From Conductance Measurements

In the approximate treatment of the conductance of weak electrolytes, the decrease in A is treated as resulting only from changes in the degree of dissociation, a. On this basis, it can be shown that an apparent degree of dissociation a can be obtained from 

However, for more precise calculations, it is necessary to consider that the mobility (hence, the conductance) of ions changes with concentration, even when dissociation is complete, because of interionic forces. Thus, Equation (20.20) is oversimplified in its use of Aq to evaluate a, because at any finite concentration, the equivalent conductances of the and Ac ions, even when dissociation is complete, do not equal Aq. 

To allow for the change in mobility resulting from changes in ion concentrations, Macinnes and Shedlovsky [5] proposed the use of a quantity Ae in place of Aq. The quantity Ae is the sum of the equivalent conductances of the and Ac ions at the concentration C, at which they exist in the acetic acid solution. For example, for acetic acid Ae is obtained from the equivalent conductances of HCl, NaAc, and NaCl at a concentration C, equal to that of the ions in the solution of acetic acid. Thus, because 

Assuming that the degree of dissociation at the stoichiometric molar concentration C is given by the expression 

Now if we insert appropriate activity coefficients, we obtain a third approximation for the dissociation constant  

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Acid K, X From conductance measurements" 10s From e.m.f. measurements... 

For weakly and moderately associated electrolytes, 10< (A<104, no problem generally occurs in obtaining reliable values for KA and A0 from conductivity measurements. Strong association, however, as known for many salts in the solvent class 6, often entails unrealistic A ... 

The pioneering work of Gilkerson and co-workers [122-130] and Huyskens and colleagues [131,132] allows the determination of the corresponding equilibrium constants from conductivity measurements. If all equilibria, Eq. (4)-(6), are involved, the association constants of an electrolyte without (K l) and with (KA ) addition of the ligand at concentration cL of the ligand L are given by the relationship [132]... 

Results from conductivity measurements can be advantageously evaluated for every temperature and solvent composition using the nonlinear fit [206]... 

Davidson and Hantzsch (1898) and later Engler and Hantzsch (1900) investigated this system on the supposition that it corresponds to that of the common dibasic acids. From conductivity measurements they calculated basic dissociation constants for the diazohydroxides, but it is now known that their assumptions were incorrect. In fact, at the turn of the century it was practically impossible to reach the right solution. On the one hand, Hantzsch did not have at his disposal the current poten-tiometric technique for protolytic equilibria, and on the other hand, the system of Scheme 5-1 is a special case for a dibasic acid, the principle of which was not grasped in Hantzsch s time. 

Salts such as silver chloride or lead sulfate which are ordinarily called insoluble do have a definite value of solubility in water. This value can be determined from conductance measurements of their saturated solutions. Since a very small amount of solute is present it must be completely dissociated into ions even in a saturated solution so that the equivalent conductivity, KV, is equal to the equivalent conductivity at infinite dilution which according to Kohlrausch s law is the sum of ionic conductances or ionic mobilities (ionic conductances are often referred to as ionic mobilities on account of the dependence of ionic conductances on the velocities at which ions migrate under the influence of an applied emf) ... 

Shedlovsky, T Kay, R. L., The ionization constant of acetic acid in water-methanol mixtures at 25°C from conductance measurements, J. Am. Chem. Soc. 60,151-155 (1956). 

Hawes, J. L. Kay, R. L., Ionic association of potassium and cesium chloride in ethanol-water mixtures from conductance measurements at 25°, J. Phys. Chem. 69, 2420-2431 (1965). 

Feed solution used in all experiments contained sodium chloride at a concentration level of 5,000 ppm. Membrane salt rejection is evaluated from conductance measurements of product water and expressed as percent rejection, %R, or desalination ratio, D. . These units are defined by the following equations in which Cp and Cf are sodium chloride concentrations in feed and product respectively. Note that D. is very sensitive to concentration changes and expands rapidly as 100% rejection is approached. 

At CMC, micelles (aggregates of SD" with some counterions, such as Na+) are formed, and some Na+ ions are bound to these, which is also observed from conductivity data. In fact, these data analyses have shown that approximately 70% Na+ ions are bound to SD" ions in the micelle. The surface charge was estimated from conductivity measurements (Birdi, 2002). Therefore, the concentration of Na+ will be higher than SD" ions after CMC. A large number of reports are found in the literature, in which the transition from the monomer phase (before CMC) to the micellar phase (after CMC) have been analyzed. 

For most of the systems reported in the literature, C/K is not known—very often, neither K nor C is known. For two-component initiator-coinitiator systems, C is usually taken to he the initiator concentration [YZ] when the coinitiator is in excess or the coinitiator concentration [I] when the initiator is in excess. C may be lower than [YZ] or [I] due to association that is, only a fraction of [YZ] or [I] may be active in polymerization. This may also he the case for one-component initiators such as triflic acid. It would be prudent to determine the actual value of C in any polymerization system—usually a difficult task and seldom achieved. Experimental difficulties have also limited our knowledge of K values, which are obtained most directly from conductivity measurements or, indirectly, from kinetic data. A comparison of polymerization in the absence and presence of a common ion salt (e.g., tetra-n-butylammonium triflate for the triflic acid initiated polymerization) is useful for ascertaining whether significant amounts of free ions are present in a reaction system. 

Equations 5-92 and 5-97 allow one to obtain k, kj, and K from k pp values obtained in the absence and presence of added common ion. A plot of obtained in the absence of added common ion versus [M-]-1/2 yields a straight line whose slope and intercept are (k — feJ)X 1/2 and kj, respectively. A plot of fc pp obtained in the presence of added common ion versus [CZ]-1 yields a straight line whose slope and intercept are (k — kJ)K and kj, respectively. Figures 5-5 and 5-6 show these plots for polystyryl sodium in 3-methyl-tetrahydrofuran at 20°C. The combination of the two slopes and two intercepts allows the individual calculation of fc-, kj, and K. [Note K as well as [P-] and [P (C+)] can also be independently determined from conductivity measurements.]... 

It has been established from conductivity measurements that thermally activated and field-assisted hole hopping is responsible for the charge transport in solid polysilanes [48,49]. The mobility of the hole is as high as 10 m /V sec, while the mobility of the electron is a few orders of magnitude lower. In this section, we will show the reason why only the hole is mobile in polysilanes and how we can construct electron-conductive polysilanes. 

The number of delocalizable electrons can be increased. This is possible because the activation energy of the dark conduction, like the intramolecular excitation energy of the electrons, decreases with increasing number N of delocalizable electrons in agreement with the electron gas theory. Hence, if the relationship between and N for the open [Eq. (48)] and cyclic [Eq. (49)] electron systems is represented graphically, the values obtained from conductivity measurements will generally lie between the two curves see e.g. 13>64>. 

From conductance measurements in nitrobenzene and IR spectroscopy, Selbin and Holmes suggested the formulation (VO(NCS)(AA)2][VO(NCS)3(AA)] (AA = phen or bipy). 

The magnitude of the ohmic drop at a microelectrode can be evaluated quite readily for case 1 from a knowledge of the specific solution resistance (obtained from conductivity measurements such as in Table 12.1) and the expressions for the voltammetric current for the specific microelectrode employed. Case 2 is also straightforward if the free concentration of ions exceeds that of the electroactive species. However, the situation is somewhat more complicated for the third class. In this case, and in case 2 for fully associated electrolyte, migration as well as diffusion can affect the observed voltammetric signals. In all three cases, the situation may be further complicated by a change in structure of the double layer. However, this is ignored for now, and is considered in the section on very small electrodes. 

NH2CH2COO" (aq.). Louguinine1 found Q=2.97 for the reaction of aqueous aminoacetic acid with aqueous OH- to form aqueous glycinate, or aminoacetate, ion. Branch and Miyamoto,1 from conductivity measurements, calculated the heat of ionization of aqueous aminoacetic acid into aqueous H+ and aqueous glycinate ion to be —10.70. 

Poly(N-vinyl-imidazole) is an essentially monofunctional polybase, as shown by the sharpness of the jump in the titration curve 89). From conductance measurements, it was found that the data fitted the Henderson-Hasselbach expression with a term for the ionic strength ... 

Thus, has been determined from conductance measurements at a number of low HAc concentrations, one can plot log against and make a linear extrapolation to c = 0 to obtain K . 

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