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1 IRan Education & Research NETwork (IRERNET) madsg.com

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Debye–Hückel theory 2

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Agenda Biography Introduction The model of DH Theory Mathematical development Extended Debye-Hückel Equation 3

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Biography Peter Joseph William Debye BornMarch 24, 1884 Maastricht, Netherlands DiedNovember 2, 1966 (aged 82) New York, USA FieldsPhysicsPhysics, ChemistryChemistry Institutions University of ZürichUniversity of Zürich (1911–12) University of Utrecht (1912–14) University of Utrecht University of GöttingenUniversity of Göttingen (1914–20) ETH Zürich (1920–27) University of Leipzig (1927–34) Cornell University (1940–50) ETH Zürich University of Leipzig Cornell University Known for Debye–Hückel theory determination of molecular structure using diffraction of X-rays Notable awards Nobel Prize in ChemistryNobel Prize in Chemistry (1936) Priestley Medal (1963) National Medal of Science (1965) Priestley Medal National Medal of Science Erich Armand Arthur Joseph Hückel BornAugust 9, 1896, Berlin DiedFebruary 16, 1980 (aged 84) Marburg FieldsPhysicist, physical chemist Institutions University of Göttingen University of Göttingen (1914–21) University of Göttingen (1921–22) University of Göttingen ETH ZürichETH Zürich (1923–27) Technische Hochschule (1927–34) Phillips University (1935–61) Technische Hochschule Phillips University Known for Debye–Hückel theory Hückel molecular orbital method Notable awards………………. 4

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In the early 1900s, Several physical chemists, including Niels Bjerrum 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. Introduction The Debye–Hückel theory is a theoretical explanation for departures from ideality in electrolytes solutions. 5

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Ideal Solution: Measurement quantity are proportional to the concentration of the solute. Real Solution: Measurement quantity are proportional to the activation of the solute. Introduction A B C mole fraction Measurement quantity The Debye-Hückel limiting law enables to determine the activity coefficient of an ion in a dilute solution of known ionic strength. 6

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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

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i: is a species s: is the number of different particle types in solution N i : is the number of particles of species i : is the particle specific Gibbs free entropy of species i k B : is Boltzmann's constant : is the mole fraction of species i Mathematical development U e = ? 8 D&H use the Helmholtz and Gibbs free entropies to express the effect of electrostatic forces in an electrolyte solution.

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Mathematical development Step1: Poisson equation & Step2: Boltzmann distribution 9 r

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Mathematical development With using first order Taylor series approximation for the exponential function: for The Poisson-Boltzmann equation is transformed to: & 10

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Mathematical development The equation has the following general solution: D&H say that the total potential inside the sphere is B i is a constant that represents potential added by the ionic atmosphere and be caused non-ideal behavior. 11

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Mathematical development The definition of the Gibbs free entropy is: paper Debye in 1924 reformulated his original paper with Hückel (1923), which dealt with osmotic coefficient. This equation (Debye-Hückel limiting law ) is one studies in modern physical chemistry textbooks. 12

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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 NO 3- 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

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Eponyms of Debye 14 Debye shieldingDebye shielding – In plasmas, semiconductors and electrolytes, the process by which a fixed electric charge is shielded by redistributing mobile charged particles around it. Debye lengthDebye length – The typical distance in a plasma required for full Debye shielding. Debye modelDebye model – A model of the heat capacity of solids as a function of temperature DebyeDebye – a unit of electric dipole moment Debye frequencyDebye frequency - a characteristic vibration frequency of a crystalline lattice. Debye relaxationDebye relaxation – The dielectric relaxation response of an ideal, no interacting population of dipoles to an alternating external electric field. Debye sheathDebye sheath – The non-neutral layer, several Debye lengths thick, where a plasma contacts a material surface. Debye-Hückel equationDebye-Hückel equation – A method of calculating activity coefficients. Debye functionDebye function – A function used in the calculation of heat capacity. Debye-Scherrer method Debye-Scherrer method – A technique used in X-ray powder diffraction. Debye-Waller factorDebye-Waller factor – A measure of disorder in a crystal lattice. Lorenz-Mie-Debye theoryLorenz-Mie-Debye theory Theory of light scattering by a spherical particle. Debye (crater)Debye (crater) – A lunar crater located on the far side and in the northern hemisphere of the moon.

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