Molar conductivity concentration dependence

In the case of strong electrolyte systems, the molar conductivity Am depends on concentration, according to Kohlrausch s law [28] ... 

For such electrolytes, since Cactmi = acstoich, the molar conductivity will depend on the stoichiometric concentration in a precise manner reflecting the fraction ionised. Because weak electrolytes are often only slightly ionised at low concentrations it is possible to treat the solutions as ideal. However, at higher concentrations corrections will have to be made for non-ideality. 

Table 2.5.1 lists the molar conductivities of some ions in dilute solution. There is a strong temperature dependence and, as with mass diffusivity, the conductivity increases exponentially with absolute temperature. The molar conductivity also depends on the electrolyte concentration falling off with increasing concentration, the drop being more rapid for weak electrolytes than for strong ones (see, e.g., Castellan 1983). 

In conclusion, from a non-selective conductivity measurement, it is possible to find specific ion concentrations by recording the conductivity at different temperatures. The key to this is that every ion has its own specific limiting molar conductivity which depends uniquely on temperature. This method needs an assumed set of ions the electrolyte conductivity is a linear combination of the specific ionic conductivities of these ions. 

Since analysts are concerned with concentrations, it is preferable to compare molar conductivities, which depend on the chacteiistics of the ions. 

In the classical theory of conductivity of electrolyte solutions, independent ionic migration is assumed. However, in real solutions the mobilities Uj and molar conductivities Xj of the individual ions depend on the total solution concentration, a situation which, for instance, is reflected in Kohhausch s square-root law. The values of said quantities also depend on the identities of the other ions. All these observations point to an influence of ion-ion interaction on the migration of the ions in solution. 

A study of the concentration dependence of the molar conductivity, carried out by a number of authors, primarily F. W. G. Kohlrausch and W. Ostwald, revealed that these dependences are of two types (see Fig. 2.5) and thus, apparently, there are two types of electrolytes. Those that are fully dissociated so that their molecules are not present in the solution are called strong electrolytes, while those that dissociate incompletely are weak electrolytes. Ions as well as molecules are present in solution of a weak electrolyte at finite dilution. However, this distinction is not very accurate as, at higher concentration, the strong electrolytes associate forming ion pairs (see Section 1.2.4). 

Because of the interionic forces, the conductivity is directly proportional to the concentration only at low concentrations. At higher concentrations, the conductivity is lower than expected from direct proportionality. This decelerated growth of the conductivity corresponds to a decrease of the molar conductivity. Figure 2.4 gives some examples of the dependence of... 

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)...

Interionic forces are relatively less important for weak electrolytes because the concentrations of ions are relatively rather low as a result of incomplete dissociation. Thus, in agreement with the classical (Arrhenius) theory of weak electrolytes, the concentration dependence of the molar conductivity can be attributed approximately to the dependence of the degree of dissociation a on the concentration. If the degree of dissociation... 

Fig. 2.5 Dependence of the molar conductivity of the strong electrolyte (HC1) and of the weak electrolyte (CH3COOH) on the square root of concentration...

The conductance of an electrolyte solution characterizes the easiness of electric conduction its unit is reciprocal ohm, = siemens = S = A/V. The electric conductivity is proportional to the cross-section area and inversely proportional to the length of the conductor. The unit of conductivity is S/m. The conductivity of an electrol3de solution depends on the concentration of the ions. Molar conductivity, denoted as X, is when the concentration of the hypothetical ideal solution is 1 M = 1000 mol/m. Hence, the unit of molar conductivity is either Sm M , or using SI units, Sm mol . For nonideal solutions, X depends on concentration, and the value of X at infinite dilution is denoted by subscript "0" (such as >,+ 0, and X for cation and anion molar conductivity). The conductivity is a directly measurable property. The molar conductivity at infinite dilution may be related to the mobility as follows ... 

Fig. 17. Concentration dependence of the specific conductance of PDADMAC with different average molar masses Mn (T=20 °C) (Data taken from [38])...

The molar conductivity depends on the concentration in agreement with the Kohlrauch s law,... 

Fig. 4. The concentration dependence of various electronic properties of metal-ammonia solutions, (a) The ratio of electrical conductivity to the concentration of metal-equivalent conductance, as a function of metal concentration (240 K). [Data from Kraus (111).] (b) The molar spin (O) and static ( ) susceptibilities of sodium-ammonia solutions at 240 K. Data of Hutchison and Pastor (spin, Ref. 98) and Huster (static, Ref. 97), as given in Cohen and Thompson (37). The spin susceptibility is calculated at 240 K for an assembly of noninteracting electrons, including degeneracy when required (37).

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 ... 

The temperature dependence of molar conductivity, calculated from ionic conductivity determined from complex impedance measurements and molar concentrations, and the VFT fitting curves are shown Figure 5.8. The VFT equation for molar conductivity is... 

Insight into the conductivity is provided by measuring the electrical conductivity of aqueous ionic solutions (Fig. 22.20 this topic is referred to in Chapters 11 and 15). The conductivity of pure water, multiply distilled to remove all impurities, is about 0.043 X lO (O cm) h Exposed to the air, pure water dissolves CO2, which forms carbonic acid, H2CO3 dissociation produces H30 and HCO3, which increase the conductivity to about 1 X 10 (O cm) . As ionic solutes are added to water, the conductivity increases rapidly a 1.0-M solution in NaOH has conductivity of about 0.180 (El cm) at 25°C. The conductivity depends strongly on both concentration and ionic species. The concentration dependence is summarized by the molar... 

Many studies of electrolyte conductivity have been carried out [7]. This work certainly helped to confirm modern ideas about electrolyte solutions. One aspect of the behavior of strong electrolytes which was initially not well understood is the fact that their molar conductance decreases with increase in concentration. Although this is now attributed to ion-ion interactions, early work by Arrhenius [8] ascribed the decrease in all electrolytes to partial dissociation. However, it is clear from the vast body of experimental data that one can distinguish two types of behavior for these systems, namely, that for strong electrolytes and that for weak electrolytes, as has been illustrated here. The theory of the concentration dependence of the molar conductance of strong electrolytes was developed earlier this century and is discussed in detail in the following section. 

In the development of the theory of ionic conductance it has been shown that the viscosity of the solvent is an important parameter determining ionic mobility. Initially, conductivity data were only available in water so that attention was focused on the effects of ionic size, structure, and charge in determining mobility and its concentration dependence. More recently, data have become available in a wide variety of non-aqueous solvents [11, 12], that is, in media with a wide range of permittivities and viscosities. On the basis of these data one may examine in more detail the role of solvent viscosity in determining the transport properties of single ions. Values of the limiting ionic molar conductance for selected monovalent cations and anions are summarized in tables 6.4 and 6.5, respectively. 

The conductivity behavior of polyelectrolytes does not correspond to either of these low-molecular electrolytes. A considerable amount of experimental work has been carried out with various polyelectrolyte systems. The results of these investigations exhibit a wide diversity of conductivity behavior. Even measurements with the same kind of polyelectrolyte, carried out by different investigators, may differ considerably with regard to the value of equivalent conductivity, as well as to its concentration dependence. The factors that may affect the results are the purity of samples, the molar mass of the polyelectrolyte, and its molecular mass distribution. Polyelectrolytes that have been extensively studied and for which these factors can reasonably be controlled are polystyrene sulphonates (PSS). The acid (HPSS) can easily be prepared from narrow molecular mass polystyrene by sulphonation with concentrated sulphuric acid [25], As it is a strong acid, it... 

Dependence of molar conductivity on concentration for a strong electrolyte the ideal case... 

DEPENDENCE OE MOLAR CONDUCTIVITY ON CONCENTRATION EOR A WEAK ELECTROLYTE 433... 

It is very important to be able to measure transport numbers over a range of concentrations as this is the only way to determine the dependence of individual molar ionic conductivities as a function of concentration. If this can be done, then it means that observed molar conductivities for any electrolyte at given concentrations can be split up into the contributions from the ions of the electrolyte. 

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