Solving Problems Involving Weak-Acid Equilibria

4 SOLVING PROBLEMS INVOLVING WEAK-ACID EQUILIBRIA 

Just as you saw in Chapter 17 for equilibrium problems in general, tha-e are two types of equilibrium problems involving weak acids and their conjugate bases  

Z Given and some concentration information, find the other equilibrium concentrations. 

For all of these problems, we ll apply the same problem-solving approach, notation system, and assumptions  

Write the balanced equation and /fj, expression these will tell you what to find. 

The Brensted-Lowry acid-base definition does not require that bases contain OH or that acid-base reactions occur in aqueous solution. It defines an acid as a species that donates a proton and a base as one that accepts It. An acid and a base act together in proton transfer. When an acid donates a proton, it becomes the conjugate base when a base accepts a proton, it becomes the conjugate acid. In an acid-base reaction, acids and bases form their conjugates. A stronger acid has a weaker conjugate base, and vice versa. Thus, the reaction proceeds in the net direction in which a stronger acid and base form a weaker base and acid. 

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Solving Problems Involving Weak-Acid Equilibria Rnding Kg Given Concentrations... 

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). 

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. 

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. 

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

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. 

You follow the three steps for solving equilibrium problems that were introduced in Example 15.7. In the last step, you solve the equilibrium-constant equation for the equilibrium concentrations. The resulting equation is quadratic, but because the equilibrium concentration of a weak acid is usually negligibly different from its starting value, the equation simplifies so that it involves only the square of the unknown, which is easily solved by taking the square root. (You will need to check that this assumption is valid.)... 

In this section, we will work through some additional examples, all of which involve the ionization of a weak acid or a weak base in water. Typically, we are required to find the equilibrium concentrations or determine the pH. To do so, we must solve an equilibrium problem. 

Consider, for example, how you could answer the following questions What is the hydronium-ion concentration of 0.10 M niacin (nicotinic acid) What is the hydronium-ion concentration of the solution obtained by dissolving one 5.00-grain tablet of aspirin (acetylsalicylic acid) in 0.500 L of water If these were solutions of strong acids, the calculations would be simple 0.10 M monoprotic acid would yield 0.10 M HsO ion. However, because niacin is a weak monoprotic acid, the HsO concentration is less than 0.10 M. To find the concentration, you need the equilibrium constant for the reaction involved, and you need to solve an equilibrium problem. 

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