Weak-acid equilibrium, problem solving concentrations

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. 

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. 

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. 

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). 

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. 

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. 

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.)... 

Think About It For each point in a titration, decide first what species are in solution and what type of problem it is. If the solution contains only a weak acid (or weak base), as is the case before any titiant is added, or if it contains only a conjugate base (or conjugate acid), as is the case at the equivalence point, when pH is determined by salt hydrolysis, it is an equilibrium problem that requires a concentration, an ionization constant, and an equilibrium table. If the solution contains comparable concentrations of both members of a conjugate pair, which is the case at points prior to the equivalence point, it is a buffer problem and is solved using the Henderson-Hasselbalch equation. If the solution contains excess titrant, either a strong base or strong acid, it is simply a pH problem requiring only a concentration. 

The pH of the acetic acid solution is higher (it is less acidic) because acetic acid only partially ionizes. Calculating the [H30 ] formed by the ionization of a weak acid requires solving an equilibrium problem similar to those in Chapter 14. Consider, for example, a 0.10 M solution of the generic weak acid HA with an acid ionization constant K. Since we can ignore the contribution of the autoionization of water, we only have to determine the concentration of H30 formed by the following equilibrium ... 

In a weak acid solution, the hydrogen ion concentration— which can be determined by solving an equilibrium problem—is lower than the initial acid concentration. 

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. 

To calculate how the pH of a buffer solution changes when small amounts of a strong acid or base are added, we must first use stoichiometric principles to establish how much of one buffer component is consumed and how much of the other component is produced. Then the new concentrations of weak acid (or weak base) and its salt can be used to calculate the pH of the buffer solution. Essentially, this problem is solved in two steps. First, we assume that the neutralization reaction proceeds to completion and determine new stoichiometric concentrations. Then these new stoichiometric concentrations are substituted into the equilibrium constant expression and the expression is solved for [H30 ], which is converted to pH. This method is applied in Example 17-6 and illustrated in Figure 17-6. 

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