Concentration weak-acid equilibrium problem

Two common types of weak-acid equilibrium problems involve finding Kg from a concentration and finding a concentration from Kg. We summarize the information in a reaction table, and we simplify the arithmetic by assuming (1) is so... 

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. 

Analyze We are asked to determine the pH at the equivalence point of the titration of a weak acid with a strong base. Because tire neutralization of a weak acid produces the corresponding conjugate base, we ejqsect the pH to be basic at the equivalence point. Plan We should first determine how many moles of acetic acid there are initially. This win teU us how many moles of acetate ion there will be in solution at the equivalence point. We then must determine the final volume of the resulting solution, and the concentration of acetate ion. From this point this is simply a weak-base equilibrium problem like those in Section 16.7. 

To find the pH, you must find the equilibrium concentration of H30. Treat the problem as a weak acid pH problem with a single ionizable proton. The second proton contributes a negligible amount to the concentration of H30 and can be ignored. Follow the procedure from Example 15.6, shown in condensed form here. Use for ascorbic acid from Table 15.10. 

If we make the same x is small approximation that we make for weak acid or weak base equilibrium problems, we can consider the equilibrium concentrations of HA and A to be essentially identical to the initial concentrations of HA and A (see step 4 of Example 16.1). Therefore, to determine [H30 ] for any buffer solution, we multiply by the ratio of the... 

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- ... 

The only substance remaining in the solution that can influence the pH is the nitrite ion. This ion is the conjugate base of a weak acid. Since a base is present, the pH will be above 7. The presence of this weak base means this is a Kb problem. However, before we can attack the equilibrium portion of the problem, we must finish the stoichiometry part by finding the concentration of the nitrite ion. 

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. 

The problem is to find the pH of a solution of the weak acid HA, given the formal concentration of HA and the value of Ka.4 Let s call the formal concentration F and use the systematic treatment of equilibrium ... 

Once the Ka value for a weak acid has been measured, it can be used to calculate equilibrium concentrations and the pH in a solution of the acid. We ll illustrate the approach to such a problem by calculating the concentrations of all species present (H30+,CN-, HCN, and OH-) and the pH in a 0.10 M HCN solution. The approach we ll take is quite general and will be useful on numerous later occasions. 

In Chapter 7 we were concerned with calculating the equilibrium concentrations of species (particularly H+ ions) in solutions containing an acid or a base. In this section we discuss solutions that contain not only the weak acid HA but also its salt NaA. Although this case appears to be a new type of problem, it can be handled rather easily by using the procedures developed in Chapter 7. 

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. 

In problems that involve the common ion effect, we are usually given the starting concentrations of a weak acid HA and its salt, such as NaA. As long as the concentrations of these species are reasonably high (> 0.1 M), we can neglect the ionization of the acid and the hydrolysis of the salt. This is a valid approximation because HA is a weak acid and the extent of the hydrolysis of the A ion is generally very small. Moreover, the presence of A (from NaA) further suppresses the ionization of HA and the presence of HA further suppresses the hydrolysis of A. Thus we can use the starting concentrations as the equilibrium concentrations in Equation (16.1) or Equation (16.4). 

We have seen earlier how calculations of pH in solutions with strong acid and strong base are relatively simple because strong acids and strong bases are completely dissociated. On the contrary, pH calculations in cases where the titrated acid is weak is not as simple. In order to be able to calculate the concentration of HsO ions after the addition of a given amount of strong base it is necessary to look at the weak acids dissociation equilibrium. Calculations of pH curves for titration of a weak acid with a strong base involve a series of buffer-related problems. 

A1 acetic acid is now brought to acetate form (CH3COO ). The problem is now to determine pH in a solution of a weak base with a concentration of 0.05 M (half of the initial concentration). The base equilibrium and the corresponding base equilibrium constant Kb (5.6 10 ° M) are to be written ... 

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). 

The compounds at the beginning of Table 4.2 are very strong acids. Their equilibrium constants are very large and cannot be measured accurately because the concentrations of the reactants are extremely small. The equilibrium constants for these compounds are determined by some indirect method and only approximate values can be obtained. Because the pKg values cannot be determined very precisely, they are listed without any figures right of the decimal place. A similar problem occurs with the extremely weak acids at the end of the table. 

Because acid-base reactions in solution generally are so rapid, we can concern ourselves primarily with the determination of species concentrations at equilibrium. Usually, we desire to know [H+], [OH ], and the concentration of the acid and its conjugate base that result when an acid or a base is added to water. As we shall see later in this text, acid-base equilibrium calculations are of central importance in the chemistry of natural waters and in water and wastewater treatment processes. The purpose of this section is to develop a general approach to the solution of acid-base equilibrium problems and to apply this approach to a variety of situations involving strong and weak acids and bases. 

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. 

The initial pH is that of the weak acid solution to be titrated. Calculate the pH by working an equilibrium problem (similar to Examples 15.5 and 15.6) using the concentration of the weak acid as the initial concentration. 

At the equivalence point, the acid has all been converted into its conjugate base. Calculate the pH by working an equilibrium problem for the ionization of water by the ion acting as a weak base (similar to Example 15.14). (Calculate the concentration of the ion acting as a weak base by dividing the number of moles of the ion by the total volume at the equivalence point.)... 

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