Bases equilibria problems

Let s begin with a series of acid-base equilibria problems. 

A wide variety of acid—base equilibria problems can be solved using the relationships between pH, hydrogen ion concentration and hydroxide ion concentration in conjunction with the ionic product constant of water. 

This is a quantitative acid-base equilibrium problem, so we use the seven-step method. 

Problems that involve the concentrations of ions formed in aqueous solutions are considered to be equilibrium problems. The steps for solving acid and base equilibrium problems are similar to the steps you learned in Chapter 7 for solving equilibrium problems. 

The steps that you will use to solve acid and base equilibrium problems will vary depending on the problem. Below are a few general... 

The key to solving acid-base equilibrium problems is to think about the chemistry—that is, to consider the possible proton-transfer reactions that can take place between Bronsted-Lowry acids and bases. 

No all-purpose rules can be given for acid-base equilibrium problems. Skill increases with experience ... 

Recognize acid or base strengths from Ka or pKa values and use these to predict the position of an acid-base equilibrium. (Problems 4.23.4.34.4.35,4.36.4.37, and 4.41)... 

Having a conceptual understanding of the effect is a good starting point, but we still need to be able to understand the quantitative relationships between the different components in the equilibrium mixture. In this section, we will see how to deal with the common-ion effect in acid-base equilibrium problems. You will find that these problems are very similar to the weak acid problems earlier in the chapter. 

In this chapter we have encountered many different situations involving aqueous solutions of acids and bases, and in the next chapter we will encounter still more. In solving for the equilibrium concentrations in these aqueous solutions, you may be tempted to create a pigeonhole for each possible situation and to memorize the procedures necessary to deal with each particular situation. This approach is just not practical and usually leads to frustration Too many pigeonholes are required, because there seems to be an infinite number of cases. But you can handle any case successfully by taking a systematic, patient, and thoughtful approach. When analyzing an acid-base equilibrium problem, do not ask yourself how a memorized solution can be used to solve the problem. Instead, ask yourself this question What are the major species in the solution, and how does each behave chemically ... 

The most important part of doing a complicated acid-base equilibrium problem is the analysis you do at the beginning of a problem ... 

Example 14.13 illustrates how a typical weak base equilibrium problem should be solved. Note two additional important points ... 

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. 

Checking the assumption that 2S 10 we find 2S = 7 x 10 which is not IQ- The assumption is not valid. We will therefore proceed as we did in the solution of acid-base equilibrium problems and make the opposite assumption, that is, assume that 2S lO-". Then... 

As an example of an acid-base equilibrium problem, consider water in equilibrium with atmospheric carbon dioxide. The value of [COj (aq)] in water at 25°C in equilibrium with air that is 390 parts per million COj (close to the concentration of this gas in the atmosphere) is 1.277 X 10 mol/L. The carbon dioxide dissociates partially in water to produce equal concentrations of H+ and HCO3" ... 

Analyze We are asked to determine the pH at the equivalence point of the titration of a weak acid with a strong base. Because tire neutralization of a weak acid produces the corresponding conjugate base, we ejqsect the pH to be basic at the equivalence point. Plan We should first determine how many moles of acetic acid there are initially. This win teU us how many moles of acetate ion there will be in solution at the equivalence point. We then must determine the final volume of the resulting solution, and the concentration of acetate ion. From this point this is simply a weak-base equilibrium problem like those in Section 16.7. 

Refer to the steps for solving weak acid equilibrium problems. Use the same systematic approach for weak base equilibrium problems. 

Often we know the value of Kgp for a compound and are asked to calculate the compound s molar solubility. The procedure for solving such a problem is essentially identical to the p ocedure for solving weak acid or weak base equilibrium problems ... 

If we make the same x is small approximation that we make for weak acid or weak base equilibrium problems, we can consider the equilibrium concentrations of HA and A to be essentially identical to the initial concentrations of HA and A (see step 4 of Example 16.1). Therefore, to determine [H30 ] for any buffer solution, we multiply by the ratio of the... 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

It is well known that the rates of all azo coupling reactions in aqueous or partly aqueous solutions are highly dependent on acidity. Conant and Peterson (1930) made the first quantitative investigation of this problem. They demonstrated that the rate of coupling of a series of naphtholsulfonic acids is proportional to [OH-] in the range pH 4.50-9.15. They concluded that the substitution proper is preceded by an acid-base equilibrium in one of the two reactants, which was assumed to be the equilibrium between the diazohydroxide and the diazonium ion, in other words, that the reacting equilibrium forms are the undissociated naphthol and the diazohydroxide. 

Solutions to complex ionic equilibrium problems may be obtained by a graphical log concentration method first used by Sillen (1959) and more recently described by Butler (1964) and Morel (1983). These types of problems are described further in Chapter 16 as they relate to natural systems. Computer-based numerical methods are also used to solve these problems (Morel, 1983). 

The examples of this section illustrate the general approach to equilibrium problems. Notice that these examples include gas-phase, precipitation, and acid-base chemishy. We use a variety of equilibrium examples to emphasize that the general strategy for working with equilibria is always the same, no matter what type of equilibrium is involved. In Chapters T7 and 18 we apply these ideas in more detail to important types of equilibria. 

C17-0037. Outline the procedure for working an equilibrium problem for a weak acid-base system. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

GASEQ A Chemical Equilibrium Program for Windows. GASEQ is a PC-based equilibrium program written by C. Morley that can solve several different types of problems including composition at a defined temperature and pressure, adiabatic temperature and composition at constant pressure, composition at a defined temperature and at constant volume, adiabatic temperature and composition at constant volume, adiabatic compression and expansion, equilibrium constant calculations, and shock calculations. More information can found at the website http //www.arcl02.dsl.pipex.com/gseqmain.htm. 

Solving Equilibrium Problems That Involve Acids and Bases... 

Many of these are substantially non-nucleophilic and unlikely to effect the rate or course of the reaction, although this should always be checked. References 29 to 31 relate some problems in the use of some of these buffers. Occasionally, one of the reactants being used in excess may possess buffer capacity and this obviates the necessity for added buffer. The situation will often arise in the study of complex ion-ligand interactions when either reactant may be involved in an acid-base equilibrium. 

For an advanced equilibrium problem based on the bromine Latimer diagram, see T. Michalowski, Calculation of pH and Potential E for Bromine Aqueous Solution, J. Chem. Ed. 1994, 71, 560. 

One thing is clear there can be no acid-base equilibrium between states of different multiplicities thus it is correct to consider only the pK of the singlet state , or the pA of the triplet state . However, the question of the protolytic equilibrium between an mr singlet and a tttt or charge transfer (CT) singlet remains open. This problem is illustrated in Figure 4.48 for the case of 4-hydroxybenzophenone, in which there is a reversal in the order of mr and CT states between the acid and base forms. Excitation of the protonated molecule in ethanol for example leads to the ground state deprotonated form, but the detailed mechanism of this process is not known. 

---