Charge balance equivalent

Charge balance equivalent (CBE). The total concentration of positively charged species should be equal to that of the negatively charged species, maintaining electrical neutrality in the solution. 

Table 11-6 gives useful equations derived by writing a charge balance and substituting fractional compositions for various concentrations. For titration of the diprotic acid, H2A, ct> is the fraction of the way to the first equivalence point. When = 2, we are at the second equivalence point. It should not surprise you that, when cj> = 0.5, pH = pAj and, when = 1.5, pH pAT2. When = 1, we have the intermediate HA " and pH j(pAj -I- pA j). 

It has long been known that defect thermodynamics provides correct answers if the (local) equilibrium conditions between SE and chemical components of the crystal are correctly formulated, that is, if in addition to the conservation of chemical species the balances of sites and charges are properly taken into account. The correct use of these balances, however, is equivalent to the introduction of so-called building elements ( Bauelemente ) [W. Schottky (1958)]. These are properly defined in the next section and are the main content of it. It will be shown that these building units possess real thermodynamic potentials since they can be added to or removed from the crystal without violating structural and electroneutrality constraints, that is, without violating the site or charge balance of the crystal [see, for example, M. Martin et al. (1988)]. 

In our simulations, we assumed that seawater compositions during the Neoproterozoic era would have been similar to present-day seawater, except for high Fe(II) concentrations. We arbitrarily assigned our hypothethical ocean a Fe(II) concentration of 0.01065 m, the same concentration as Ca to maintain a charge balance, we removed an equivalent amount of Na (from 0.48610 to 0.46480m) (Fig. 5.6). 

In principle, the negatively charged, presumably planar network I can be combined with one molar equivalent of tetraalkylammonium ion IGN"1" of the right size as interlayer template to yield a crystalline inclusion compound of stoichiometric formula (IGN+) I C(NIG ) ICO2 that is reminiscent of the graphite intercalates. Anionic network n, on the other hand, needs twice as many monovalent cations for charge balance, and furthermore possesses honeycomb-like host cavities of diameter 700 pm that must be filled by... 

Consider the situation under potentiostatic conditions. Here, the potential control takes care that the sum of the potential drop across the double layer, DL, and through the electrolyte up to the position of the RE (and possibly additional external series resistances) is constant, i.e. that U = DL + I Rn or / = (U - DL)/Rn. Rn is the sum of the uncompensated cell resistance and possible external resistances and I the total current through the cell. Hence, a perturbation of a state on the NDR branch towards larger values of Dl causes, on the one hand, a decrease of the faradaic current If, and, on the other hand, a decrease of the current through the electrolyte, I. The charge balance through the cell, which can be readily obtained from the general equivalent circuit of an electrochemical cell (Fig. 8), tells us whether the fluctuation is enhanced or decays ... 

CHARGE BALANCE Aqueous charge balance in equivalents... 

Since there are six carbon atoms on the left side, one must also have six on the right, and thus x — 6/4 = 3/2. With the same rationale as above, the oxidation state of carbon in fumaric acid is +2/4 = +1/2. Then one needs to remove an equivalent of 1.5 electrons from each carbon in benzene, i.e., 1.5 x 6 = 9 = 2. The charge balance requires 9 protons = y = z, and thus there is a total of y + 3/2(6) =18 hydrogens on the product side, which leads tow = 18/2 = 9. Then,... 

Example 11 An ionic charge balance in terms of equivalents for a carbonate system is shown as follows ... 

We realize that [Aik] and [H-Acy] also can be expressed by a charge balance— the equivalent sum of conservative cations, less the sum of conservative anions ([Aik] = a — b). The conservative cations are the base cations of the strong bases Ca(OH)2, KOH, and the like the conservative anions are those that are the conjugate bases of strong acids (SOj , NO, and Cl ). 

In a similar way, we have implicitly considered the phase rule when we stated, in introducing the tableaux, that the number of components equals the number of species minus the number of independent reactions. An equivalent statement is that in each phase C — 1 concentration conditions (including relations for charge balance or proton conditions), at a given temperature and pressure, are necessary in order to describe the system. 

Acids and bases that make up the total alkalinity must protonate in solution in a way that achieves charge balance. For example, the difference in equivalents evaluated in Table 4.2 determines the relative abundances of [HCO3 ] and [CO3 ] that are required for charge balance. As the difference between Ax and DIG increases (becomes a larger positive number) there must be a higher carbonate concentration to achieve charge balance because CO3 carries two equivalents and HCOs only one. 

We cannot assume a mass balance for total bicarbonate because the system is open to atmospheric CO2. The charge-balance equation states that in any water the total equivalents of the cations must equal that of the anions. Here, the charge-balance equation is... 

Third is the charge-balance equation, which describes the fact that the total of the equivalents (eq) or milliequivalents (meq) of cations in a given volume or weight of water must equal the same sum for the anions. The charge-balance equation in this example is... 

Here, the hydrogen ions are used to mobilize carbon as bicarbonate and, as in the case of silicate weathering, an equivalent amount of C02 is used up to establish charge balance. 

Here k is the total number of non-equivalent sites (3 for the X, Y, and Si sites in this example) rij is the number of times the constituent in question appears in the formula for the jth site in the solution (when considering single ions such as Mg, Fe, and Si" ", etc., as in this example, n = 3 for the X sites, 2 for the Y s, and 3 for the Si sites) Xi,j is the mole fraction of the ith constituent (or ion in this example) on the jth site (X, Y, or Si site). One thing to watch for in applying this equation is to make sure that a charge balance is maintained. In other words, the substitutions should be independent of one another. See Ulbrich and Waldbaum (1976) for a detailed discussion of this topic. 

In addition, it should be noted that, although the generic formula of some minerals listed in Table XII-1 does not mention thorium, this element is often present in such minerals by snbstitution for quadrivalent or tervalent species, in percentages that may be in excess of 10%. This is, for instance, the case for Sm-monazites. Of course, in such substitutions charge balance must be maintained and the replacement of a tervalent ion by thorinm mnst be accompanied by an equivalent increased amount of a lower-valent cation (often Ca ) in the stmctnre. 

A variety of techniques to identify and quantify acid and base components in rainwater are applied to data for southern California. Charge balance calculations using major cation and anion concentration data indicate southern California probably had alkaline rain in the 1950 s and the 1960 s with the exception of the Los Angeles area which probably had acidic precipitation. Measurements of the chemical composition of precipitation collected in Pasadena, California, from February 1976 to September 1977 are compared with the charge balance and conductivity balance constraints. A chemical balance is used to determine the relative importances of different sources. The pH is found to be controlled by the interaction of bases and strong acids with nitric acid being 32% more important on an equivalent basis than sulfuric acid. The uncertainties in the various calculations are discussed. 

Fig. 5 shows the results of both titration experiments. The experimental results are in good agreement with the predictions based upon the equilibrium expressions for Kb the Ka for each indicator, and the mass and charge balances[13]. The data from the acid titration show a sharp equivalence point at approximately 10 m HCl, which suggests that B(OH)4 is still a strong base at 350°C and 0.622 g/mL and capable of neutralizing HCl. This strong acid base titration curve, as was also observed for HCl and KOH, may be contrasted with the weak acid-base behavior observed for the sulfuric acid-ammonia system at 380 C[41]. 

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