Molar electrolytic conductivity

Besides the ionic conductivities the molar electrolyte conductivity A and specific conductivity k of the solution are also introduced. The following relations can be written ... 

Equation (43) is the basic relationship of electrolyte conductivity. An electrolyte C +A - shows the molar electrolyte conductivity... 

Molar electrolyte conductivity for completely dissociated electrolytes are represented in the form... 

The concentration dependence of ionic conductivity has been discussed briefly above. Due to ion-ion interactions, the conductivity per ion falls as the ion concentration is increased. Two specific interactions have been identified the electrophoretic effect due to the tendency of the ion atmosphere to move in the opposite direction of the ion and the relaxation effect due to the finite time required for the ion atmosphere to re-arrange itself due to the asymmetry imposed by the electric field. Onsager produced a limiting law that showed that the molar electrolytic conductivity fell with the square root of the ion concentration ... 

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. 

The influence of the charge density on the electrolytic conductivity is demonstrated for high molar mass PDADMAC and the AAM-copolymers in Fig. 21. 

Molar ionic conductivity — This quantity, first introduced by -> Kohlrausch, is defined by A = Zi Fui (SI unit Sm2 mol-1), where Zj and 14 are the charge number and -> ionic mobility of an ion, respectively. The molar -> conductivity of an electrolyte M +X (denoted by A) is given by A = u+X+ + i/ A, where A+ and A are the molar ionic conductivities of the cation and anion. The A value of an ion at infinite dilution (denoted by A°°) is specific to the ion. For alkali metal ions and halide ions, their A values in water decrease in the orders K+ > Na+ > Li+ and Br- > Cl- > F-. These orders are in conflict with those expected from the crystal ionic radii, because the smaller ions are more highly hydrated, so that the -> hydrated ions become larger and thus less mobile. Based on Stokes law, the radius of a hydrated ion... 

We may consider, for example, a reaction consisting of the recombination of the ions of a weak electrolyte. Conductivity data indicate that the time of relaxation in this case is about 10 sec. The volume change Vp p = (dvld )p is of the order of the partial molar volumes of the components, say several cm. /mole. If then the system is subjected to a compression of one atmosphere a second, the quantity a in (19.10) will be of the order of 10 c.g.s. units, and A ar lO ergs/mole 10 cal./mole. The value of the affinity is therefore very small indeed. To obtain larger effects it is necessary to consider systems in which the Cf. Harned and Owen, [27], p. 222. 

Experiment 2 Molar Conductivity Measurements Considering Arrhenius s electrolytic theory of dissociation, Werner noted that evidence for his coordination theory may be obtained by determining the electrolytic conductivity of the metal complexes in solution. Werner and Jprgensen assumed that acid (ionic) residues bound directly to the metal would not dissociate and would thus behave as nonconductors, while those loosely held would be conductors. Molar conductivities of 0.1 molar percent aqueous solutions of some tetravalent platinum and trivalent cobalt ammines are given in Table 2.3. 

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. 

It is common to introduce A the molar ionic conductivity for electrolytes, which is the conductivity of a specific volume of an electrolyte containing one mole of solution between electrodes placed one meter apart ... 

Ri and R% were tubes of an electrolyte consisting of a solution which is molar with respect to both mannite and boric acid. This has been found by Magnanini 4 to have a very low temperature coefficient of conductance. The liquid whose dielectric constant was desired was placed in a vessel of the type shown in Fig. 3. The metal shell, B, and the metal plate, A, held apart by the insulating cap, /, form the condenser Cg, of Fig. 2. The bridge was balanced by adjusting the distance between the plates of an air condenser, C4, consisting of two sheets of brass, insulated from each other, which could be set at accurately known distances apart Since most liquids and solutions have at least a slight electrolytic conductance, an adjustable electrolytic resistance, was... 

The values for the transport numbers are internally self consistent between the calculation from molar ionic conductivities and from the ionic mobilities. This is as it should be. The sum of the transport numbers for the ions of a given electrolyte is unity. This, again, is as it should be. 

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. 

The equation for the molar ionic conductivity for a symmetrical electrolyte is ... 

Kohlrausch realized that the electrolytic conductivity is not a suitable quantity for comparing the conductivities of different solutions. If a solution of one electrolyte is much more concentrated than another, it may well have a higher conductivity simply because it contains more ions the value of the electrolytic conductivity thus does not immediately tell us anything of significance about the solution. What is needed instead is a property in which there has been some compensation for the differences in concentrations. Such a property, first defined and used by Kohlrausch, is now called the molar conductivity and given the symbol A (lambda). It can be... 

The (specific) electrolytic conductivity of a saturated solution of silver chloride, AgCl, in pure water at 25 C is 1.26 x 10 O " cm higher than that of the water used. Calculate the solubility of AgCl in water if the molar ionic conductivities are Ag", 61,8 Cl , 76.4 cm moPh... 

To compare electrolyte conductivities with concentration normalized, we define a molar conductivity by... 

Because of their high molar conductivity, the hydrogen ions will often dominate the conductance found. Because of electroneutraUty, there are equal numbers H and Cl when the strong acid, hydrochloric acid (HCl), dissociates. However, the electrolytic conductivity contribution from the hydrogen ions is approximately 5 times as large as that of Cl . From Table 2.4 it is seen that for NaCl the contribution is largest from the CP ions for potassium chloride the contributions from each ion are approximately equal. 

The type of solid electrolyte used is yttria-stabilised 7J rcon a Zr02- 20z- / molar), and conducts with oxide ions. 3oth the interior and exterior surfaces of the tube are coaX-ed with platinum paint, and constitute the electrodes. The reference electrode of the cell is the oxygen in the air in contact with the inside wall of the tube. The external surface of the tube is in contact with the exhaust gases. The measuring electrode is protected by a metal cover and a porous oxide layer. 

Electrolyte membrane Molar composition Conductivity (S cm ) Anodic breakdown voltage vs. U /LP (V)... 

Two of the more recently developed detectors, namely, the Hall electrolytic conductivity detector (ELCD) and the photoionization detector (PID) are recommended by the EPA for the analysis of volatile and semivolatile halogenated organic compounds and low molar mass aromatics. Chemical emission based detectors, such as the thermal energy analyzer (TEA) for its determination of... 

For unsymmetrical electrolytes, conductivity equations have been developed by Lee and Wheaton [10] and by Quint and Viallard [11]. The molar conductivity A of the solution is calculated from the ionic conductivities A,- of all ions present according to... 

The most characteristic properties of ions are their abilities to move in solution in the direction of an electrical field gradient imposed externally. The conductivity of an electrolyte solution is readily measured accurately with a 1 kHz alternating potential in a virtually open circuit, in order to avoid electrolysis. The molar conductance of a completely dissociated electrolyte is A2 = A2°° - 2 + EC2 In C2 + J iR ) C2 — J" R")c2, where S, E, f, and f are explicit expressions, containing contributions from ionic atmosphere relaxation and electrophoretic effects, the latter two depending also on ion-distance parameters R. The infinite dilution can be split into the limiting molar ionic conductivities by using experimentally measured transport numbers extrapolated to infinite dilution, t+° and i °° = 1 - <+°°. For a binary electrolyte, Aa = 2+°° -I- and = i+ A2. Values of the limiting ionic molar conductivities in water at 298.15 K [1] are accurate to 0.01 S cm mol (S = Q ). 

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. 

The molar conductivity of an electrolyte is the more generally useful quantity since the Kohlrausch law allows its limiting value to be resolved into those of its constituent ions. Comparison between different electrolytes with a common ion therefore allows the determination of an unknown molar conductivity. However, the quantity typically measured is the overall electrolytic conductivity. A way to apportion the conductivity (and hence mobility) to the individual ions of the electrolyte is required. Equation (20.1.2-11) shows that resolution of the molar conductivity into the terms arising from its constituent ions is possible if the transference number of the ion is found. Although this property and the methods developed to measure it may seem rather arcane, it has been of fundamental importance in the understanding of the conductivity and diffusion potentials developed within electrolyte solutions. Experimentally, a number of ways of measuring transference numbers have been developed these are summarised below. 

The essential point with regard to the interpretation of data is that the molar conductivity (see equation (20.1.2-10)) at infinite dilution can be broken down into terms due to the constituent ions. Some knowledge of the transference properties of the individual ions can be used to determine the fraction of electrolyte conductivity attributable to each ion. 

Determination of the degree of dissociation of weak electrolytes is a common application of conductivity measurements. This approach will be briefly outlined here with a sample calculation illustrating the utility of the method. From the data presented in the next section, the limiting molar conductivity of acetic acid can be seen to be 389.9 S cm mol (from addition of the limiting values for the proton and the acetate ion). At finite concentrations, this weak acid will only be partially deprotonated. The ratio of observed to predicted electrolytic conductivity can be used to determine the degree of dissociation, a. At 0.01 M, the observed molar conductivity of acetic acid was found to be 14.30 S cm mol . Thus... 

Ionic Conductivities in Aqueous Solutions The thermodynamic quantities for ions in solution dealt with in the previous sections could be measured only for complete electrolytes (or for charge balanced differences between ions of the same sign) but not for individual ions. On the contrary, this is not the case for ionic conductivities (and diffusion coefficients, see Section 2.3.2.2). These can be determined experimentally for individual ions from the electrolyte conductivities and the transference numbers. The conductivity of an electrolyte solution is accurately measured with an alternating external electric field at a rate of lkHz imposed on the solution with a high impedance instrument in a virtually open circuit (zero current). The molar conductivity, Ag, can then be determined per unit concentration. Ion-ion interactions cause the conductivities of electrolytes to diminish as the concentration... 

The limiting molar ionic conductivities, AJ , are obtained by application of the experimentally measured (and extrapolated to infinite dilution) transference numbers, C and r=l-C Thus A" = t"-A"/v and A = r-A"/v, so that A = v+A -ev A", the being the stoichiometric coefficients of the electrolyte. The limiting (standard) molar ionic conductivities AJ for many ions in water at 25 C are shown in Table 2.11 with uncertainties not larger than 0.01 S cm mol. Between 0 and 100°CA increase about fivefold, mainly because the viscosity of the solvent diminishes in this direction by a similar factor. The transference numbers and t are temperature dependent too, but only mildly. 

Chemical transformations of MCMs in aqueous and polar solvents are accompanied by ionization and dissociation. This also can result in the formation of products devoid of the metal. The degree of dissociation depends both on the nature of solvent and the temperature (Fig. 9). This is especially so in the case of transition metal carboxylates, which are strong electrolytes in water. In aqueous or water-oiganic media at pH > 7, salts of unsaturated carboxylic acids are almost completely dissociated (the molar electrical conductivity at infinite dilution, A, , is 146-154cmOhm mol ) hence instead of MCMs, other species such as acrylate and methacrylate ions (specially, metal acrylates and methacrylates) act as monomers. Similarly, in the acrylonitrile-sodium prop-2-enesulfonate system, which undergoes copolymerization in DMSO-H2O mixtures at various pH values (at 45°C with AIBN as the initiator), the relative reactivities of the comonomers change in different media due to the increase in the solvation capacity of water. Actually, copolymerization in these systems involves three types of monomers CH2=CH CH2SO3 Na... 

Aqueous solutions of Cu ", Co " and acrylates are medium-strength electrolytes a plot of the molar electrical conductivity vj. concentration is described satisfactorily by the Kolrausch equation. For 0.05 M aqueous solutions of calcium acrylate (Acr) and methacrylate at 25°C, the specific electrical conductivities, AT, are 5.16 x 10 5 and 2.787 X 10 Ohm mol and the degrees of dissociation, a, are 0.46 and 0.2, respectively. The degrees of dissociation of Zn, Pb, and Ba acrylates (M(Acr)2) in methanol are sufficient for the M(Acr)+ cations that are formed to react with radical initiators (e.g., alkylcobalt chelates with tridentate Schilf bases) to give alkyl free radicals, which induce radical polymeri2ation of MCM even at low temperatures (5-10°C). For other types of MCM ( v-, n-types, see above), metal elimination processes are less typical and in some cases (i.e., chelate type), these processes do not occur at all. 

Molar ionic conductivity — This quantity, first introduced by Kohlrausch, is defined by A = Zi FMi (SI unit Sm mol ), where Z and m are the charge number and ionic mobility of an ion, respectively. The molar -> conductivity of an electrolyte (denoted by... 

It is convenient to define the molar ionic conductivity of individual ions (i.e., the conductivity of ions carrying 1 mole of charges), in the same manner as molar conductivity of electrolytes [Eqs. (D.8) and... 

The molar conductivity of an electrolyte salt at sufficient dilution is then simply the sum of the molar ionic conductivity of the ions produced by dissociation of the salt [Eq. (D.IO)] ... 

The concentration scale of a standard chemical potential and an activity coefficient are specified by additional symbols placed as either the subscript or superscript. For example, the mole fraction scale is specified in Equation 1.3. In this equation, if we want to be precise, should be called the standard chemical potential on the mole fraction concentration scale. Equation 1.3 is usually used for solutions of nonelectrolytes, such as 02(aq), and for solvent (water) in electrolyte solutions. Also, this equation can be used for solid solutions such as metal alloys. For electrolyte solutions, molality is commonly used except (1) electrolyte conductivity and (2) electrochemical kinetics, where molarity is commonly used. 

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