Kohlrausch equation

Kohlrausch equation This equation, which describes the behaviour of strong electrolytes on dilution, states that... 

This section would not be complete without mention of the complementary indirect m.b. method. Here the concentration of the adjusted Kohlrausch solution behind the boundary is measured the transference number of the following ion-constituent can then be calculated from the Kohlrausch equation and a knowledge of the transference number of the leading ion-constituent. 6.S. Hartley and his co-coworkers (21) were the first to develop this approach which has proved valuable for determining transference numbers of very slow ion-constituents such as cetyltrimethylammonium (6 1) and other surfactant species and, quite recently, of cadmium in dilute aqueous CdCl solutions (62.). ... 

For transitions which involve reanangemenl of the structure, sudi as the glass transitions, the temperature dependence of parameter T in the Kohlrausch equation is... 

As already mentioned, the criterion of complete ionization is the fulfilment of the Kohlrausch and Onsager equations (2.4.15) and (2.4.26) stating that the molar conductivity of the solution has to decrease linearly with the square root of its concentration. However, these relationships are valid at moderate concentrations only. At high concentrations, distinct deviations are observed which can partly be ascribed to non-bonding electrostatic and other interaction of more complicated nature (cf. p. 38) and partly to ionic bond formation between ions of opposite charge, i.e. to ion association (ion-pair formation). The separation of these two effects is indeed rather difficult. 

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. 

Where p defines the shape of the hole energy spectrum. The relaxation time x in Equation 3 is treated as a function of temperature, nonequilibrium glassy state (5), crosslink density and applied stresses instead of as an experimental constant in the Kohlrausch-Williams-Watts function. The macroscopic (global) relaxation time x is related to that of the local state (A) by x = x = i a which results in (11)... 

Na and K azides were detd in solns of varying concns by Petrikalns Ogrins (Ref 12).They also detd the density and refractive index for crystn Na and K azides. The ionic conductance of solid Li azide, as detd by Jacobs Tomkins (Ref 18), obeyed the general equation log k = log A - (E/2.303RT) where k is the specific conductivity in ohm-1 cm"1 A is a constant and E is activation energy in kcal/ mol. For Li azide log A 0.840, E is 19.1 and T, the temp range 300 370°K. The Raman Effect of crystn Li azide was detd by Kahovec Kohlrausch (Ref 14/, the observed frequency, 1368.7 cm-1, corresponded to the oscillation in a linear triatomic molecule. 

Kohlrausch s law can be assumed to apply at concentrations up to about HF4 kmol/mJ. For a fully dissociated electrolyte at these concentrations, from equations 6.72 and 6.73 ... 

We now explore whether the pattern of reactivity predicted by the Marcus theory is found for methyl transfer reactions in water. We use equation (29) to calculate values of G from the experimental data where, from (27), G = j(JGlx + AG Y). The values of G should then be made up of a contribution from the symmetrical reaction for the nucleophile X and for the leaving group Y. We then examine whether the values of G 29) calculated for the cross reactions from (29) agree with the values of G(27) calculated from (27) using a set of values for the symmetrical reactions. The problem is similar to the proof of Kohlrausch s law of limiting ionic conductances. 

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 ... 

Feb. 19,1859, Wijk, Sweden - Oct. 2,1927, Stockholm, Sweden). Arrhenius developed the theory of dissociation of electrolytes in solutions that was first formulated in his Ph.D. thesis in 1884 Recherches sur la conductibilit galvanique des dectrolytes (Investigations on the galvanic conductivity of electrolytes). The novelty of this theory was based on the assumption that some molecules can be split into ions in aqueous solutions. The - conductivity of the electrolyte solutions was explained by their ionic composition. In an extension of his ionic theory of electrolytes, Arrhenius proposed definitions for acids and bases as compounds that generate hydrogen ions and hydroxyl ions upon dissociation, respectively (- acid-base theories). For the theory of electrolytes Arrhenius was awarded the Nobel Prize for Chemistry in 1903 [i, ii]. He has popularized the theory of electrolyte dissociation with his textbook on electrochemistry [iv]. Arrhenius worked in the laboratories of -> Boltzmann, L.E., -> Kohlrausch, F.W.G.,- Ostwald, F.W. [v]. See also -> Arrhenius equation. 

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 has the familiar form of the Kohlrausch-Williams-Watts (KWW) equation [17], except that p and x are not empirical constants here, and they will be discussed in the next two sections. 

Thus, the theory of ionic ciouds has been abie to give rise to an equation that has the same form as the empiricai iaw of Kohlrausch (Section 4.3.9). 

From Kohlrausch s measurements on the conductance of saturated solutions of pure silver chloride the specific conductance at 25 may be estimated as 3.41 X lO" ohm cm. the specific conductance of the water used was 1.60 X 10 ohm cm. , and so that due to the salt may be obtained by subtraction as 1.81 X 10 ohm cm. This is the value of K to be employed in equation (26). From Table XIII the equivalent conductance of silver chloride at infinite dilution is 138.3 ohms cm.2 at 25 , and so if this is assumed to be the equivalent conductance in the saturated solution of the salt, it follows from equation (26) that... 

If Kohlrausch s law of independent ionic migration is applicable to solutions of appreciable concentration, as well as to infinite dilution, as actually appears to be the case, the equivalent conductance of an electrolyte MA may be represented by an equation similar to the one on page 57, viz.. 

One of the features observed in many glass-forming liquids is the non-linear nature of any relaxation processes that occur around and below Tg. The relaxation rate is found to depend on the sign of initial departure of actual sample from the equilibrium state. The relaxation rate is described well by the Kohlrausch-Williams-Watts (KWl O empirical equation. ... 

---