Electrolytic conductivity

The electrolytic conductivity is the electrical conductivity of an electrolyte solution . The electrical conductivity is defined as the constant of proportionality between the electrical current density and the electrical field strength according to . ${\displaystyle {\vec {J}}}$ ${\displaystyle {\vec {E}}}$ ${\displaystyle {\vec {J}}=\sigma \;{\vec {E}}}$

In an electrolyte, ions move when an electric field is applied, depending on the polarity of their electric charge, preferably in the direction of the field or against it; thereby they cause an electric current . This ion current depends on:

1. the electric field strength and thus a geometry factor (depending on the shape of the measuring cell) of the applied voltage ; ${\displaystyle U}$
2. the charge carrier concentration or the ion concentration , in each case expressed as particle density ; ${\displaystyle n}$ ${\displaystyle n_{i}}$
3. the amount of charge that each ion carries due to its valence and elementary charge ; ${\displaystyle z_{i}}$ ${\displaystyle e}$
4. the average drift speed of the individual ion types in the field direction. ${\displaystyle {\vec {v}}_{i}}$

Theoretical background

Resistance and measuring cell

For the electrical current strength within the solution, Ohm's law is empirically well confirmed : ${\displaystyle I}$

${\displaystyle I={\frac {U}{R}}}$.

The independent parameters are summarized in the factor , the conductance or reciprocal resistance . ${\displaystyle U}$ ${\displaystyle 1/R}$

Two electrodes are required to apply a voltage . As a result of the current through the electrolyte / electrode interface, reactions occur on this surface, which create a counter voltage. This process is known as electrolytic polarization . This creates a systematic measurement deviation that falsifies the measurement . It can be avoided as follows:

1. The measuring cell is constructed in such a way that the electrolyte has a high resistance; the voltage then required is so great that the polarization voltage, on the other hand, is negligibly small.
2. The voltage is not measured between the electrodes through which there is current, but between two probes attached at defined points in the measuring cell, through which only a very low current flows and therefore are not polarized.
3. AC voltage with a relatively high frequency is the most common measurement. This ensures that the substance conversions that cause the polarization are low in the short term and are reversed during the half-period with the opposite sign.

The resistance of any conductor depends on two parameters: the specific resistance (or conductivity ) and a geometry factor . In electrolyte measuring cells, this factor is called the cell constant. This is true ${\displaystyle R}$ ${\displaystyle \rho }$ ${\displaystyle 1/\rho =\sigma }$ ${\displaystyle Z}$

${\displaystyle R=\rho \cdot Z}$.

In the ideal case of a uniformly current-carrying conductor , where is the length and the cross-sectional area of ​​the conductor. Otherwise the manufacturer gives the cell constant or it has to be determined by measuring the resistance of a calibration solution with a known one . ${\displaystyle Z=l/q}$ ${\displaystyle l}$ ${\displaystyle q}$ ${\displaystyle \rho }$

Ion transport

As the cause of the current, an ion experiences a force with the charge in the electric field ${\displaystyle z_{i}\;e}$ ${\displaystyle {\vec {E}}}$ ${\displaystyle {\vec {F}}_{e}}$

${\displaystyle {\vec {F}}_{e}=z_{i}\;e\ {\vec {E}}}$.

As a result, it starts moving more quickly. As a result of the speed-proportional hydrodynamic friction force

${\displaystyle {\vec {F}}_{h}=-{\frac {1}{\mu _{i}}}\;{\vec {v}}_{i}}$

After a very short start-up time ( ) , this accelerated movement changes into a movement with a stationary drift speed , so that is. With the mobility as the proportionality constant between the speed of the ion type and the field strength, we get: ${\displaystyle 10^{-13}{\text{ s}}}$ ${\displaystyle {\vec {v}}_{i}}$ ${\displaystyle {\vec {F}}_{e}=-{\vec {F}}_{h}}$ ${\displaystyle b_{i}}$

${\displaystyle {\vec {v}}_{i}=\mu _{i}\;{\vec {F}}_{e}=\mu _{i}\;z_{i}\;e\;{\vec {E}}=b_{i}\;{\vec {E}}}$.

In the case of freely moving charge carriers, a current density arises proportional to the speed

${\displaystyle {\vec {J}}=e\;n\;{\vec {v}}}$.

The electrolyte contains cations and anions with their valencies and and their concentrations and . They move with the speeds and due to the different signs of their charges in opposite directions and together contribute to the current density ${\displaystyle z_{+}}$ ${\displaystyle z_{-}}$ ${\displaystyle n_{+}}$ ${\displaystyle n_{-}}$ ${\displaystyle {\vec {v}}_{+}}$ ${\displaystyle {\vec {v}}_{-}}$

${\displaystyle \sigma \cdot {\vec {E}}={\vec {J}}=e\;z_{+}\;n_{+}\;{\vec {v}}_{+}\ -e\;\ z_{-}\;n_{-}\;{\vec {v}}_{-}=e\,(z_{+}\;n_{+}\;b_{+}\ +\ z_{-}\;n_{-}\;b_{-})\cdot {\vec {E}}}$.

The conductivity can be read off immediately:

${\displaystyle \sigma =e\,(z_{+}\;n_{+}\;b_{+}\ +\ z_{-}\;n_{-}\;b_{-})}$.

It is therefore dependent on the ion concentrations, which are, however, evaluated with the factors of value and mobility of the ion types. With the sizes

• Number of positive or negative ions into which a molecule dissociates , ${\displaystyle w_{i}}$
• Molecular concentration , expressed as the particle density of the dissolved molecules, ${\displaystyle n_{m}}$
• electrochemical valence ${\displaystyle z_{e}=w_{+}z_{+}=w_{-}z_{-}}$

surrendered

${\displaystyle n_{+}=w_{+}\;n_{m}\ ;\quad n_{-}=w_{-}\;n_{m}}$

${\displaystyle \sigma =e\;z_{e}\;n_{m}\,(b_{+}\ +\ b_{-})}$.

Thus the conductivity in each solution is proportional to the concentration of the dissociated molecules, whereby the proportionality constant also contains the valencies and mobilities of the individual types of ions.

Molar values

A conversion to molar sizes

• using Faraday's constant with Avogadro's constant ${\displaystyle F=N_{\mathrm {A} }\;e}$ ${\displaystyle N_{\mathrm {A} }}$
• and the molar concentration ${\displaystyle c=n_{m}/N_{\mathrm {A} }}$

results

${\displaystyle \sigma =F\;z_{e}\;c\;(b_{+}+b_{-})}$.

According to Kohlrausch , the quantities are usually summarized and referred to as equivalent ion mobilities. Kohlrausch also introduced the term equivalent conductivity , where is the equivalent concentration. ${\displaystyle F\;b_{i}=l_{i}}$ ${\displaystyle \Lambda ={\frac {\sigma }{c_{e}}}}$ ${\displaystyle c_{e}=c\;z_{e}}$

According to the equations above, the equivalent conductivity is made up of the additive ion mobility and should be independent of the ion concentration. In reality this is only true for infinitely great dilutions; at higher concentrations, a decrease in is always observed, which is due to the influence of the dissociation equilibrium and the influence of the interionic interaction forces. ${\displaystyle \Lambda }$

The influence of the dissociation equilibrium

With incomplete dissociation depends on dissociation from: . ${\displaystyle \Lambda }$ ${\displaystyle \alpha }$ ${\displaystyle \Lambda =\alpha \cdot \Lambda _{\infty \ }}$

Since the degree of dissociation has its maximum value at infinite dilution ( ) and becomes smaller and smaller with increasing concentration, a decrease in the equivalent conductivity is understandable, which was recognized early on ( Ostwald's law of dilution ). ${\displaystyle \alpha =1}$

The influence of the interionic interaction forces

The ions do not move freely. Rather, as a result of the far-reaching electrostatic forces, there is a mutual hindrance of the migrating ions. Due to its electrostatic effect, an ion is surrounded on average by more oppositely charged particles than those with the same charge. This "ion cloud" agglomerates more and more with increasing concentration and has the following effects:

1. As a result of its movement, the ion must first build up a new ion cloud at each location. The effect of this is as if the ion is always ahead of its ion cloud, which causes the ion to slow down.
2. The cloud, the ions of which move in the opposite direction in the field, creates a current against which the central ion has to swim, causing it to experience a further delay.

Both effects increase with concentration.

The theory of Debye , Hückel and Onsager based on this model provides the expression for small concentrations:

${\displaystyle \Lambda =\Lambda _{\infty }-a\;{\sqrt {c}}}$.

This result (square root law) was found experimentally much earlier by Kohlrausch. Where and are constants for isothermal measurement. By Debye, Hückel, and Onsager, Kohlrausch's square root law was specified by exchanging the concentration (below the root) for the ionic strength . For ionic strengths below 0.001 mol / liter it should then also be valid for solutions of multivalent ions. See: ${\displaystyle a}$ ${\displaystyle \Lambda _{\infty }}$ ${\displaystyle I}$

• Debye-Hückel-Onsager law for the conductivity of ions

Effects on the conductivity of electrolyte solutions

In solutions, the conductivity is not only dependent on the temperature, but also on other effects:

• The relaxation effect disrupts the short-range order of the ion cloud around a central ion when an electric field is applied. Since ions are accelerated in an electric field in the direction of the oppositely charged poles, the ion cloud becomes distorted. The central ion always hurries ahead of the charge center of its ion cloud and an additional electrical potential is created against which the ion must be transported.

• The electrophoretic effect describes the reduction in conductivity by increasing the forces that act on the central ion when the ion cloud moves in the opposite direction to the central ion.

• The Wien effect describes an increased conductivity in a strong E-field when a central ion moves faster than its ion cloud and so there is no relaxation effect .

literature

• GM Barrow: Physical Chemistry , Vol. II, Chapter 18.
• Moore-Hummel: Physical Chemistry , p. 506 ff.
• PW Atkins: Physical Chemistry , Chapter 27.1.
• Brdička: Physical Chemistry , p. 570.
• K.Rommel: The Little Conductivity Primer, Introduction to Conductometry for Practitioners , WTW Eigenverlag, 1980

See also

• Conductivity meter
• Conductometry
• Molar conductivity

Web links

• Video: How well do electrolytes conduct electricity? - a question of ion mobility and concentration . Jakob Günter Lauth (SciFox) 2013, made available by the Technical Information Library (TIB), doi : 10.5446 / 15231 .

Commons : Conductometry  - collection of images, videos and audio files

Individual evidence

1. ^ Brockhaus ABC Chemie , VEB FA Brockhaus Verlag Leipzig 1965, p. 1151.
2. ↑ PW Atkins, J. de Paula: Physikalische Chemie , 5th ed., WILEY-VCH, 2010, pp. 809-811.
3. ↑ PW Atkins, J. de Paula: Physikalische Chemie , 5th ed., WILEY-VCH, 2010, pp. 809-811.