Charge balance equations

The second type of equation is a charge balance equation. A charge balance equation is a statement of solution electroneutrality. 

Note that the concentration of Ca + is multiplied by 2, and that the concentrations of H3O+ and OH are also included. Charge balance equations must be written carefully since every ion in solution must be included. This presents a problem when the concentration of one ion in solution is held constant by a reagent of unspecified composition. For example, in many situations pH is held constant using a buffer. If the composition of the buffer is not specified, then a charge balance equation cannot be written. 

Write a mass balance and charge balance equations for a 0.10 M solution of NaHC03. 

Substituting these equations, along with the equation for into the charge balance equation gives us... 

Substituting equation 6.46 into the charge balance equation and solving for [A ] gives... 

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

If an ion is doubly charged, wc multiply its concentration by 2 in the charge balance equation, and likewise for triply charged ions. 

In very dilute solutions of strong acids and bases, the pH is significantly affected by the autoprotolysis of water. The pH is determined by solving three simultaneous equations the charge-balance equation, the material-balance equation, and the expression for Kw. 

In addition to the material balance equation for the surface hydroxyl groups listed above, a charge balance equation can be written ... 

Because we are generally able to define the chemistry of an aqueous solution containing n chemical elements by analytical procedures, n equations such as 8.48 and 8.49 exist, relating the bulk concentration of a given element mj to all species actually present in solution. Associated with mass balance equations of this type may be a charge balance equation expressing the overall neutrality of the solution ... 

Substituting (2.56) into the charge balance equation and using (2.53) to eliminate [OH ] we obtain the fith-order polynomial equation in [H+] ... 

We may now also generalize the charge-balance equation. In Eq. (B20), the left-hand side (LHS) becomes... 

Equation (B29) is a generalization of the simple charge-balance equation represented by Eq. ( 17). Inclusion of centers that can have both donor and acceptor states results in a slight modification of Eq. (B29), and will be considered in the next section. 

The usefulness of Eq. (B26) is obvious here, because, although we could probably have written down the charge-balance equations for the previous cases by inspection, we certainly could not have done so for the double-charge-state case. 

The complexity of this example (Cu in GaAs) can be increased by supposing that a single-donor state is also possible, i.e., that one of the two (p+, p ) electrons can be excited by less than band-gap energy. Then the / = 0 state has one electron, and a degeneracy gAQ = 4 /3 l = 4. Similarly, gA1 = 4 /2 2 = 6, gA2 = 4, and gA3 = 1. The charge-balance equation must include these additional electrons available for distribution. Thus, Eq. (B28) becomes... 

Step 2 Charge balance. Equating positive and negative charges gives... 

If additional salt is added to yield a concentratiCtii, the free acid precipitates, and the pH of the solution increases owing to protons being removed from the solution. By utilizing the mass balance and the charge balance equations for the solutions, they derived an expression for the proton activity ... 

Complexation of cations and anions is achieved by introducing mass action expressions for the formation of the cation or anion surface complex into the mass balance for the total number of surface complexation sites and, if the new surface species is charged, into the charge balance equation, e.g. metal surface complexes, Cd2+. 

If we double the mass balance equation and subtract the charge balance equation, the result is ... 

The interface-corrected data (dashed line) in FIGURE 3 show the expected freezeout of carriers as the temperature is lowered and can be analysed by means of the charge-balance equation ... 

Mass balance and charge balance equations can be given by ... 

The titration curve of a polyprotic acid can be obtained by using the same approach as for monoprotic weak acids or weak bases. The mass and charge balance equations... 

If we were to include [Na+], we would have this charge balance equation, plus four more equations, totaling 5 equations in the 5 unknowns [CH3COOH], [CH3COO-], [H+], [OH-], and [Na+] ... 

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