Homework Help
Homework Help
View Details
Assignment Help
Assignment Help
View Details
Online Tutoring
Online Tutoring
View Details
Home » Chemistry Homework Help » Physical Chemistry » Solution Ionic Strength
Solution Ionic Strength
The Debye Huckel theory shows how the potential energy of an ion in solution depends on the ionic strength of the solution.

Except at infinite dilution, electrostatic interaction between ions alters the properties of the solution from those excepted from the free ion model that leads to ideal behavior.

The treatment of ion-ion interactions by Debye-Huckel in 1923 and 1924 led to an explanation of the properties of relatively dilute solutions, less than about 0.01 M. even this limited success has provided valuable in such a way to expolarate available experimental data to the limit of infinite dilution was provided. Also provided was a base for one empirical extension to higher concentrations. It is worthwhile, therefore, to follow through the Debye-Huckel derivation in some detail.

The Debye Huckel treatment deals with the distribution of ions around a given ion and the net effect these neighboring ions have on the ions of the solution.

Consider one of the ions, a positive ion to be specific, of an aqueous solution of an electrolyte. It will be affected by coulombic interactions with the other ions of the solution. These interactions are described by a potential energy term that is distance between them. Thus a nearby ion will have a greater effect on the reference ion than a far off ion will. But the number of such distant ions increases as the volume of a spherical shell, i.e. as r2. Thus these more distant ions, and therefore the bulk of the solution, might appear to require our attention in the deduction of the affect on the reference ion. Fortunately, ions of opposite charge can be expected to distribute themselves uniformly at some distance from a given ion to produce electrical neutrality well removed from a given ion.

Consider first how the ions in a solution distribute themselves relative to each other. The two factors that determine the distribution are thermal jostlings and the electric interaction between charged particles. Suppose that on the average there are n, ions of the I type per unit volume. Around any positive ion there will be an increase in the concentration of negative ions and a decrease in the concentration of positive ions. These changes results from the ions moving to the energetically more favored regions, i.e. those in which their potential energy is low. The tendency for this movement must complete with the traditional thermal motion.

Boltzmann’s equation can be used to give the number of ions that on average are a distance r from the positive charge. The energy of ions of charge Zie in a potential value is (eZi) potential value. If Zi is positive, the energy is higher near the reference positive charge; if Zi is positive, the energy is lower. Boltzmann’s equation gives:

Ni (r)= nie –(eZi∫)/ (kT)


Where ni (r) is the number of ith ions per unit volume at a distance r from the reference positive charge and ni is the average number per unit volume in the solution.

This expression cannot be used directly to calculate the density of ions of each type in the neighborhood of the reference ion, determine the potential ∫. Some manipulation of expression for change densities and potentials is necessary to get around this difficulty.

To provide a reference for this more complex situation, let us first describe the density of ions about the reference positive ion if only the reference change affected the distribution. Then we could write:

∫ = e/(4∏ε)/r

Where e is the charge of the reference ion. The number of ions of type I per unit volume at a distance r form the reference ion is now given by;

ni (r) = nie –e2Zi/(4∏εrkT)

or,

ni (r) /ni = ee2Zi/(4∏εrkT)

the results of the above eq. must be corrected to take into account the effect of the ions that surround the reference ion. To do so, we develop an expression for the net excess negative charge in the region around the reference, positively charged ion.

Charge density around the reference ion: the charge density at a distance r from the unit positive charge given by the number of ions ni(r) of a particular type times the charge eZi of these ions. Thus the charge density can be expressed by:

p(r) = Σ (eZi)ni(r)

if the potential at a distance r is eq, can be used to write:

p(r) = e Σi ni Zie -eZi∫/(kT)

Services:- Solution Ionic Strength Homework | Solution Ionic Strength Homework Help | Solution Ionic Strength Homework Help Services | Live Solution Ionic Strength Homework Help | Solution Ionic Strength Homework Tutors | Online Solution Ionic Strength Homework Help | Solution Ionic Strength Tutors | Online Solution Ionic Strength Tutors | Solution Ionic Strength Homework Services | Solution Ionic Strength

Submit Your Query ???
Topics
Covalent Radii Crystal Shapes, Point Groups Diffraction Pattern Assignments Electron Diffraction Ionic Radii Lattice Energies Diffraction Lattices, Unit Cells Neutron Diffraction Waals Radii X-ray Diffraction Bond Moments Electric Capacitor Atoms, Molecules Properties Paramagnetism Electrolytic Dissociation Solution Ionic Strength Solvent Dielectric Effect Electrolysis Solutions Ionic Mobilities Electrolytes In Solutions Solutions Molar Conductance Solutions Specific Conductance Electrochemical Cell EMF Electrodes Ion Selective Electrodes Junction Potentials Cells Electromotive Force Standard Electrode Potentials Collision Theory Gas Viscosity Theory Elementary Reactions Lasers Molecule-Molecule Collisions Electrochemical Cell Photochemical Quenching Surface Decompositions Atomic Molecular Energies Molecular Energies Particle-in-a-box Particle-on-a-line Rotational Energies Schrodinger Wave Equation De Broglie Wave Length Vibrational Energies Waves And Particles Boltzmann Distribution Gas Heat Capacities Metals Heat Capacities Molecules Collection Energies One Dimensional Motion Partition Function Rotational Motions Thermal Energy Three Dimensional Motion Vibrational Motions Aqueous Ion Energies Bond Energies Chemical Systems Energy Enthalpy, Chemical Reactions Chemical System Enthalpy Thermodynamics First Law Heat Capacities Thermodynamics Molecular Thermal Energy Standard Enthalpy Substance Carnot Cycle Absolute Zero Entropies Entropy Thermodynamics Laws Entropy Molecular Basis Third Law Molecular Basis Rotational Energy Thermodynamics Second Law Thermodynamics Third Law Vapourization Entropy Vibrational Entropy Equilibria And Distributions Real Gases Equilibria Free Energy Equilibrium Constant Free Energy And Pressure Free Energy, Temperature Free Energy Function Free Energy Real Gases Free Energy Fugacity Non-ideal Gases Fugacity Thermodynamic Properties Chemical Equilibria Boyle Gas Pressure Continuity Of States Critical Point Gas Mixtures Kinetic Molecular Theory Gases-Properties, Theories Molecular Energies, Speed Molecular Interactions Real Gas PVT Temperature Volume Waals Gases Behaviour Waals Critical Point Molecular Diameters Virial Equation Diffusion Coefficient Diffusion Molecular View Donnan Membrane Equilibria Electrophoresis Macromolecular Dynamics Average Mass Range Solution Viscosity Sedimentation And Velocity Colloids Macromolecules Micelles Adsorption Isotherm Adsorption Of Gases Boiling Point Diagrams Pressure Temperature Relation Distillation Eutectic Formation Immiscible Liquids Phase Equilibria Liquid Surfaces Phase Rule Pressure Phase Diagrams Solid Compound Foundation Surface Tension Vapour Pressure Three Component System Vapour Pressure Composition Atomic States Bohr Atom Electron Spin Angular Momentum Hydrogen Hydrogen Atom Spectra Hydrogen Radical Factor Quantum Atomic Structure Quantum Mechanical Operators Variation Theorem Enzymes Catalyzed Reactions First Order Rate Equations Flash Photolysis Chemical Reactions Mechanism Enzyme Reactions Mechanism Reactions Mechanisms Photochemical Reactions Rate Equation Second Order Rate Equations Temperatures And Rates Unimolecular Gas Reactions Absorption Coefficient Einstein Coefficient Electromagnetic Induction Electronic Spectra Electron Spin Spectroscopy Infrared Adsorption Spectroscopy Microwave Absorption Nuclear Spin States Nuclear Magnetic Resonance Photoelectron Spectroscopy Polyatomic Vibrational Spectra Rotational Vibrational Spectra Conjugated Systems Spectra Transition Moment Character Tables Symmetry Group Theory Molecular Symmetry Types Orbital Symmetries Point Groups Reducible Representation Symmetry Elements, Operations Molecular Properties Symmetry Transformation Matrices Diatomic Molecule Orbitals Electronegativity Hybridization Hydrogen Molecule Ion Ionic Bond Molecular Orbitals Orbitals Pie Electrons Two Electron Bond Virial Theorem Partial Molal Properties Solute Free Energy Ideal Mixtures Solution Thermodynamic Property Liquid Vapour Free Energies Osmotic Pressure Partial Molal Quantities Solvent Free Energy Vapour Pressure Lowering