The Conductivity of Electrolyte Solutions

Electrolyte solutions contain ions which can move in response to a gradient in electrical potential. The transport properties of these systems are important in devices such as batteries and in living systems. The movement of ions in solution is very different from the movement of electrons in metallic conductors, and it is important to understand the fundamental laws which govern the conductivity of electrolyte solutions. Ions move according to the classical laws of physics, whereas the movement of electrons is quantal. 

Since cations and anions move in opposite directions under the influence of an electrical field, the vector for a cation is in the opposite direction to that for an anion /x- This means that the flux /, multiplied by the ionic valence z, has the same sign for all ions as a result each ion contributes to the solution conductivity in such a way that it becomes larger. 

The phenomenological coefficient relating the current density and the macroscopic potential gradient is the conductivity due to the ion, k,. Thus, one has the general relationship 

The minus sign reflects the fact that a positive ion moves in the direction opposite to the increase in electrical potential. If V ) is positive, the electrical potential increases in a specified direction, for instance the x-direction, but a cation moves in the opposite direction. This equation is a special form of Ohm s law written in terms of the current density and the potential gradient, rather than the current and the potential difference. The experimentally measured quantity is the conductivity Kg, which is the sum of the contributions from each ion in solution  

In order to measure the conductivity of an electrolyte solution, a special cell is constructed in which the two electrodes of accurately known dimensions are placed at a known distance from one another (fig. 6.5). The electrodes are usually made of an inert material such as platinum. If a d.c. voltage is applied to such a cell, no current flows until a certain minimum value is reached. Below this minimum, no reactions occur at the electrodes, and the electrode solution interface behaves as a capacitor. When d.c. current flows, reactions occur at each electrode and ions move in the electrolyte solution. The nature of the reactions depends on the nature of the electrolyte but certainly the component ions are involved in these reactions. For this reason, d.c. experiments are not used in the precise determination of solution conductivity. On the other hand, if an a.c. voltage of low amplitude is applied to the cell, its conductivity may be determined in the absence of any net change in the composition of the solution. Traditionally, this experiment was carried out by making the conductance cell one arm of an a.c. Wheatstone bridge designed to measure resistance. 

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Conductimetry is a method of obtaining analytical and physicochemical information by measuring the conductivities of electrolyte solutions [25]. Conductivity cells have two or four electrodes, but the processes that occur at or near the electrodes are not directly related to the information obtained by conductimetric measurements. 

As described in Section 5.8, the conductivity of electrolyte solutions is a result of the transport of ions. Thus, conductimetry is the most straightforward method for studying the behavior of ions and electrolytes in solutions. The problems of electrolytic conductivity and ionic transport number in non-aqueous solutions have been dealt with in several books [1-7]. However, even now, our knowledge of ionic conductivity is increasing, especially in relation to the role of dynamical solvent properties. In this chapter, fundamental aspects of conductimetry in non-aqueous solutions are outlined. 

The conductivity of electrolyte solutions depends on the concentration and the charge number of the ions in the solution. It is expressed as the molar or equivalent conductivity or molar conductivity, which is given by ... 

Table 7 Selected Data on the Conductivity of Electrolyte Solutions Based on Polar Aprotic Systems... 

The phenomenon of electrolysis also receives a simple explanation on the basis of the theory of electrolytic dissociation. The conductance of electrolyte solutions is due to the fact that ions (charged particles) are present in the solution, which, when switching on the current, will start to migrate towards the electrode with opposite charge, owing to electrostatic forces. In the case of hydrochloric acid we have hydrogen and chloride ions in the solution ... 

This empirical relationship between the equivalent conductivity and the square root of concentration is a law named after Kohlrausch. His extremely careful measurements of the conductance of electrolytic solutions can be considered to have played a leading role in the initiation of ionics, the physical chemistry of ionic solutions. 

In 1884 Arrhenius obtained his Ph.D. from the University of Uppsala with a thesis on the conductivities of electrolytic solutions. Although poorly rated by his examiners, his thesis attracted the attention of the most distinguished physicists and physical chemists in Europe at the time. Arrhenius collaborated with a number of them from 1886 until 1890. Based on his international reputation, he secured a post at the Technical High School in Stockholm, first as a lecturer, then as a professor, and finally as its rector. He later became director of the new physical chemistry institute of the Nobel Foundation in 1905. By that time, his interests had already shifted toward other fields of science. 

The conductivity of electrolyte solutions is equal to the sum of the conductivities of each type of ion present. For a single dissolved salt, the equivalent conductance can be expressed as... 

Two aspects will merit attention in the future Experimental methods applied in measuring conductivity and modification (improvement, enhancement) of the conductivity of electrolyte solutions as employed, e.g., in primary or secondary batteries. Combinations of liquids and electrolyte (salts) aiming at reduced viscosity in an ever wider range of temperatures... 

A major objective in improving battery performance is the optimization of the power of a ceU. The power of the cell is governed by thermodynamic, kinetic, transport, and geometric parameters [14-25]. The conductivity of electrolyte solutions is mainly determined by following parameters [26] ... 

Conduction equations are often defined in terms of molar conductivity A (S cm moP ) as the conductivity of electrolyte solutions is dependent upon the salt concentration. Thus, A is related to the conductivity K or ct (S cm ) by... 

The conductivity of metals is generally high The conductivity of electrolytic solutions is generally low... 

R. Fernandez Prini, Trans. Faraday Soc., 66, 3311 (1969). A modified expression for the concentration dependence for the conductance of electrolyte solutions. 

As PILs can be mixed with molecular solvents, this provides new opportunities to study the conductivity of electrolyte solutions in salt-rich regions up to 15 mol. L Numerous studies concern the specific conductivity and viscosities of pure PILs [70-73], since it is desirable and of great importance to understand and predict the transport properties of PIL-i-molecular solvent solutions using classical and theoretical models. 

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