Acid-base equilibria solving

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. 

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 ... 

Thus, for every [H ], seven equations have to be solved simultaneously in order to compute the relative concentrations of each species present. Five mass laws (four stability expressions for the four different amine complexes and the acid-base equilibrium of NH4 -NH3) and two concentration conditions make up the seven equations. As concentration conditions one can formulate equations defining Cut- and NH3/. 

Solutions Manual (0-13-147882-6) The Solutions Manual, prepared by Jan W. Simek of California Polytechnic State University, contains complete solutions to all the problems. The Solutions Manual also gives helpful hints on how to approach each kind of problem. This supplement is a useful aid for any student, and it is particularly valuable for students who feel they understand the material but need more help with problem solving. Appendix 1 of the Solutions Manual summarizes the lUPAC system of nomenclature. Appendix 2 reviews and demonstrates how acidity varies with structure in organic molecules, and how one can predict the direction of an acid-base equilibrium. Brief answers to many of the in-chapter problems are given at the back of this book. These answers are sufficient for a student on the right track, but they are of limited use to one who is having difficulty working the problems. 

A typical CFD model for acid base and equilibrium chemistry solves Eqs. (25)-(29), and then uses Eq. (55) to approximate ft. Once ft is known, the expected values of the reactant concentrations are computed by numerical quadrature from the formula... 

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... 

Very many problems in solution chemistry are solved with use of the acid and base equilibrium equations. The uses of these equations in discussing the titration of weak acids and bases, the hydrolysis of salts, and the properties of buffered solutions are illustrated in the following sections of this chapter. 

In the chapters so far we have considered the phase rule somewhat intuitively for example, in solving equilibrium problems we used the obvious principle that an equilibrium problem can be solved if for n unknowns (e.g., activities or concentrations of n species) n equations are available. For example, in a closed dissolved carbonate system we need to define the system (H2CO3, HC03 , CO H, OH ) and two concentration conditions (e.g., Ct and pH, or [Aik] and H2CO ]), in addition to temperature and pressure, because the five species are interconnected by three mass laws (two acid-base equilibria and the ion product of H2O). In the example given P = 1 (aqueous solution), C = 3 le.g., HCO, H", H20(l)], andF = 4 (pressure, temperature, and two concentration conditions). 

This equation is used to directly calculate the pH of a buffer without using an equilibrium calculation. It is important that you know how to do equilibrium calculations before you use this equation. The equation makes the calculation much faster, but there are frequently conceptual questions about acid-base equilibria that require a solid understanding of the topic. Therefore, make sure you truly understand what you are doing before using this calculation. The problems that use the Henderson-Hasselbalch equation can be solved using equilibrium calculation tables as well. 

In addition to n-alanine and n-glutamate, many bacterial cell walls also contain meso-diaminopimelate (DAP) [2]. DAP is produced by epimerization from l,l-DAP to d,l-DAP by the cofactor independent diaminopimelate epimerase [97, 98]. The structure of this enzyme has been solved and two cysteines in the active site were proposed to be the acid-base catalysts [99]. The pattern of label incorporation from tritiated water is consistent with a two-base mechanism [97]. The enzyme has been shown to be stoichiometrically inhibited by the thiol alkylating agent aziDAP [97]. Interestingly, DAP epimerase has an equilibrium constant of 2 (Keq = [d,l]/[l,l]) duc to the statistically expected higher concentration of the [d,l] form at equilibrium between these species [100]. 

The concept of eqnilibrinm constants is extremely important in chemistry. As you will soon see, equilibrinm constants are the key to solving a wide variety of stoichiometry problems involving eqnilibrium systems. For example, an industrial chemist who wants to maximize the yield of sulfuric acid, say, must have a clear understanding of the equilibrium constants for all the steps in the process, starting from the oxidation of sulfur and ending with the formation of the final product. A physician specializing in clinical cases of acid-base imbalance needs to know the equilibrium constants of weak acids and bases. And a knowledge of equilibrium constants of pertinent gas-phase reactions will help an atmospheric chemist better understand the process of ozone destraction in the stratosphere. 

So far, there has been no need to use electrical neutrality. But, as with acid-base equilibria and ion pair formation, sometimes it is needed when the equilibrium relation(s) and stoichiometric relations are fewer in number than the number of unknowns which have to be found. The following illustrative problem cannot be solved easily without invoking the relation describing electrical neutrality. 

We can now write some general rules for solving chemical equilibrium problems, using the approximation approach. These rules should be applicable to acid-base dissociation, complex formation, oxidation-reduction reactions, and others. That is, all equilibria can be treated similarly. 

Salt of strong base weak acid (represented as MA) NaCN (salt of NaOH and HCN) Hydrolysis of conjugate base (A ) of weak acid > basic solution A + H.O HA + OH-. K Solve weak base equilibrium for A using Xj, = j. K for HA 18-8... 

Solve Because HF is a weak acid and HCl is a strong add, the major species in solution are HF, H, and Cl. The Cl, which is the conjugate base of a strong acid, is merely a spectator ion in any acid-base chemistry. The problem asks for [F ], which is formed by ionization of HF. Thus, the important equilibrium is HF(aq)... 

Plan We will first use the Henderson-Hasselbalch equation, which relates pK and ratio of acid-base concentrations to the pH. This will be straightforward. Then, we will redo the calculation making no assumptions about any quantities, which means we will need to write out the initial/change/ equilibrium concentrations, as we have done before. In addition, we will need to solve for quantities using the quadratic equation (since we cannot make assumptions about unknowns being small). 

Comment In Sample Exercise 17.3, the calculated pH is the same whether we solve exactly using the quadratic equation or make the simplifying assumption that the equilibrium concentrations of acid and base are equal to their initial concentrations. The simplifying assumption works because the concentrations of the acid-base conjugate pair are both a thousand times larger than K. In this Sample Exercise, the acid-base conjugate pair concentrations are only 10-100 as large as Therefore, we cannot... 

Write the chemical equation for the equilibrium involving the conjugate acid and base. Write the Kl expression. Put into this the values known, and x for the unknown quantity desired. Solve roughly for X using all / values equal to 1. Use approximate equations (3-3), (3-4), or (3-5) for acid, base, or buffer mixtures. 

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 ... 

To classify redox couples with respect to their strength, a trick is used that is similar to that used with acid-base equilibria. Consider what would happen if the redox couple studied was brought to react with a standard partner . Long ago, the couple hydrogen gas/hydrogen ion (H2/H30 ) was chosen to act as the standard partner. To solve the problem of comparing the strength of redox couples, we simply initiate the reaction and, after equilibrium has been established, determine the actual equilibrium constant (as with acid-base equilibria). This time, however, the classification is done in a somewhat different way. 

IN THIS CHAPTER, we apply the equilibrium concepts learned in the previous chapter to acid-base phenomena. Acids are common in many foods, such as limes, lemons, and vinegar, and in a number of consumer products, such as toilet cleaners and batteries. Bases are less common in foods but are key ingredients in consumer products such as drain openers and antacids. We will examine three different models for acid-base behavior, all of which define that behavior differently. In spite of their differences, the three models coexist, each being useful at explaining a particular range of acid-base phenomena. We also examine how to calculate the acidity or basicity of solutions and define a useful scale, called the pH scale, to quantify acidity and basicity. These types of calculations often involve solving the kind of equilibrium problems that we explored in Chapter 14. 

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- ... 

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