Acid-base equilibria calculations

Acid solutions are often analyzed by titration with a solution of a strong base of known concentration similarly, solutions of bases are analyzed by titration with a strong acid. In either case, the measured pH is plotted as a function of the titrant volume. Calculation of a pH titration curve is a particularly good introduction to acid-base equilibrium calculations since a variety of calculations are involved. 

How valid is the approximation that [HF] = 1.00 M Because this question will arise often in connection with acid-base equilibrium calculations, we will consider it carefully. The validity of the approximation depends on how much accuracy we demand for the calculated value of [H+], Typically, the Ka values for acids are known to an accuracy of only about 5%. Therefore, it is reasonable to apply this figure when determining the validity of the approximation... 

In this text, we use the symbol H30 in those chapters that deal with acid/base equilibria and acid/base equilibrium calculations. In the remaining chapters, we simplify to the more convenient H", with the understanding that this symbol represents the hydrated proton. 

The acidity or basicity of a solution is frequently an important factor in chemical reactions. The use of buffers of a given pH to maintain the solution pH at a desired level is very important. In addition, fundamental acid-base equihbria are important in understanding acid-base titrations and the effects of acids on chemical species and reactions, for example, the effects of complexation or precipitation. In Chapter 6, we described the fundamental concept of equilibrium constants. In this chapter, we consider in more detail various acid-base equilibrium calculations, including weak acids and bases, hydrolysis, of salts of weak acids and bases, buffers, polyprotic acids and their salts, and physiological buffers. Acid-base theories and the basic pH concept are reviewed first. 

Because acid-base reactions in solution generally are so rapid, we can concern ourselves primarily with the determination of species concentrations at equilibrium. Usually, we desire to know [H+], [OH ], and the concentration of the acid and its conjugate base that result when an acid or a base is added to water. As we shall see later in this text, acid-base equilibrium calculations are of central importance in the chemistry of natural waters and in water and wastewater treatment processes. The purpose of this section is to develop a general approach to the solution of acid-base equilibrium problems and to apply this approach to a variety of situations involving strong and weak acids and bases. 

We must be aware that equilibrium calculations and log-concentration diagrams of systems involving heterogeneous equilibria may only provide us with the boundary conditions of the system rather than the situation that truly exists. Thus equilibrium calculations involving solids in waters and wastewaters are generally less representative of the true situation than acid-base equilibrium calculations for the following reasons. 

Acid-Base Equilibrium Calculations with the Spreadsheet... 

In aqueous solutions, two ions have dominant roles. These ions, the hydronium ion, H30 (or hydrogen ion, H" ), and the hydroxide ion, (OH ), are available in any aqueous solution as a result of the self-ionization of water, a reaction of water with itself, which we will describe in the next section. This will also give us some background to acid-base equilibrium calculations, which we will discuss in Chapter 17. 

Equation (11.7) has an equilibrium constant (often represented as K ) of approximately 1.0 X 10 (at 298 K), and a simple acid-base equilibrium calculation yields the result that, in pure water, [H30 ] = [OH ] = 1.0 X lO M. It follows that the pH (-log[H30+] = -log[H ]) ofwater is 7.00 at room temperature. Equation (11.7), then, is the basis of the pH scale as commonly presented in general chemistry. Any substance that raises the concentration of H30 ions produces a pH less than 7 and is an acid. Any substance that lowers the concentration of the hydronium ion or raises the concentration of the hydroxide ion produces a pH greater than 7 and is a base. Note that the small value of indicates that the self-ionization process occurs only to a very small extent. Another way to appreciate just how few hydronium ions there are in pure water is to realize that the concentration of water molecules in pure water is 55.6 M therefore, for every hydronium ion, there are (55.6/1.0 X 10 =) 556 X 10, or 556 million water molecules. 

Solutions of Salts of Polyprotic Acids 17-6 Acid-Base Equilibrium Calculations A Summary... 

Acid-Base Equilibrium Calculations A Summary— As a general summary of acid-base equilibrium calculations, the essential factors are identifying all the species in solution, their concentrations, the possible reactions between them, and the stoichiometry and equilibrium constants of those reactions. 

C18-0040. List all the types of calculations described in Chapter 18 in which acid-base equilibrium expressions play a role. 

The concentration of X is essentially constant throughout the reaction [see part (t )J. The equilibrium constant of part () is amended to include that constant concentration the new constant is K. That constant is just as effective in calculating the equilibrium concentration of Y as is the original constant, K. This is the same effect as using Ka, not K and [H.O], for weak acid and weak base equilibrium calculations. 

Acid-base equilibrium constants have been used to calculate the a-values of azoles as substituents on an aromatic ring or on an aliphatic chain. An example of this last case is the determination of ct, values of 1- (acetic acids 740,741, and 721 (Table 11-5) (82KGS264). 

The biological implication of this study is highly relevant to the fact that the enzyme s mechanism is pH-dependent and, in the case that a hydroxide is the fourth zinc ligand at pH 5, the deprotonation of the Zn—OH2 could not be simply described by the acid/base equilibrium with a pK, value close to 7.0. The combination of the Zn NMR spectroscopy data and ab initio structure calculations supports the existence of a hydroxide instead of... 

Finally, we recognize, as shown, that an acid-base equilibrium consists of two related reactions for which K.A values can be calculated and that at equilibrium, the [H+] is equivalent for each equation. 

These two solids will, of course, exhibit different catalytic effects. The equilibrium constant of reaction (XIV) is KAgCiIKAgBT which in water at 25°C equals 500. The tendency for reactions like (XIII) and (XIV) to occur can thus be calculated from known solubility products and stability constants. In the case of solids like oxides or carbonates, one must also take into account the relevant acid-base equilibrium constants because here dissolution can occur if the solution is made sufficiently acid or alkaline. 

In solvents of low dielectric constant, difficulties arise in the determination of the protolysis constants as lack of knowledge of the species present makes uncertain the calculation of the acid-base ratio. In aprotic solvents the solvent does not participate in the acid-base equilibrium, and it is necessary to have a second acid-base system to exhibit the acidity function. In the absence of a solvent, hydrogen chloride reacts with aniline as follows ... 

Changing the pH of a solution shifts the positions of all acid-base equilibria, including those involving polyprotic acids. Acid-base equilibrium expressions and equilibrium constants are used to calculate the amount of the change. For example, the two equilibria that apply to solutions containing H2CO3, HCOJ, and... 

Sections 15.4 and 15.5 outline methods for calculating equilibria involving weak acids, bases, and buffer solutions. There we assume that the amount of hydronium ion (or hydroxide ion) resulting from the ionization of water can be neglected in comparison with that produced by the ionization of dissolved acids or bases. In this section, we replace that approximation by a treatment of acid-base equilibria that is exact, within the limits of the mass-action law. This approach leads to somewhat more complicated equations, but it serves several purposes. It has great practical importance in cases in which the previous approximations no longer hold, such as very weak acids or bases or very dilute solutions. It includes as special cases the various aspects of acid-base equilibrium considered earlier. Finally, it provides a foundation for treating amphoteric equilibrium later in this section. 

Nevskaya, E.Yu., et al.. Calculations of acid-base equilibrium constants from the pH dependence of the electrokinetic potential and potentiometric titration data on aluminum oxides and hydroxides, Russ.. 1. Phys. Chem., Ti, 1421, 1999. 

From what we have said above, it follows that the acid-base equilibrium in the solutions containing metal cations and oxide ions in different sections of the titration curve is described either by the dissociation constant (in unsaturated solutions) or by the values of solubility product (in saturated solutions). In Refs. [175, 330] we proposed a method based on the analysis of the scatter in the calculated equilibrium parameters corresponding to the titration process. Indeed, in the unsaturated solution section there is no oxide precipitation and the calculated value of the solubility product increases monotonously (the directed shift) whereas the calculated value of the dissociation constant fluctuates about a certain value, which is the concentration-based dissociation constant of the studied oxide. 

We have seen earlier how calculations of pH in solutions with strong acid and strong base are relatively simple because strong acids and strong bases are completely dissociated. On the contrary, pH calculations in cases where the titrated acid is weak is not as simple. In order to be able to calculate the concentration of HsO ions after the addition of a given amount of strong base it is necessary to look at the weak acids dissociation equilibrium. Calculations of pH curves for titration of a weak acid with a strong base involve a series of buffer-related problems. 

The importance of water as a medium for inorganic reactions stems not only from the fact that it is far more readily available than any other solvent, but also because of the abundance of accurate physicochemical data for aqueous solutions compared with the relative scarcity of such data for solutions in non-aqueous solvents. This chapter is concerned mainly with equilibria and we begin by reviewing calculations involving acid-base equilibrium constants. 

Multiprotic Acid-Conjugate Base Equilibrium Calculations 125... 

MULTIPROTIC ACID-CONJUGATE BASE EQUILIBRIUM CALCULATIONS... 

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