Molar and Equivalent Conductivity

Note that in the past, the equivalent conductivity A. = A/(v zJ was widely used, where is defined as 

1-1 electrolytes (e.g., NaCl). Connected to the equivalent conductivity, the equivalent 

FIGURE 3.18 Conductivity of two aqueous solutions as a function of molar concentration [1, Chapter 10, Table 10.10]. 

The literature is confusing with regard to the molar and equivalent conductivities. The preceding equations should help to sort this mess out. 

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It will be seen from the above equation that in the case of electrolytes composed of two univalent ions there is no difference between molar and equivalent conductances. In case of electrolytes with bivalent ions the molar conductance is double of the equivalent conductance, with triva-lent ions treble and so on. 

In an electrochemical cell, the conductivity is inversely related to the resistance in the electrolyte/test medium. The presence of certain chemical or ionic species may affect the resistance of the electrochemical cell. This change in resistance or conductivity can then be used to quantify the amount of the analyte presented. Molar and equivalent conductivities are commonly used to express the conductivity in an electrochemical cell. The conductivity measurement can be made relatively straightforward, using a DC mode or with a potential or current excitation. However, any faradaic or change transfer process occurring at the electrode surface will affect the conductivity measurement in an electrochemical cell. Furthermore, conductivity measurement in general does not provide sufficient specificity or sensitivity to quantify the analyte. This limits the use of conductivity of an electrochemical cell for sensing applications. 

Molar and Equivalent Conductances. A quantity much used in computations and in tables of constants is the molar conductance, Am. It can be computed from the specific conductance, l, and the concentration, C, of the solute, which is usually stated in mols per liter of solution, by means of the formula... 

Molar conductivity can easily be calculated if conductivity and molar concentration are known. While the equivalent conductivity is not recommended by lUPAC, a reader should know how it can be handled. The molar and equivalent conductivity for 1-1 electrolytes are equal. 

The terms specifie conductivity and equivalent conductivity were previously used. However, these terms are not recommended for use as the SI units. They should be replaced by molar conductivity according to the SI recommendation, which states as follows, When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Thus, when we previously used equivalent conductivity, we should now use molar conductivity, where we define the molar unit so that it is equal to the equivalent unit previously used. For example, we define (l/2)Ca, (l/3)La, (l/2)CO and Alj/jF as molar units. 

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 ... 

Second, the specific conductivity can easily be related to the molar and equivalent A conductivities. Take the case of a z z-valent electrolyte. With Eqs. (4.161), (4.136), and (4.138), it is found that... 

Values of limiting molar ionic conductivities for a few common ions are shown in Table 1. The data tabulated are referred to 25°C temperature. The term limiting molar ionic conductivity is used according to lU-PAC recommendation, rather than the formerly used limiting ionic equivalent conductivity. The molar and equivalent values are interconvertible through stoichiometric coefficient z. 

One gram mol of a salt contains vs equivalents, so that the relation between the molar conductance, A, and equivalent conductance, A, is... 

The molar conductance and equivalent conductance of the magnesium ion in water at 25 °C extrapolated to infinite dilution are respectively... 

For the sake of uniformity we convert the molar conductances to equivalent conductances. We also convert molar and equivalent concentrations into ionic strengths by multiplication by 6 and 2 respectively. We thus construct table 2. We plot A against in fiig. 1 and by a... 

Moreover, the quantity of an ion usually considered was not the mole, but the gram-equivalent—that is, the quantity associated with 1 Faraday of electricity. Concentrations were therefore given in g-equiv. dm", and equivalent conductivities, rather than molar conductivities, were quoted. To convert an equivalent conductivity to a molar conductivity, divide by 10" and multiply by the number of electric charges associated with the ionised molecule (e.g. 6 for Al2(S04)3). 

In aqueous solutions, concentrations are sometimes expressed in terms of normality (gram equivalents per liter), so that if C is concentration, then V = 103/C and a = 103 K/C. To calculate C, it is necessary to know the formula of the solute in solution. For example, a one molar solution of Fe2(S04)3 would contain 6 1CT3 equivalents cm-3. It is now clear as to why A is preferred. The derivation provided herein clearly brings out the fact that A is the measure of the electrolytic conductance of the ions which make up 1 g-equiv. of electrolyte of a particular concentration - thereby setting conductance measurements on a common basis. Sometimes the molar conductance am is preferred to the equivalent conductance this is the conductance of that volume of the electrolyte which contains one gram molecule (mole) of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart. 

As in the case of solutions, the specific conductance, K, the equivalent conductance, a, and the molar conductance, am, are also distinguished for molten electrolytes. These are defined in the same manner as done for the case of solutions of electrolytes. It may, however, be pointed out that molten salts generally have much higher conductivities than equivalent aqueous systems. 

The influence of NaCl on the equivalent conductivity of PDADMAC with different molar masses is demonstrated in Figs. 19 a and b. Amax decreases with increasing cs and is observed at higher cp. 

Plotting A vs. the ratio of the polyelectrolyte to the salt concentration, cp/cs, the largest change of the slope is located in the cp/cs region between 1 and 3. An example is given in Fig. 20 for the lowest molar mass and holds for all ionic strengths and molar masses that have been investigated. This implies that a linear increase of the equivalent conductivity below the overlap concentration will only be found if the polyelectrolyte concentration exceeds the concentration of monovalent low molecular electrolyte by a factor of two to three. 

Fig- 23. Temperature dependence of the maximum equivalent conductivity Amax for PDADMAC with different molar masses and DADMAC (Data taken from [38])... 

Fig. 2.10. Equivalent conductance (A) and transport number of anion (T-) and cation (T+) for CTAB solutions at 35 °C plotted versus the square root of surfactant molarity. (From Ref.13))...

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).

Here, Amoi and Aeq are the molar and the equivalent conductivity, C is the molar concentration of the electrolyte in the solution, za and zc are the charge numbers of the anion and cation, respectively, and va and vc are the stoichoimetric coefficients of the anion and cation, respectively. 

Apart from the equivalent conductance another quantity is used, namely the molar conductance p under this we understand the conductance of that volume of solution which contains one mole of dissolved substance and is placed between two parallel electrodes of sufficient size and set 1 cm apart. If one gram-molecule of a substance corresponds to n — vz gram-equivalents of the ions (z being the number of charges of an ion and v the number anions or cations formed byjhe dissociation of the molecule) then the following relation can be... 

Equivalent conductivities (and ionic mobilities) of the melts are similar to that of aqueous solutions. Very high specific conductivities are typical for molten salts, as seen in Table 1 [49], The reason for this is the fact that molten salts are very concentrated solutions (for example, the concentration of molten LiF is about 65 molar the concentration of molten KC1 is about 20 molar, etc.). The electrical conductivities of various molten salts cannot be compared at constant temperature because of their different melting points. Therefore, in Table 1 the values of conductivities were selected at 50° above the melting point of each salt. 

Note that A has units of m equiv In this experiment, we are concerned with simple one-one electrolytes A B. In this case, where v = 1 equiv moE, there is no distinction between equivalents and moles and the equivalent conductance is the same as the molar... 

Fig, 4,96, Equivalent conductivity of aqueous electrolyte solutions as a function of the square root molarity (+), experimental values Debye-HuckeHDnsager limiting law (- - -) and (—), theoretical values predicted by Blum s approach, (a) Aqueous NaCI solutions, (b) Aqueous KBr solutions, (c) Aqueous BaCl2 solutions, (d) Aqueous LaCIs solutions. Reprinted from 0. Bernard, W. Kunz, P. Turq, and L. Btum, J. Phys, ChemM 3833, 1992.)... 

The equivalent conductivities of KCl and MgCl, aqueous solutions at 25 °C were estimated as 146.95 and 124.11 (S cm eq ), respectively. Calculate the molar and the specific conductivities when the concentrations of both solutions wa-e g-eq per 1000 cm. What would be the measured resistance of these two solutions when two planar Pt electrodes of 2-cm area and 0.5 cm apart are employed Measurements of the specific conductivity and hence of the solution resistance are usually carried out under a small ac field. Explain why a small ac field is used. (Bock)... 

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