Ion and a Dipole

The problem is to calculate the interaction energy between a dipole and an ion placed at a distance r from the dipole center, the dipole being oriented at an angle 0 to the line joining the centers of the ion and dipole G ig. A2.2.1). (By convention, the direction of the dipole is taken to be the direction from the negative end to the positive end of the dipole.) 

The ion-dipole interaction energy U, i, is equal to the charge z, of the ion times the potential due to the dipole at the site P of the ion 

the problem reduces to the calculation of the potential v due to the dipole. According to the law of superposition of potentials, the potential due to an assembly of charges is the sum of the potentials due to each charge. Thus, the potential due to a dipole is the sum of the potentials and - /rjdue to the charges +q and -q, which 

At this stage, an important approximation is made, namely, that the distance 2d between the charges in the dipole is negligible compared with r. In other words, the approximation is made that 

It is clear that the validity of the approximation deaeases, the closer the ion comes toward the dipole, i.e., as r deaeases. 

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Properties of Different Solvents. In discussing molecular dipoles in Sec. 25, we estimated the force of attraction between an atomic ion and a dipole having the most favorable orientation and found this attraction to be very strong. In any ionic co-sphere those molecular dipoles which have a favorable orientation will bo attracted, while those that have the opposite orientation will be repelled. Since the former are more numerous the solvent in the co-sphere is, on the whole, attracted toward the ion. Since the liquid is not incompressible, we must expect that this will lead to a contraction in each co-sphere. In any ionic solution the sum of the contractions that have taken place in the co-spheres of the positive and negative ions will be apparent if we measure accurately the volume of the solution. 

Ion a charged species created when an atom or group of atoms gains or loses electrons Ion-Dipole Force intermolecular force between an ion and a dipole Ion Pair in a solution when a positive and negative ion exist as a single particle Ion Product Constant in an ionic reaction, the product of each ion s concentration in solution raised to a power equal to the coefficient in the net ionic equation, for water it equals [H+][OH ]... 

Since the potential energy of interaction between two ions is proportional to 1 /eT, then the lower the relative permittivity of a solvent, the greater will be the attraction between ions of opposite charge. A similar relation holds for the interaction between an ion and a dipole, and between two dipoles. So solvents of low relative permittivity encourage associative behaviour. 

As an ion and a dipole are separated by the distance r and the intermolecular distance is much larger than the dipole distance, the ion-dipole interaction potential is given by ... 

For a reaction between two dipoles having no net charge, the second term disappears, and the solvent effect is given entirely by the last term Eq. (5-93) then equals Eq. (5-88) in Section 5.4.3. For a reaction between an ion and a dipole (or between two charged dipoles) both terms must be included. The simplest case is for the reaction of a monovalent, structureless ion A of charge za = 0) with a neutral molecule B... 

Ion pair. A species made up of at least one cation and at least one anion held together by electrostatic forces. (12.7) Ion-dipole forces. Forces that operate between an ion and a dipole. (11.2) Ion-product constant. Product of hydrogen ion concentration and hydroxide ion concentration (both in molarity) at a particular temperature. (15.2) Ionosphere. The uppermost layer of the atmosphere. (17.1)... 

These bonds involve electrostatic forces, such as those between two ions, an ion and a dipole, or two dipoles. The ratio of the cation (r,.)to the anion (rj is called the radius ratio. As the ratio of the cation to anion decreases below 1, the lattice energy remains about the same at first and then decreases... 

Derive the expressions for the angle-averaged potential energy of interaction bet>veen an ion and a dipole given by Eqs. (7-7) and (7-8) from Eq. (7-6) and the Boltzmann expression for the equilibrium energy distribution. 

Most often, the electrostatic bond is between two ions (the ionic bond or salt linkage ). There are variants in which the bond is formed between an ion and a dipole or between two dipoles. They are all maintained by purely electrostatic forces.The ionic bond has a strength of about 5 kcal/mol and declines by the second power of the distance between the opposite charges. Sodium chloride (Na Cl ) is a typical example. In aqueous solution, each ion is able to move about freely so long as it does not leave the field of its counterion in other words, the bond is non-directional and non-rigid. 

The interaction between an ion and a dipole (Fig. 1.8) depends on the cube of the distance between them (equation 5). Like dipole-dipole interactions, these interactions depend on the orientation of the dipole with respect to the ion. 

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