1 Acid-Base Equilibria and Solubility Equilibria Chapter 16 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2 K >> 1 K << 1 Lie to the rightFavor products Lie to the leftFavor reactants Equilibrium Will K eq = [C] c [D] d [A] a [B] b aA + bB cC + dD

3 Homogenous equilibrium applies to reactions in which all reacting species are in the same phase. N 2 O 4 (g) 2NO 2 (g) K eq = [NO 2 ] 2 [N 2 O 4 ] Heterogenous equilibrium applies to reactions in which reactants and products are in different phases. CaCO 3 (s) CaO (s) + CO 2 (g) K eq = [CO 2 ] The concentration of solids and pure liquids are not included in the expression for the equilibrium constant.

4 The common ion effect is the shift in equilibrium caused by the addition of a compound having an ion in common with the dissolved substance. The presence of a common ion suppresses the ionization of a weak acid or a weak base. Consider mixture of CH 3 COONa (strong electrolyte) and CH 3 COOH (weak acid). CH 3 COONa (s) Na + (aq) + CH 3 COO - (aq) CH 3 COOH (aq) H + (aq) + CH 3 COO - (aq) common ion

5 Consider mixture of salt NaA and weak acid HA. HA (aq) H + (aq) + A - (aq) NaA (s) Na + (aq) + A - (aq) K a = [H + ][A - ] [HA] [H + ] = K a [HA] [A - ] -log [H + ] = -log K a - log [HA] [A - ] -log [H + ] = -log K a + log [A - ] [HA] pH = pK a + log [A - ] [HA] pK a = -log K a Henderson-Hasselbalch equation pH = pK a + log [conjugate base] [acid]

Example (a)Calculate the pH of a 0.20 M CH 3 COOH solution. (b) What is the pH of a solution containing both 0.20 M CH 3 COOH and 0.30 M CH 3 COONa? The K a of CH 3 COOH is 1.8 x

Example Solution (a) In this case, the changes are CH 3 COOH(aq)H + (aq) +CH 3 COO - (aq) Initial (M): Change (M):-x-x+x+x+x+x Equilibrium (M):0.20-xxx x = [H + ] = 1.9 x M pH= -log (1.9 x ) = 2.72

Example (b) Sodium acetate is a strong electrolyte, so it dissociates completely in solution: CH 3 COONa(aq) → Na + (aq) + CH 3 COO - (aq) 0.30 M The initial concentrations, changes, and final concentrations of the species involved in the equilibrium are CH 3 COOH(aq)H + (aq) +CH 3 COO - (aq) Initial (M): Change (M):-x-x+x+x+x+x Equilibrium (M):0.20-xx0.30+x

Example From Equation (16.1), Assuming that x ≈ 0.30 and x ≈ 0.20, we obtain or x = [H + ] = 1.2 x M Thus, pH = -log [H + ] = -log (1.2 x ) = 4.92

10 A buffer solution is a solution of: 1.A weak acid or a weak base and 2.The salt of the weak acid or weak base Both must be present! A buffer solution has the ability to resist changes in pH upon the addition of small amounts of either acid or base. Add strong acid H + (aq) + CH 3 COO - (aq) CH 3 COOH (aq) Add strong base OH - (aq) + CH 3 COOH (aq) CH 3 COO - (aq) + H 2 O (l) Consider an equal molar mixture of CH 3 COOH and CH 3 COONa

Example (a) KH 2 PO 4 /H 3 PO 4 (b) NaClO 4 /HClO 4 (c) C 5 H 5 N/C 5 H 5 NHCl (C 5 H 5 N is pyridine; its K b is given in Table 15.4) Explain your answer. Which of the following solutions can be classified as buffer systems?

Example Solution The criteria for a buffer system is that we must have a weak acid and its salt (containing the weak conjugate base) or a weak base and its salt (containing the weak conjugate acid). (a) H 3 PO 4 is a weak acid, and its conjugate base,,is a weak base (see Table 15.5). Therefore, this is a buffer system. (b) Because HClO 4 is a strong acid, its conjugate base,, is an extremely weak base. This means that the ion will not combine with a H + ion in solution to form HClO 4. Thus, the system cannot act as a buffer system. (c) As Table 15.4 shows, C 5 H 5 N is a weak base and its conjugate acid, C 5 H 5 N + H (the cation of the salt C 5 H 5 NHCl), is a weak acid. Therefore, this is a buffer system.

Example (a) Calculate the pH of a buffer system containing 1.0 M CH 3 COOH and 1.0 M CH 3 COONa. (b) What is the pH of the buffer system after the addition of 0.10 mole of gaseous HCl to 1.0 L of the solution? Assume that the volume of the solution does not change when the HCl is added.

Example Strategy (a)The pH of the buffer system before the addition of HCl can be calculated with the procedure described in Example 16.1, because it is similar to the common ion problem. The K a of CH 3 COOH is 1.8 x (see Table 15.3). (b) It is helpful to make a sketch of the changes that occur in this case.

Example Solution (a) We summarize the concentrations of the species at equilibrium as follows: CH 3 COOH(aq)H + (aq) +CH 3 COO - (aq) Initial (M):1.00 Change (M):-x-x+x+x+x+x Equilibrium (M):1.0-xx1.0+x

Example Assuming x ≈ 1.0 and x ≈ 1.0, we obtain or x = [H + ] = 1.8 x M Thus, pH = -log (1.8 x ) = 4.74

Example (b) When HCl is added to the solution, the initial changes are The Cl - ion is a spectator ion in solution because it is the conjugate base of a strong acid. The H + ions provided by the strong acid HCl react completely with the conjugate base of the buffer, which is CH 3 COO -. At this point it is more convenient to work with moles rather than molarity. The reason is that in some cases the volume of the solution may change when a substance is added. A change in volume will change the molarity, but not the number of moles. HCl(aq)→H + (aq) +Cl - (aq) Initial (mol): Change (mol): Final (mol):00.10

Example The neutralization reaction is summarized next: Finally, to calculate the pH of the buffer after neutralization of the acid, we convert back to molarity by dividing moles by 1.0 L of solution. CH 3 COO - (aq)+ H + (aq)→CH 3 COOH(aq) Initial (mol): Change (mol): Final (mol):

Example CH 3 COOH(aq)H + (aq) +CH 3 COO - (aq) Initial (M): Change (M):-x-x+x+x+x+x Equilibrium (M):1.1-xx0.90+x

Example Assuming x ≈ 0.90 and x ≈ 1.1, we obtain or x = [H + ] = 2.2 x M Thus, pH = -log (2.2 x ) = 4.66 Check The pH decreases by only a small amount upon the addition of HCl. This is consistent with the action of a buffer solution.

21 HCl H + + Cl - HCl + CH 3 COO - CH 3 COOH + Cl -

Example Describe how you would prepare a “phosphate buffer” with a pH of about 7.40.

Example Strategy For a buffer to function effectively, the concentrations of the acid component must be roughly equal to the conjugate base component. According to Equation (16.4), when the desired pH is close to the pK a of the acid, that is, when pH ≈ pK a, or

Example Solution Because phosphoric acid is a triprotic acid, we write the three stages of ionization as follows. The K a values are obtained from Table 15.5 and the pK a values are found by applying Equation (16.3).

Example The most suitable of the three buffer systems is, because the pK a of the acid is closest to the desired pH. From the Henderson-Hasselbalch equation we write

Example Taking the antilog, we obtain Thus, one way to prepare a phosphate buffer with a pH of 7.40 is to dissolve disodium hydrogen phosphate (Na 2 HPO 4 ) and sodium dihydrogen phosphate (NaH 2 PO 4 ) in a mole ratio of 1.5:1.0 in water. For example, we could dissolve 1.5 moles of Na 2 HPO 4 and 1.0 mole of NaH 2 PO 4 in enough water to make up a 1-L solution.

27 Titrations (Review) In a titration, a solution of accurately known concentration is gradually added to another solution of unknown concentration until the chemical reaction between the two solutions is complete. Equivalence point – the point at which the reaction is complete Indicator – substance that changes color at (or near) the equivalence point Slowly add base to unknown acid UNTIL the indicator changes color (pink)

28 Alternative Method of Equivalence Point Detection monitor pH

29 Strong Acid-Strong Base Titrations NaOH (aq) + HCl (aq) H 2 O (l) + NaCl (aq) OH - (aq) + H + (aq) H 2 O (l)

30 Weak Acid-Strong Base Titrations CH 3 COOH (aq) + NaOH (aq) CH 3 COONa (aq) + H 2 O (l) CH 3 COOH (aq) + OH - (aq) CH 3 COO - (aq) + H 2 O (l) CH 3 COO - (aq) + H 2 O (l) OH - (aq) + CH 3 COOH (aq) At equivalence point (pH > 7):

Example Calculate the pH in the titration of 25.0 mL of M acetic acid by sodium hydroxide after the addition to the acid solution of (a) 10.0 mL of M NaOH (b) 25.0 mL of M NaOH (c) 35.0 mL of M NaOH

Example Strategy The reaction between CH 3 COOH and NaOH is CH 3 COOH(aq) + NaOH(aq) CH 3 COONa(aq) + H 2 O(l) We see that 1 mol CH 3 COOH 1 mol NaOH. Therefore, at every stage of the titration we can calculate the number of moles of base reacting with the acid, and the pH of the solution is determined by the excess acid or base left over. At the equivalence point, however, the neutralization is complete and the pH of the solution will depend on the extent of the hydrolysis of the salt formed, which is CH 3 COONa.

Example 33 Solution (a) The number of moles of NaOH in 10.0 mL is The number of moles of CH 3 COOH originally present in 25.0 mL of solution is We work with moles at this point because when two solutions are mixed, the solution volume increases. As the volume increases, molarity will change but the number of moles will remain the same. 16.5

Example CH 3 COOH (aq)+ NaOH (aq)→CH 3 COONa(aq)+ H 2 O(l) Initial (mol):2.50 x x Change (mol):-1.00 x x Final (mol):1.50 x x The changes in number of moles are summarized next: At this stage we have a buffer system made up of CH 3 COOH and CH 3 COO - (from the salt, CH 3 COONa). pH = pK a + log [A - ] [HA] pH = -log(1.8×10 –5 ) + log 1.00 x x pK a = -log K a pH = 4.57

Example (b) These quantities (that is, 25.0 mL of M NaOH reacting with 25.0 mL of M CH 3 COOH) correspond to the equivalence point. The number of moles of NaOH in 25.0 mL of the solution is The changes in number of moles are summarized next: CH 3 COOH (aq)+ NaOH (aq)→CH 3 COONa(aq)+ H 2 O(l) Initial (mol):2.50 x Change (mol):-2.50 x x Final (mol): x 10 -3

Example At the equivalence point, the concentrations of both the acid and the base are zero. The total volume is ( ) mL or 50.0 mL, so the concentration of the salt is The next step is to calculate the pH of the solution that results from the hydrolysis of the CH 3 COO - ions. CH 3 COO ― (aq)→CH 3 COOH(aq)+ OH ― (aq) Initial (mol): Change (mol):-x+x Final (mol):.0500-xxx

Example Following the procedure described in Example and looking up the base ionization constant (K b ) for CH 3 COO - in Table 15.3, we write

Example (c) After the addition of 35.0 mL of NaOH, the solution is well past the equivalence point. The number of moles of NaOH originally present is The changes in number of moles are summarized next: CH 3 COOH (aq)+ NaOH (aq)→CH 3 COONa(aq)+ H 2 O(l) Initial (mol):2.50 x x Change (mol):-2.50 x x Final (mol):01.00 x x 10 -3

Example At this stage we have two species in solution that are responsible for making the solution basic: OH - and CH 3 COO - (from CH 3 COONa). However, because OH - is a much stronger base than CH 3 COO -, we can safely neglect the hydrolysis of the CH 3 COO - ions and calculate the pH of the solution using only the concentration of the OH - ions. The total volume of the combined solutions is ( ) mL or 60.0 mL, so we calculate OH - concentration as follows:

40 Strong Acid-Weak Base Titrations HCl (aq) + NH 3 (aq) NH 4 Cl (aq) NH 4 + (aq) + H 2 O (l) NH 3 (aq) + H + (aq) At equivalence point (pH < 7): H + (aq) + NH 3 (aq) NH 4 + (aq)

Example Calculate the pH at the equivalence point when 25.0 mL of M NH 3 is titrated by a M HCl solution.

Example 42 Strategy The reaction between NH 3 and HCl is NH 3 (aq) + HCl(aq) NH 4 Cl(aq) We see that 1 mol NH 3 1 mol HCl. At the equivalence point, the major species in solution are the salt NH 4 Cl (dissociated into and Cl - ions) and H 2 O. First, we determine the concentration of NH 4 Cl formed. Then we calculate the pH as a result of the ion hydrolysis. The Cl - ion, being the conjugate base of a strong acid HCl, does not react with water. As usual, we ignore the ionization of water. 16.6

Example Solution The number of moles of NH 3 in 25.0 mL of M solution is At the equivalence point the number of moles of HCl added equals the number of moles of NH 3. The changes in number of moles are summarized below: NH 3 (aq) +HCl(aq)→NH 4 Cl(aq) Initial (mol):2.50 x Change (mol):-2.50 x x Final (mol): x 10 -3

Example At the equivalence point, the concentrations of both the acid and the base are zero. The total volume is ( ) mL, or 50.0 mL, so the concentration of the salt is The pH of the solution at the equivalence point is determined by the hydrolysis of ions.

Example 45 Step 1: We represent the hydrolysis of the cation, and let x be the equilibrium concentration of NH 3 and H + ions in mol/L: (aq)NH 3 (aq) +H + (aq) Initial (M): Change (M):-x-x+x+x+x+x Equilibrium (M):( x)xx 16.6

Example 46 Step 2: From Table 15.4 we obtain the K a for : 16.6 Thus, the pH is given by pH = -log (5.3 x ) = 5.28

47 Acid-Base Indicators HIn (aq) H + (aq) + In - (aq)  10 [HIn] [In - ] Color of acid (HIn) predominates  10 [HIn] [In - ] Color of conjugate base (In - ) predominates

48 pH Solutions of Red Cabbage Extract

49 The titration curve of a strong acid with a strong base.

Example 50 Which indicator or indicators listed in Table 16.1 would you use for the acid-base titrations shown in (a) Figure 16.4? 16.7

Example 51 (b) Figure 16.5? 16.7

Example (c) Figure 16.6?

Example Strategy The choice of an indicator for a particular titration is based on the fact that its pH range for color change must overlap the steep portion of the titration curve. Otherwise we cannot use the color change to locate the equivalence point.

Example 54 Solution (a) Near the equivalence point, the pH of the solution changes abruptly from 4 to 10. Therefore, all the indicators except thymol blue, bromophenol blue, and methyl orange are suitable for use in the titration. (b) Here the steep portion covers the pH range between 7 and 10; therefore, the suitable indicators are cresol red and phenolphthalein. (c) Here the steep portion of the pH curve covers the pH range between 3 and 7; therefore, the suitable indicators are bromophenol blue, methyl orange, methyl red, and chlorophenol blue. 16.7

55 Solubility Equilibria AgCl (s) Ag + (aq) + Cl - (aq) K sp = [Ag + ][Cl - ]K sp is the solubility product constant MgF 2 (s) Mg 2+ (aq) + 2F - (aq) K sp = [Mg 2+ ][F - ] 2 Ag 2 CO 3 (s) 2Ag + (aq) + CO (aq) K sp = [Ag + ] 2 [CO ] Ca 3 (PO 4 ) 2 (s) 3Ca 2+ (aq) + 2PO (aq) K sp = [Ca 2+ ] 3 [PO ] 2 Dissolution of an ionic solid in aqueous solution: Q = K sp Saturated solution Q < K sp Unsaturated solution No precipitate Q > K sp Supersaturated solution Precipitate will form

56

57 Molar solubility (mol/L) is the number of moles of solute dissolved in 1 L of a saturated solution. Solubility (g/L) is the number of grams of solute dissolved in 1 L of a saturated solution.

Example The solubility of calcium sulfate (CaSO 4 ) is found to be 0.67 g/L. Calculate the value of K sp for calcium sulfate.

Example Strategy We are given the solubility of CaSO 4 and asked to calculate its K sp. The sequence of conversion steps, according to Figure 16.9(a), is solubility ofmolar solubility [Ca 2+ ] and K sp of CaSO 4 in g/Lof CaSO 4 [ ]CaSO 4

Example Solution Consider the dissociation of CaSO 4 in water. Let s be the molar solubility (in mol/L) of CaSO 4. CaSO 4 (s) Ca 2+ (aq) +(aq) Initial (M):00 Change (M):-s-s+s+s+s+s Equilibrium (M):ss The solubility product for CaSO 4 is K sp = [Ca 2+ ][ ] = s 2

Example First, we calculate the number of moles of CaSO 4 dissolved in 1 L of solution: From the solubility equilibrium we see that for every mole of CaSO 4 that dissolves, 1 mole of Ca 2+ and 1 mole of are produced. Thus, at equilibrium, [Ca 2+ ] = 4.9 x M and [ ] = 4.9 x M

Example Now we can calculate K sp : K sp = [Ca 2+ ] ][ ] = (4.9 x )(4.9 x ) = 2.4 x 10 -5

Example Using the data in Table 16.2, calculate the solubility of copper(II) hydroxide, Cu(OH) 2, in g/L.

Example Strategy We are given the K sp of Cu(OH) 2 and asked to calculate its solubility in g/L. The sequence of conversion steps, according to Figure 16.9(b), is K sp of[Cu 2+ ] andmolar solubiltysolubility of Cu(OH) 2 [OH - ]of Cu(OH) 2 Cu(OH) 2 in g/L

Example Cu(OH) 2 (s) Cu 2+ (aq) +2OH - (aq) Initial (M):00 Change (M):-s-s+s+s+2s Equilibrium (M):s2s Solution Consider the dissociation of Cu(OH) 2 in water: Note that the molar concentration of OH - is twice that of Cu 2+. The solubility product of Cu(OH) 2 is K sp = [Cu 2+ ][OH - ] 2 = (s)(2s) 2 = 4s 3

Example From the K sp value in Table 16.2, we solve for the molar solubility of Cu(OH) 2 as follows: Hence Finally, from the molar mass of Cu(OH) 2 and its molar solubility, we calculate the solubility in g/L:

67

Example 68 Exactly 200 mL of M BaCl 2 are mixed with exactly 600 mL of M K 2 SO 4. Will a precipitate form? 16.10

Example The total volume after combining the two solutions is 800 mL. The concentration of Ba 2+ in the 800 mL volume is

Example The number of moles of in the original 600 mL solution is The concentration of in the 800 mL of the combined solution is

Example Now we must compare Q and K sp. From Table 16.2, BaSO 4 (s) Ba 2+ (aq) + (aq) K sp = 1.1 x As for Q, Q = [Ba 2+ ] 0 [ ] 0 = (1.0 x )(6.0 x ) = 6.0 x Therefore, Q > K sp The solution is supersaturated because the value of Q indicates that the concentrations of the ions are too large. Thus, some of the BaSO 4 will precipitate out of solution until [Ba 2+ ][ ] = 1.1 x

Example A solution contains M Cl - ions and M Br - ions. To separate the Cl - ions from the Br - ions, solid AgNO 3 is slowly added to the solution without changing the volume. What concentration of Ag + ions (in mol/L) is needed to precipitate as much AgBr as possible without precipitating AgCl?

73 The Common Ion Effect and Solubility The presence of a common ion decreases the solubility of the salt.

Example Calculate the solubility of silver chloride (in g/L) in a 6.5 x M silver nitrate solution.

75 pH and Solubility The presence of a common ion decreases the solubility. Insoluble bases dissolve in acidic solutions Insoluble acids dissolve in basic solutions Mg(OH) 2 (s) Mg 2+ (aq) + 2OH - (aq) K sp = [Mg 2+ ][OH - ] 2 = 1.2 x K sp = (s)(2s) 2 = 4s 3 4s 3 = 1.2 x s = 1.4 x M [OH - ] = 2s = 2.8 x M pOH = 3.55 pH = At pH less than Lower [OH - ] OH - (aq) + H + (aq) H 2 O (l) remove Increase solubility of Mg(OH) 2 At pH greater than Raise [OH - ] add Decrease solubility of Mg(OH) 2

Example 76 Which of the following compounds will be more soluble in acidic solution than in water: (a)CuS (b) AgCl (c) PbSO

Example Calculate the concentration of aqueous ammonia necessary to initiate the precipitation of iron(II) hydroxide from a M solution of FeCl 2.

78 Complex Ion Equilibria and Solubility A complex ion is an ion containing a central metal cation bonded to one or more molecules or ions. Co 2+ (aq) + 4Cl - (aq) CoCl 4 (aq) 2- K f = [CoCl 4 ] [Co 2+ ][Cl - ] 4 2- The formation constant or stability constant (K f ) is the equilibrium constant for the complex ion formation. Co(H 2 O) 6 2+ CoCl 4 2- KfKf stability of complex HCl

79

Example 80 A 0.20-mole quantity of CuSO 4 is added to a liter of 1.20 M NH 3 solution. What is the concentration of Cu 2+ ions at equilibrium? 16.15

Example 81 Calculate the molar solubility of AgCl in a 1.0 M NH 3 solution

82 AgNO 3 + NaCl AgCl Effect of Complexation on Solubility Add NH 3 Ag(NH 3 ) 2 +

83

84 Qualitative Analysis of Cations

85 Flame Test for Cations lithium sodium potassiumcopper