Weak-acid equilibrium, problem solving

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

As is often the case with equilibrium problems, we arrive at a quadratic equation in Jc, which we can solve using the quadratic formula (see Appendix IC). However, in many cases we can apply the x is small approximation (first discussed in Section 14.8). In Examples 15.5 and 15.6, we examine the general procedure for solving weak acid equilibrium problems. In both of these examples, the x is small approximation works well. In Example 15.7, we solve a problem in which the x is small approximation does not work. In such cases, we can solve the quadratic equation explicitly, or apply the method of successive approximations (also discussed in Section 14.8). Einally, in Example 15.8, we work a problem in which we find the equilibrium constant of a weak acid from its pH. 

To find [CHO2 ] we must solve an equilibrium problem. However, the initial concentration of H30 in this case is not negligible (as it has been in all the other weak acid equilibrium problems that we have worked so far) because HCl has formed a significant amount of H30. The concentration of H3O+ formed by HCl becomes the initial concentration of H30 in the ICE table for HCHO2 as shown here ... 

Plan Although we are dealing specifically with the ionization of a weak acid, this problem is very similar to the equilibrium problems we encountered in Chapter 15. We can solve this problem using the method first outlined in Sample Exercise 15.9, starting with the chemical reaction and a tabulation of initial and equilibrium concentrations. 

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 ... 

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- ... 

In this section, you compared strong and weak acids and bases using your understanding of chemical equilibrium, and you solved problems involving their concentrations and pH. Then you considered the effect on pH of buffer solutions solutions that contain a mixture of acid ions and base ions. In the next section, you will compare pH changes that occur when solutions of acids and bases with different strengths react together. 

This problem illustrates all the important steps required for solving a typical equilibrium problem involving a weak acid. These steps are summarized below. 

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 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. 

Generally, we can calculate the hydrogen ion concentration or pH of an acid solution at equilibrium, given the initial concentration of the acid and its value. Alternatively, if we know the pH of a weak acid solution and its initial concentration, we can determine its K. The basic approach for solving these problems, which deal with equilibrium concentrations, is the same one outlined in Chapter 14. However, because acid ionization represents a major category of chemical equilibrium in aqueous solution, we will develop a systematic procedure for solving this type of problem that will also help us to understand the chemistry involved. 

We have in prior chapters seen how the presence of foreign ions may influence equilibrium. We shall in this section. We shall in this section quite similar look at how the presence of HsO ions may influence pH. E.g. will we look at a solution containing not just the weak acid (in general presented as HA), but also at the same time contains its salt (in general presented as NaA). Even though it may seem as if we now have a completely new type of problem it will in fact turn out to be a type of problem we can solve analogously to prior problems. This we will look into in the following example. 

The second type of equilibrium problem involving weak acids gives some concentration data and the value and asks for the equilibrium concentration of some component. Such problems are very similar to those we solved in Chapter 17 in which a substance with a given initial concentration reacted to an unknown extent (see Sample Problems 17.6 to 17.8). 

A buffer generally contains a weak acid and its weak conjugate base, or a weak base and its weak conjugate acid, in water. You can solve for the pH by setting up the equilibrium problem using the reaction of the weak acid or the K, reaction of the conjugate base. Both reactions give the same answer for the pH of the solution. Explain. 

Sketch the titration curve for a weak acid titrated by a strong base. When performing calculations concerning weak acid-strong base titrations, the general two-step procedure is to solve a stoichiometry problem first, then to solve an equilibrium problem to determine the pH. What reaction takes place in the stoichiometry part of the problem What is assumed about this reaction ... 

At the various points in your titration curve, list the major species present after the strong base (NaOH, for example) reacts to completion with the weak acid, HA. What equilibrium problem would you solve at the various points in your titration curve to calculate the pH Why is pH > 7.0 at the equivalence point of a weak acid-strong base titration Does the pH at the halfway point to equivalence have to be less than 7.0 What does the pH at the halfway point equal Compare and contrast the titration curves for a strong acid-strong base titration and a weak acid-strong base titration. 

In order to calculate either the value for a weak acid or the pH of its solutions, we will use many of the skills for solving equilibrium problems developed in Section 15.5. In many cases the small magnitude of allows us to use approximations to simplify the problem. In doing these calculations, it is important to realize that proton-transfer reactions are generally very rapid. As a result, the measured or calculated pH for a weak acid always represents an equilibrium condition. 

Plan We will use essentially the same procedure here as used in solving problems involving the ionization of weak acids, that is, write the chemical equation and tabulate initial and equilibrium concentrations. 

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)... 

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