Law Kohlrausch

The porous medium under investigation must be filled with an electrically conducting liquid, that is, an electrolyte solution. The electric conductivity is given by the empirical Kohlrausch law [53]... 

This equation is valid for both strong and weak electrolytes, as a = 1 at the limiting dilution. The quantities A = zf- FU have the significance of ionic conductivities at infinite dilution. The Kohlrausch law of independent ionic conductivities holds for a solution containing an arbitrary number of ion species. At limiting dilution, all the ions conduct electric current independently the total conductivity of the solution is the sum of the contributions of the individual ions. 

Fig. 2.4 Dependence of molar conductivity of strong electrolytes on the square root of concentration c. The dashed lines demonstrate the Kohlrausch law (Eq. 2.4.15)...

The first we will consider is based on the Kohlrausch law, which for stress relaxation is given by... 

Figure 4.16 The conductivity of a solution. The total transfer of electricity is not necessarily shared equally because different ions move at different speeds. The Kohlrausch law says that the total conductivity of an electrolyte is the sum of the conductivities of the anions and the cations.

Kohlrausch law phys chem 1. The law that every ion contributes a definite amount to the equivalent conductance of an electrolyte in the limit of infinite dilution, regardless of the presence of other ions. 2. The law that the equivalent conductance of a very dilute solution of a strong electrolyte is a linear function of the concentration. kol,raush, l6 ... 

Furthermore, the equivalent conductivity is known to decrease with concentration as c1/2 for dilute solutions (Kohlrausch law). At higher concentrations the conductivity usually increases above the Kohlrausch law value [107]. Furthermore, in weakly polar solvents, there is extensive evidence that strong electrolytes do not dissociate completely, but neutral ion pairs remain in solution [107]. Indeed, solutions of alkali metals in ethers have received considerable attention and two forms of alkali-metal-cation—solvated electron ion pair have been characterised by Seddon et al. [108]. Reactions of an ion as an ion or when ion-paired should be considered as two totally different processes. 

On the other hand the equivalent conductance of weak electrolytes rises much steeper on dilution yet it doesn t nearly attain its limit value A° at concentrations mentioned in the previous case. As the measurement of the conductance at still higher dilution is extremely inaccurate due to high resistances of the solution, the same method of extrapolation as used with the strong electrolytes is unsuitable for determination of A0 of weak electrolytes. In such cases we resort to the Kohlrausch law of independent migration of ions, to l e discussed further on. 

The method of calculating the degree of dissociation using equation (III-27) will be demonstrated for example by phosphoric acid of 0.1 gram-equivalent per litre concentration which dissociates to ions H+ and H2P04. Its equivalent conductance at infinite dilution and at 18 °C will be calculated according to the Kohlrausch law ... 

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... 

The molar conductivity of an electrolyte is the more generally useful quantity since the Kohlrausch law allows its limiting value to be resolved into those of its constituent ions. Comparison between different electrolytes with a common ion therefore allows the determination of an unknown molar conductivity. However, the quantity typically measured is the overall electrolytic conductivity. A way to apportion the conductivity (and hence mobility) to the individual ions of the electrolyte is required. Equation (20.1.2-11) shows that resolution of the molar conductivity into the terms arising from its constituent ions is possible if the transference number of the ion is found. Although this property and the methods developed to measure it may seem rather arcane, it has been of fundamental importance in the understanding of the conductivity and diffusion potentials developed within electrolyte solutions. Experimentally, a number of ways of measuring transference numbers have been developed these are summarised below. 

As mentioned, the detector continually measures the conductivity of the buffer solution in the capillary. If an ionic component enters the detector cell, the local conductivity will change. At first glance, one would expect the conductivity to increase, because of additional ionic material. This is a simplified and incorrect approach, however. Suppose, in a buffer consisting of O.OIM potassium and 0.02M acetate (pH 4.7), a 10" M sodium solution is analyzed. Electroneutrality requires that with an increase of the sodium concentration from zero to, in this case, initially 10 Af, the potassium and/or charged acetate concentration cannot remain unchanged. This process is governed by the so-called Kohlrausch law. For strong ions, this equation reads... 

Fig. 6.21 Comparison of the simulation data (solid line) and various fitting formulae at r = 0.19. The short time expansion of the Rouse model and the Kohlrausch law are represented by a dashed line with long dashes and by a dashed-dotted line, respectively. The dashed line with the short heavy dashes corresponds to the short time expansion of the scaling function (eq. [6.29]) whereas the dotted line refers to its long time part. The model is the same as in Fig. 6.20.

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