Weak acids equilibrium problems

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... 

Strategy The pH of a buffer system can be calculated in a similar manner to a weak acid equilibrium problem. The difference is that a common-ion is present in solution. The of CH3COOH is 1.8 x 10 (see Table 15.3 of the text). 

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 ... 

An equilibrium problem. The position of the weak acid equilibrium is determined, and the pH is calculated. 

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. 

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 ... 

If the acid in the problem is a weak acid, the problem is more involved since the [H+] caimot be determined directly. The determination of [H+] in that case can be calculated by using the equilibrium constant expression for weak acid ionization. The pH is then calculated from the [H+] using the method shown in Solution 12.4. This type of problem will not be discussed further here. 

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- ... 

Determine equilibrium constants for the reaction of amines with strong or weak acids. (Example 22.8 Problems 27,28) 27... 

As an example of the problem of species in solution, consider the case of a solution made by dissolving some potassium chrome alum, KCrfSO s-12H20, in water. On testing, the solution is distinctly acidic. A currently accepted explanation of the observed acidity is based upon the assumption that, in water solution, chromic ion is associated with six H20 molecules in the complex ion, Cr(H20) a. This complex ion can act as a weak acid, dissociating to give a proton (or hydronium ion). Schematically, the dissociation can be represented as the transfer of a proton from one water molecule in the Cr(H20) 3 complex to a neighboring H20 to form a hydronium ion, H30+. Note that removal of a proton from an H20 bound to a Cr+3 leaves an OH- group at that position. The reaction is reversible and comes to equilibrium ... 

Unfortunately, it is not easy to measure acid strengths of very weak acids like the conjugate acids of simple unsubstituted carbanions. There is little doubt that these carbanions are very unstable in solution, and in contrast to the situation with carbocations, efforts to prepare solutions in which carbanions such as ethyl or isopropyl exist in a relatively free state have not yet been successful. Nor has it been possible to form these carbanions in the gas phase. Indeed, there is evidence that simple carbanions such as ethyl and isopropyl are unstable toward loss of an electron, which converts them to radicals. Nevertheless, there have been several approaches to the problem. Applequist and O Brien studied the position of equilibrium for the reaction... 

C17-0037. Outline the procedure for working an equilibrium problem for a weak acid-base system. 

We can ignore ions such as Sr2+, which come from strong acids or strong bases in this type of problem. Ions, such as C2H3O2", from a weak acid or a base, weak acid in this case, will undergo hydrolysis, a reaction with water. The acetate ion is the conjugate base of acetic acid (Ka = 1.74 x 10 5). Since acetate is a weak base, this will be a Kb problem, and OH will form. The equilibrium is ... 

The only substance present is nitrous acid, HN02, a weak acid. Since this is a weak acid, this must be a Ka problem. As a Ka problem, we can set up a simple equilibrium problem ... 

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. 

The reasoning above allows us to find good qualitative answers, but in order to be able to do quantitative problems (how much is present, etc.), the extent of the dissociation of the weak acids and bases must be known. That is where a modification of the equilibrium constant is useful. 

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. 

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