Debye-Huckel-Onsager theory conductivity

See - conductance, - conductivity cell, -> conductometry, - Debye-Falkenhagen effect, -> Debye-Huckel-Onsager theory, - electrolyte, -> ion, -> Kohlrausch square root law, - mass transport. 

Debye-Huckel-Onsager theory — (- Onsager equation) Plotting the equivalent conductivity Aeq of solutions of strong electrolytes as a function of the square root of concentration (c1/2) gives straight lines according to the - Kohlrausch law... 

As the dependency does not include any specific property of the ion (in particular its chemical identity) but only its charge the explanation of this dependency invokes properties of the ionic cloud around the ion. In a similar approach the Debye-Huckel-Onsager theory attempts to explain the observed relationship of the conductivity on c1/2. It takes into account the - electrophoretic effect (interactions between ionic clouds of the oppositely moving ions) and the relaxation effect (the displacement of the central ion with respect to the center of the ionic cloud because of the slightly faster field-induced movement of the central ion, - Debye-Falkenhagen effect). The obtained equation gives the Kohlrausch constant ... 

It is a function expressing the effect of charge of the ions in a solution. It was introduced by -> Lewis and Randall [iii]. The factor 0.5 was applied for the sake of simplicity since for 1 1 electrolytes I = c (electrolyte). It is an important quantity in all electrostatic theories and calculations (e.g., - Debye-Huckel theory, - Debye-Htickel limiting law, - Debye-Huckel-Onsager theory) used for the estimation of -> activity coefficients, -> dissociation constants, -> solubility products, -> conductivity of -> electrolytes etc., when independently from the nature of ions only their charge is considered which depends on the total amount (concentration) of the ions and their charge number (zj). 

One caimot, however, expect the Debye-Huckel-Onsager theory of the nonequilibrium conduction properties of ionic soiutions to fare better at high concentration than the corresponding Debye-Hiickel theory of the equilibrium properties (e.g.. 

Conductivity equations based on Debye-Huckel-Onsager theory, such as Equation 17.9, cannot predict the conductance maxima. They are valuable tools to study dilute solutions in a concentration range below the maximum where the solvent may be described as a homogeneous medium with permittivity and viscosity of the pure solvent compound. For extension of the transport equations in the theory of transport properties, especially the continuity equation approach, the reader is referred to Ref [183] and the references given there. 

The A, /c empirical relation found by Kohlrausch can be explained on the basis of the analogy of the gas and solution properties. According to the simple kinetic theory of gasesthe root-mean-square velocity /v is related (46) to /P by s/v = /3P7r where is the density of the gas. In dilute solutions, therefore, the conductivity (or the mobility) of the ions is proportional to /n or 7c. On the other hand, the Debye-Huckel-Onsager (D-H-0) limiting law,... 

The first chapter of the book sets the stage for many of the topics dealt with later, and, in particular, is a prelude to the development of the two major theoretical topics described in the book, namely the theory of non-ideality and conductance theory. The conventional giants of these fields are Debye and Hiickel with their theory of non-ideality and Debye, Huckel, Fuoss and Onsager with their various conductance equations. These topics are dealt with in Chapters 10 and 12. In addition, the author has included for both topics a qualitative account of modern work in these fields. There is much exciting work being done at present in these fields, especially in the use of statistical mechanics and computer simulations for the theory of nonideality. Likewise some of the advances in conductance theory are indicated. 

It is found that in many cases experimental values of conductances do not agree with theoretical values predicted by the Onsager equation (see Equation (4.18)) and that mean ion activity coefficients cannot always be properly predicted by the Debye-Huckel theory. It was suggested by Bjerrum that, under certain conditions, oppositely charged ions of an electrolyte can associate to form ion pairs. In some circumstances, even association to the extent of forming triple or quadruple ions may occur. The most favourable situation for association is for smaller ions with high charges in solvents of low dielectric constant. Hence such phenomena occur to a usually small extent in water. 

This equation is often referred to as Ostwald s dilution law. It depends on the assumptions (a) that ionic conductivities have constant values, and are not dependent on the concentration and (b) that the ions in dilute solution behave as ideal solutes. Both of these assumptions proved to be mistaken, and were finally corrected in the interionic attraction theory of Debye and Huckel and the conductance equation of Onsager (see conductance of aqueous solutions, conductance equations). 

The treatment of the uncondensed counterions bears the same logical relation to the equilibrium theory as does the Onsager conductance theory [48] to Debye-Huckel theory in simple salt solutions. The calculation shows that the net effect of the electro-... 

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