Ionic measurement

One then observes that the overall index of Scheme 1.4, Af = 1.58 = H[p°], predicting about 3/2 jr-bond multiplicity in allyl, can be reconstructed by adding to this additive-ionicity measure, the sum of the bonding (positive) entropy-covalency Si of the first MO and the antibonding (negative) contribution (—S2) due to the second MO ... 

KNs. The d.c. electrical conduction of KN3 in aqueous-solution-grown crystals and pressed pellets was studied by Maycock and Pai Verneker [127]. The room-temperature conductivity was found to be approximately 10" (ohm cm) in the pure material. Numerical values for the enthalpies of migration and defect formation were calculated from ionic measurements to be 0.79 0.05 and 1.43 0.05 eV (76 and 138 kJ/mole), respectively. In a subsequent paper [128], the results were revised slightly and the fractional number of defects, the cation vacancy mobility, and the equilibrium constant for the association reaction were calculated. The incorporation of divalent barium ions in the lattice was found to enhance the conductivity in the low-temperature region. Assuming the effect of the divalent cation was to increase the number of cation vacancies, the authors concluded that the charge-carrying species is the cation, and the diffusion occurs by means of a vacancy mechanism. 

Ionic contamination-expressed in sodium chloride equivalents is primarily used to assess the climatic resistance of electronic assemblies. Ionic measurement is suitable for statistical process control, but it does not furnish an absolute statement concerning the climatic resistance of an assembly. 

First we wish to acquaint oiurselves with a simple method, which can be used to distinguish between contact impedances of internal interfaces and electrode interfaces it is the method of many-point measurement (see also Fig. 7.31). In a four-point measurement we apply a constant (or sinusoidal) current I to the sample via electrodes applied to the end surfaces, but now we measure the voltage drop U with a high resistance voltmeter between two probes applied to the sample at a distance of Ax from each other. As before, the local current density is determined by the external current to be i=I/a (a contact area of external electrodes). The difference in the electrochemical potential of the electrons (or ions for ionic measuring electrodes ) at the probes is now proportional to the current density and to Ax. (Note that there are only marginal gradients in the relevant electrochemical potentials perpendicular to the current flow.) In the case of pure conductivity experiments, the specific conductivity becomes... 

The co-ordination number in ionic compounds is determined by the radius ratio - a measure of the necessity to minimize cationic contacts. More subtle effects are the Jahn-Teller effect (distortions due to incomplete occupancy of degenerate orbitals) and metal-metal bonding. 

Thus in the case of ions, measurements of this type are generally used to obtain values of the mobility and, through Stoke s law or related equations, an estimate of the effective ionic size. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

Much effort has gone into detenuining these quantities since they are fundamental to ionic reactivity. Examples include thenuodynamic equilibrium measurements for all quantities and photoelectron studies for detenuination of EAs and IPs. The most up-to-date tabulation on ion thenuochemistry is the NIST Chemistry WebBook (webbook.nist.gov/chemistry) [123]. 

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

All measurements were performed at constant ionic strength (2.00 M using KNO3 as background electrolyte) and at pH 7-8. Ligand-catalyst ratio. 

In an excess of nitric acid, nitrous acid exists essentially as dinitrogen tetroxide which, in anhydrous nitric acid, is almost completely ionised. This is shown by measurements of electrical conductivity, and Raman and infra-red spectroscopy identify the ionic species... 

Although it is not possible to measure an individual ionic activity coefficient,, it may be estimated from the following equation of the Debye-Hiickel theory ... 

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

The thermodynamic solubility product for Pbl2 is determined in this experiment by measuring its solubility at several ionic strengths. 

The concentration of Ca + in a water sample was determined by the method of external standards. The ionic strength of the samples and standards was maintained at a nearly constant level by making each solution 0.5 M in KNO3. The measured cell potentials for the external standards are shown in the following table. 

This experiment describes the determination of the stability (cumulative formation) constant for the formation of Pb(OH)3 by measuring the shift in the half-wave potential for the reduction of Pb + as a function of the concentration of OH . The influence of ionic strength is also considered, and results are extrapolated to zero ionic strength to determine the thermodynamic formation constant. 

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