Acid-base equilibrium problems with bases

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

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 ... 

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" ... 

The acid-base equilibrium constants of the beta-blockers atenolol, oxprenolol, timolol, and labetalol were determined by automated potentiometric titrations. The pKg values were obtained in water-rich or water methanol medium (20% MeOH) to obviate the solubility problems associated with the compounds. The initial estimates of pKa values were obtained from Gran s method and then, were refined by the NYTIT and ZETA versions of the LETAGROP computer program. The resultant values were 9.4 (/ = 0.1 M KCI, 20% methanol) for atenolol, 9.6 (/ = 0.1 M KCI) for oxprenolol, 9.4 (/ = 0.1 M KCI, 20% methanol) for timolol and 7.4 and 9.4 (/ = 0.1 M KCI) for labetalol. The potentiometric method was found to be accurate and easily applicable. The operational criteria for applying the methodology are indicated. 

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. 

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

Sn2 reactions with anionic nucleophiles fall into this class, and observations are generally in accord with the qualitative prediction. Unusual effects may be seen in solvents of low dielectric constant where ion pairing is extensive, and we have already commented on the enhanced nucleophilic reactivity of anionic nucleophiles in dipolar aprotic solvents owing to their relative desolvation in these solvents. Another important class of ion-molecule reaction is the hydroxide-catalyzed hydrolysis of neutral esters and amides. Because these reactions are carried out in hydroxy lie solvents, the general medium effect is confounded with the acid-base equilibria of the mixed solvent lyate species. (This same problem occurs with Sn2 reactions in hydroxylic solvents.) This equilibrium is established in alcohol-water mixtures ... 

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. 

New NH3/NH4+ buffer When 0.142 mol per liter of HC1 is added to the original buffer presented in (a), it reacts with the base component of the buffer, NH3, to form more of the acid component, NH4+ (the conjugate acid of NH3). Since HC1 is in the gaseous phase, there is no total volume change. A new buffer solution is created with a slightly more acidic pH. In this type of problem, always perform the acid-base limiting reactant problem first, then the equilibrium calculation. 

In a solid-fluid reaction system, the fluid phase may have a chemistry of its own, reactions that go on quite apart from the heterogeneous reaction. This is particularly true of aqueous fluid phases, which can have acid-base, complexation, oxidation-reduction and less common types of reactions. With rapid reversible reactions in the solution and an irreversible heterogeneous reaction, the whole system may be said to be in "partial equilibrium". Systems of this kind have been treated in detail in the geochemical literature (1) but to our knowledge a partial equilibrium model has not previously been applied to problems of interest in engineering or metallurgy. 

As an example of a weak acid-strong base titration, let s consider the titration of 40.0 mL of 0.100 M acetic acid with 0.100 M NaOH. Calculation of the pH at selected points along the titration curve is straightforward because we ve already met all the equilibrium problems that arise. 

The development of these ion-molecule equilibrium measurements has completely changed the status of acid/base reactions (and of other reactions cf. Sechon 5.2) in the gas phase. It is now possible to compare the complex and poorly understood situahon in solution with the simple state in the gas phase. It is also possible to determine the acidity of all acids in the gas phase, from the weakest such as methane to the strongest. In solution, however, due to the levelling effect of the solvent or solubility problems, only a certain range of acids can be measured in a given solvent. 

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. 

The construction of a good scale of inductive constants, Oj, was successful the scale for the resonance constants presents many problems. The inductive scale was constructed from several molecular reference systems such as 4-substituted bicyclo [2.2.2]octane-l-carboxylic acids (65, 66, 67), a-substituted meta-and para-toluic acids (68, 69), and from comparison of base- and acid-catalysed hydrolysis of substituted acetates (43, 11) (i.e., the polar substituent constants a which is related to Oj). The aR scale can hence be obtained from equations 46 and 47. The precision of such determinations is inadequate because the factor a in equation 47 is too small. Values of aR were also obtained from NMR (70) and IR (71) measurements. The major problem with the oR scale is that the oR values are usually small with large standard deviations. Equation 48 is used to correlate rate or equilibrium constants with the double scale of [Pg.39]

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