Ion H+ OH" Li + Na + K+ Rb + Cs + 0 5 15 18 315 171 25 35 45 55 100 in .NET

Creator barcode data matrix in .NET Ion H+ OH" Li + Na + K+ Rb + Cs + 0 5 15 18 315 171 25 35 45 55 100
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Fig. 2.6 Electrophoretic effect. The ion moves in the opposite direction to the ionic atmosphere
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electric field and of the ionic atmosphere in the opposite direction (Fig. 2.6). Both the central ion and the ions of the ionic atmosphere take the neighbouring solvent molecules with them, which results in a retardation of the movement of the central ion. For very dilute solutions, the motion of the ionic atmosphere in the direction of the coordinates can be represented by the movement of a sphere with a radius equal to the Debye length LU = K~1 (see Eq. 1.3.15) through a medium of viscosity r/ under the influence of an electric force zteExy where Ex is the electric field strength and zt is the charge of the ion that the ionic atmosphere surrounds. Under these conditions, the velocity of the ionic atmosphere can be expressed in terms of the Stokes' law (2.6.2) by the equation (2.4.18) The electrolytic mobility of the ionic atmosphere around the ith ion can then be defined by the expression zte
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(2.4.19)
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This quantity can be identified with deceleration of the ion as a result of the motion of the ionic atmosphere in the opposite direction, i.e.
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Fig. 2.7 Time-of-relaxation effect. During the movement of the ion the ionic atmosphere is renewed in a finite time so that the position of the ion does not coincide with the centre of the ionic atmosphere
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The time-of-relaxation effect (see Fig. 2.7) originates in a certain time delay (relaxation) required for the renewal of the spherical symmetry of the ionic atmosphere around the central ion moving under the influence of an applied electric field. The disappearance of the ionic atmosphere after removal of the central ion, similar to its formation, is an exponential function of time; in fact, both of these processes are complete after twice the relaxation time, which is of the order of 10~7 to 10~9 s, depending on the electrolyte concentration. If the central ion moves under the influence of an external electric field, it becomes asymmetrically located with respect to the centre of the ionic atmosphere. Thus the time average of the forces of interaction of the ionic atmosphere with the central ion is not equal to zero. The external electric field is decreased by the relaxation electric field, as it is oriented in the opposite direction to the external force. Although the relaxation time is several orders of magnitude smaller than the time required for the central ion to pass through the ionic atmosphere (about 10~3s), its effect is important because the strength of the electric field formed by the ionic atmosphere (~105 V cm"1) is greater than the strength of the external electric field. Thus, even small changes in the symmetry of the ionic atmosphere have a measurable effect acting against that of the external electric field. The mathematical theory of the time-of-relaxation effect is based on the interionic electrostatics and the hydrodynamic equation of flow continuity. It is the most involved part of the theory of strong electrolytes. Only the main conclusions will be given here.
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97 The first approximate calculation was carried out by Debye and Hiickel and later by Onsager, who obtained the following relationship for the relative strength of the relaxation field AE/E in a very dilute solution of a single uni-univalent electrolyte
In the ideal case, the ionic conductivity is given by the product Because of the electrophoretic effect, the real ionic mobility differs from the ideal by ALf, and equals U + AC/,. Further, in real systems the electric field is not given by the external field E alone, but also by the relaxation field AE, and thus equals E + AE. Thus the conductivity (related to the unit external field E) is increased by the factor (E + AE)/E. Consideration of both these effects leads to the following expressions for the equivalent ionic conductivity (cf. Eq. 2.4.9):
(2.4.22)
+ and for the overall equivalent conductivity of the electrolyte A* = F(U + + AU+ + l/L + Al/_)(l + ) - F[{U + + U _)(l + ^ \ + AU+ + AU_1 (2.4.23)