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Electro neutrality equation

There are alternative algebraic functions. Instead of writing the electro-neutrality equation, we can derive a relation called the proton condition. If we made our solution from pure H2O and HB, after equilibrium has been reached the number of excess protons must be equal to the numtier of proton deficiencies. Excess of deficiency of protons is counted with respect to a zero level reference condition representing the species that were added, that is, H2O and HB. The number of excess protons is equal to [H ] the number of proton deficiencies must equal [B ] -I-[OH ]. This proton condition gives, as in equation iva, [H" ] = [B ] -f lOH-]. [Pg.108]

To maintain electro-neutrality, the following equation is applicaable ... [Pg.121]

If the species is neutral, its chemical potential p% can be varied by changing its concentration and hence its activity ay. dpt — RT d nat. In this case the determination of the surface excesses offers no difficulty in principle. However, if a species is charged, its concentration cannot be varied independently from that of a counterion, since the solution must be electrically neutral. To be specific, we consider the case of a 1-1 electrolyte composed of monovalent ions A and D+. The electro capillary equation then takes the form ... [Pg.222]

Equation (1.57a) implies that in the locally electro-neutral ambipolar diffusion concentration of both ions evolves according to a single linear diffusion equation with an effective diffusivity given by (1.57b). Physically, the role of the electric field, determined from the elliptic current continuity equation... [Pg.17]

A somewhat similar situation occurs in one-dimensional multi-ionic systems with local electro-neutrality in the absence of electric current. It will be shown in Chapter 3 that in this case again the electric field can be excluded from consideration and the equations of electro-diffusion are reduced to a coupled set of nonlinear diffusion equations. [Pg.17]

As pointed out in the Introduction, it is customary in the treatment of such systems to assume local electro-neutrality (LEN), that is, to omit the singularly perturbed higher-order term in the Poisson equation (1.9c). Such an omission is not always admissible. We shall address the appropriate situations at length in Chapter 5 and partly in Chapter 4. We defer therefore a detailed discussion of the contents of the local electro-neutrality assumption to these chapters and content ourselves here with stating only that this assumption is well suited for a treatment of the phenomena to be considered in this chapter. [Pg.59]

Equation (4.4.1b) expresses impermeability of the ideally cation-permselective interface under consideration for anions j is the unknown cationic flux (electric current density). Furthermore, (4.4.1d) asserts continuity of the electrochemical potential of cations at the interface, whereas (4.4. lg) states electro-neutrality of the interior of the interface, impenetrable for anions. Here N is a known positive constant, e.g., concentration of the fixed charges in an ion-exchanger (membrane), concentration of metal in an electrode, etc. E in (4.4.1h) is the equilibrium potential jump from the solution to the interior of the interface, given by the expression ... [Pg.134]

Equation (4.4.17) corresponds to the ideal permselectivity of the membrane and (4.4.18) stands for local electro-neutrality within the solution (4.4.18a) and within the ideally permselective membrane (4.4.18b). [Pg.140]

Equation (5.2.42) and the treatment that leads to it remind us that in accordance with the description in the Introduction it takes about 1 je as long for an electro-diffusional system to get from an arbitrary initial state to a macroscopically locally electro-neutral one. [Pg.169]

Generalized local Darcy s model of Teorell s oscillations (PDEs) [12]. In this section we formulate and study a local analogue of Teorell s model discussed previously. The main difference between the model to be discussed and the original one is the replacement of the ad hoc resistance relaxation equation (6.1.5) or (6.2.5) by a set of one-dimensional Nernst-Planck equations for locally electro-neutral convective electro-diffusion of ions across the filter (membrane). This filter is viewed as a homogenized aqueous porous medium, lacking any fixed charge and characterized... [Pg.220]

In the following we give a short account on this theory for demonstrating that interactions between dipolar ion pairs and free ions and/or other pairs can be incorporated in a natural and transparent way [31, 32], The theories rest on the Poisson-Boltzmann equation. With the presumption of electro neutrality, the expansion in first order of f3 yields the Helmholtz equation or linearized Poisson-Boltzmann equation,... [Pg.152]

To see this, we first note that though it is true that for ionic species, equations (4.123)-(4.126) can result from the electro-neutrality conditions, the conditions themselves are not necessarily a result of the electric charge neutrality. They arise from the closure condition with respect to the fragments A and B. Thus, for a solute S dissociating into two neutral fragments A and B, as in (4.118) not necessarily ionic species as in (4.121), we still have the following conservation relations ... [Pg.134]

An actual research topic is to also capture the electrical stimulation. In this case the influence of the local change of the concentrations and the electric potential - in the solution phase - on the unknowns in the gel phase has to be considered. In Avci et al. (Avci 2008), the electro-neutrality condition is substituted by an equation for the electric potential. So the electric potential may be used as an additional degree of freedom. [Pg.148]

This equation can apply to all ions under the condition of electro-neutrality. [Pg.9]

Based on electro-neutrality, we deduce the following equation for the ion exchange membrane, where X is the fixed ion concentration of the membrane, and Q) is the sign of the fixed charge (—1 for negatively charged membranes, + 1 for positively charged membranes),... [Pg.9]

The factor q = rii+xlrii describes the distribution of aerosol particles over electric charges. Taking into account both electro-neutrality and total mass balance, the equation for electron density can be presented as... [Pg.49]

Nonstoichiometric compounds show electron defect in addition to ion defect because of electro-neutrality. In chanical terms, this can be equated to the occurrence of ions of different valency (e.g.,... [Pg.579]

The general validity of the electro-neutrality condition requires that in a closed system no net generation or net consumption of free electrons will take place. In the presence of ionizing radiation, free electrons are produced whose concentration is compensated for by unusual atomic valency states with respect to equilibrium considerations, therefore, this effect can be ignored. As long as the FP in the above formula stands for the most easily oxidizable or reducible species in the system, the equation ( 2 V-V ) = 0 is valid. A single crystallite of the UO2 material can... [Pg.97]

The first, second, and third terms on the right-hand side of Equation (12.12) respectively, represent the three governing transport mechanisms of species diffusion, migration, and eonvection. Combining Equations (12.11) and (12.12) with the condition of electro-neutrality (E ZhCh =0) gives ... [Pg.278]

In the present model. Equation (12.23) is solved for two anions Al(OH)4 and OH , and the concentration of cation, K is deduced with the electro-neutrality condition stated before from the known concentrations ofAl(OH)4 andOH The production terms (5,) forOH andAl(OH)4, evaluated using Faraday s law, respectively are ... [Pg.280]

The properties of dissolution as gas solubility and enthalpy of solution can be derived from vapor liquid equilibrium models representative of (C02-H20-amine) systems. The developments of such models are based on a system of equations related to phase equilibria and chemical reactions electro-neutrality and mass balance. The non ideality of the system can be taken into account in liquid phase by the expressions of activity coefficients and by fugacity coefficients in vapor phase. Non ideality is represented in activity and fugacity coefficient models through empirical interaction parameters that have to be fitted to experimental data. Development of efficient models will then depend on the quality and diversity of the experimental data. [Pg.487]

As the intercalation of lithium occurs as ionic species LF, the electro-neutrality of the host is maintained by the ejection into the external circuit of an electron generated by a reduction reaction of the transition-metal cation, the oxidation state of which switches Irom Ti to Ti ". The cell potential decreases uprut the Li uptake into the host framework, which follows the simple Nemst equation ... [Pg.46]

This equation describes how rapidly (positive or negative) excess neutral electrolyte is created. As discussed before, this model is representative of ion transport in double layers as occurs in electrophoresis and electro-osmosis. It is recalled that the error function erf b is defined as... [Pg.553]

In a capillary tube, the applied electric field E is expressed by the ratio VILj, where V is the potential difference in volts across the capillary tube of length Lj (in meters). The velocity of the electro-osmotic flow, Veo (in meters per second), can be evaluated from the migration time t of (in seconds) of an electrically neutral marker substance and the distance L, (in meters) from the end of the capillary where the samples are introduced to the detection windows (effective length of the capillary). This indicates that, experimentally, the electro-osmotic mobility can be easily calculated using the Helmholtz-von Smoluchowski equation in the following form ... [Pg.588]

A here and Dg are the diffusion coefficients of A and B in water, r is the separation distance at which A and B are considered to be in contact, and Nq is Avogadro s number. If A and B are ions of the same charge (e.g., A and B, or A" and B ), the value of kj) predicted from equation 1.104 is higher than that observed electrostatic repulsion in this case reduces the probability of direct encounter between A and B. High electrolyte (salt) concentrations in solution shield the individual ions from his repulsion, so that reaction 1.103 has a rate constant that increases with increas-ng electrolyte concentration. If, on the other hand, A and B have opposite charge, he intrinsic rate constant should be higher but will decrease with increasing electro->te concentration. For reactions between neutral molecules, the rate constant should be fairly insensitive to electrolyte concentration. [Pg.27]

The schematic representation of a CE apparatus is shown in Fig. 1. The mechanism of separation of water pollutants in CE is based on the electro-osmotic flow (EOF) and electrophoretic mobilities of the pollutants. The EOF propels all pollutants (cationic, neutral, and anionic) toward the detector and, ultimately, separation occurs due to the differences in the electrophoretic migration of the individual pollutants. Under the CE conditions, the migration of the pollutant is controlled by the sum of the intrinsic electrophoretic mobility (//ep) and the electro-osmotic mobility (/r o), due to the action of EOF. The observed mobility (Mobs)of the pollutants is related to and p p by the following equation ... [Pg.792]


See other pages where Electro neutrality equation is mentioned: [Pg.90]    [Pg.90]    [Pg.1925]    [Pg.189]    [Pg.189]    [Pg.221]    [Pg.289]    [Pg.250]    [Pg.147]    [Pg.249]    [Pg.1925]    [Pg.242]    [Pg.288]    [Pg.13]    [Pg.25]    [Pg.141]    [Pg.616]    [Pg.217]    [Pg.116]    [Pg.552]    [Pg.912]    [Pg.645]    [Pg.168]    [Pg.217]    [Pg.100]   
See also in sourсe #XX -- [ Pg.321 ]




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