a fixed electric charge is shielded by redistributing mobile charged particles around it. • Debye length – The typical distance in a plasma required for full Debye shielding. • Debye model – A model of the heat capacity of solids as a function of temperature • Debye – a unit of electric dipole moment • Debye frequency - a characteristic vibration frequency of a crystalline lattice. • Debye relaxation – The dielectric relaxation response of an ideal, no interacting population of dipoles to an alternating external electric field. • Debye sheath – The non-neutral layer, several Debye lengths thick, where a plasma contacts a material surface. • Debye-Hückel equation – A method of calculating activity coefficients. • Debye function – A function used in the calculation of heat capacity. • Debye-Scherrer method – A technique used in X-ray powder diffraction. • Debye-Waller factor – A measure of disorder in a crystal lattice. • Lorenz-Mie-Debye theoryTheory of light scattering by a spherical particle. • Debye (crater) – A lunar crater located on the far side and in the northern hemisphere of the moon.