19-1 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 19 Ionic Equilibria in Aqueous Systems

19-2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Ionic Equilibria in Aqueous Systems 19.1 Equilibria of Acid-Base Buffer Systems 19.2 Acid-Base Titration Curves 19.3 Equilibria of Slightly Soluble Ionic Compounds 19.4 Equilibria Involving Complex Ions

19-3 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.1 The effect of addition of acid or base to … an unbuffered solution or a buffered solution acid addedbase added acid addedbase added Figure 19.2

19-4 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 19.1 The Effect of Added Acetate Ion on the Dissociation of Acetic Acid [CH 3 COOH] initial [CH 3 COO - ] added % Dissociation*pH * % Dissociation = [CH 3 COOH] dissoc [CH 3 COOH] initial x

19-5 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.3 How a buffer works. Buffer with equal concentrations of conjugate base and acid OH - H3O+H3O+ Buffer after addition of H 3 O + H 2 O + CH 3 COOH H 3 O + + CH 3 COO - Buffer after addition of OH - CH 3 COOH + OH - H 2 O + CH 3 COO -

19-6 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.1Calculating the Effect of Added H 3 O + or OH - on Buffer pH PROBLEM:Calculate the pH: (a) of a buffer solution consisting of 0.50M CH 3 COOH and 0.50M CH 3 COONa (b) after adding 0.020mol of solid NaOH to 1.0L of the buffer solution in part (a) (c) after adding 0.020mol of HCl to 1.0L of the buffer solution in part (a) K a of CH 3 COOH = 1.8x (Assume the additions cause negligible volume changes. PLAN:We know K a and can find initial concentrations of conjugate acid and base. Make assumptions about the amount of acid dissociating relative to its initial concentration. Proceed step-wise through changes in the system. Initial Change Equilibrium x 0.50-x x xx - x SOLUTION: CH 3 COOH( aq ) + H 2 O( l ) CH 3 COO - ( aq ) + H 3 O + ( aq )Concentration (M) (a)

19-7 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.1Calculating the Effect of Added H 3 O + and OH - on Buffer pH continued (2 of 4) [CH 3 COOH] equil ≈ 0.50M[CH 3 COO - ] initial ≈ 0.50M[H 3 O + ] = x K a = [H 3 O + ][CH 3 COO - ] [CH 3 COOH] [H 3 O + ] = x = K a [CH 3 COO - ] [CH 3 COOH] = 1.8x10 -5 M Check the assumption:1.8x10 -5 /0.50 X 100 = 3.6x10 -3 % CH 3 COOH( aq ) + OH - ( aq ) CH 3 COO - ( aq ) + H 2 O ( l )Concentration (M) Before addition Addition After addition (b) [OH - ] added = mol 1.0L soln = 0.020M NaOH

19-8 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.1Calculating the Effect of Added H 3 O + and OH - on Buffer pH continued (3 of 4) Set up a reaction table with the new values. CH 3 COOH( aq ) + H 2 O( l ) CH 3 COO - ( aq ) + H 3 O + ( aq )Concentration (M) Initial Change Equilibrium x x x + x x [H 3 O + ] = 1.8x = 1.7x10 -5 pH = 4.77 CH 3 COO - ( aq ) + H 3 O + ( aq ) CH 3 COOH( aq ) + H 2 O ( l )Concentration (M) Before addition Addition After addition (c)[H 3 O + ] added = mol 1.0L soln = 0.020M H 3 O

19-9 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.1Calculating the Effect of Added H 3 O + and OH - on Buffer pH continued (4 of 4) Set up a reaction table with the new values. CH 3 COOH( aq ) + H 2 O( l ) CH 3 COO - ( aq ) + H 3 O + ( aq )Concentration (M) Initial Change Equilibrium x x x + x x [H 3 O + ] = 1.8x = 2.0x10 -5 pH = 4.70

19-10 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The Henderson-Hasselbalch Equation HA + H 2 O H 3 O + + A - K a = [H 3 O + ] [A - ] [HA] [H 3 O + ] = K a [HA] [A - ] - log[H 3 O + ] = - log K a + log [A - ] [HA] pH = pK a + log [base] [acid]

19-11 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Buffer Capacity and Buffer Range Buffer capacity is the ability to resist pH change. Buffer range is the pH range over which the buffer acts effectively. The more concentrated the components of a buffer, the greater the buffer capacity. The pH of a buffer is distinct from its buffer capacity. A buffer has the highest capacity when the component concentrations are equal. Buffers have a usable range within ± 1 pH unit of the pK a of its acid component.

19-12 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.4 The relation between buffer capacity and pH change.

19-13 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Preparing a Buffer 1. Choose the conjugate acid-base pair. 2. Calculate the ratio of buffer component concentrations. 3. Determine the buffer concentration. 4. Mix the solution and adjust the pH.

19-14 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.2Preparing a Buffer SOLUTION: PROBLEM:An environmental chemist needs a carbonate buffer of pH to study the effects of the acid rain on limsetone-rich soils. How many grams of Na 2 CO 3 must she add to 1.5L of freshly prepared 0.20M NaHCO 3 to make the buffer? K a of HCO 3 - is 4.7x PLAN:We know the K a and the conjugate acid-base pair. Convert pH to [H 3 O + ], find the number of moles of carbonate and convert to mass. HCO 3 - ( aq ) + H 2 O( l ) CO 3 2- ( aq ) + H 3 O + ( aq ) K a = [CO 3 2- ][H 3 O + ] [HCO 3 - ] pH = 10.00; [H 3 O + ] = 1.0x x = [CO 3 2- ](0.20) 1.0x [CO 3 2- ] = 0.094M moles of Na 2 CO 3 = (1.5L)(0.094mols/L)= 0.14 = 15 g Na 2 CO moles g mol

19-15 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. pH Figure 19.5 Colors and approximate pH range of some common acid-base indicators.

19-16 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.6 The color change of the indicator bromthymol blue. acidic basic change occurs over ~2pH units

19-17 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.7 Curve for a strong acid-strong base titration.

19-18 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.8 Curve for a weak acid- strong base titration. Titration of 40.00mL of M HPr with M NaOH [HPr] = [Pr - ] pH = 8.80 at equivalence point pK a of HPr = 4.89 methyl red

19-19 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.3Calculating the pH During a Weak Acid- Strong Base Titration PROBLEM:Calculate the pH during the titration of mL of M propanoic acid (HPr; K a = 1.3x10 -5 ) after adding the following volumes of M NaOH: (a) 0.00mL(b) 30.00mL(c) 40.00mL(d) 50.00mL PLAN:The amounts of HPr and Pr - will be changing during the titration. Remember to adjust the total volume of solution after each addition. SOLUTION:(a) Find the starting pH using the methods of Chapter 18. K a = [Pr - ][H 3 O + ]/[HPr][Pr - ] = x = [H 3 O + ] x = 1.1x10 -3 ; pH = 2.96 (b) Before addition Addition After addition HPr( aq ) + OH - ( aq ) Pr - ( aq ) + H 2 O ( l )Amount (mol)

19-20 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.3Calculating the pH During a Weak Acid- Strong Base Titration continued [H 3 O + ] = 1.3x mol mol = 4.3x10 -6 MpH = 5.37 (c) When 40.00mL of NaOH are added, all of the HPr will be reacted and the [Pr - ] will be ( mol) ( L) + ( L) = M K a x K b = K w K b = K w /K a = 1.0x /1.3x10 -5 = 7.7x [H 3 O + ] = K w / = 1.6x10 -9 MpH = 8.80 (d) 50.00mL of NaOH will produce an excess of OH -. mol XS base = (0.1000M)( L L) = mol M = ( ) (0.0900L) M = [H 3 O + ] = 1.0x / = 9.0x M pH = 12.05

19-21 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 19.9 Curve for a weak base- strong acid titration. Titration of 40.00mL of M NH 3 with M HCl pH = 5.27 at equivalence point pK a of NH 4 + = 9.25

19-22 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Ion-Product Expression (Q sp ) and Solubility Product Constant (K sp ) At equilibrium Q sp = [M n+ ] p [X z- ] q = K sp For the hypothetical compound, M p X q

19-23 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.4Writing Ion-Product Expressions for Slightly Soluble Ionic Compounds SOLUTION: PROBLEM:Write the ion-product expression for each of the following: (a) Magnesium carbonate(b) Iron ( II ) hydroxide (c) Calcium phosphate(d) Silver sulfide PLAN:Write an equation which describes a saturated solution. Take note of the sulfide ion produced in part (d). K sp = [Mg 2+ ][CO 3 2- ](a) MgCO 3 ( s ) Mg 2+ ( aq ) + CO 3 2- ( aq ) K sp = [Fe 2+ ][OH - ] 2 (b) Fe(OH) 2 ( s ) Fe 2+ ( aq ) + 2OH - ( aq ) K sp = [Ca 2+ ] 3 [PO 4 3- ] 2 (c) Ca 3 (PO 4 ) 2 ( s ) 3Ca 2+ ( aq ) + 2PO 4 3- ( aq ) (d) Ag 2 S( s ) 2Ag + ( aq ) + S 2- ( aq ) S 2- ( aq ) + H 2 O( l ) HS - ( aq ) + OH - ( aq ) Ag 2 S( s ) + H 2 O( l ) 2Ag + ( aq ) + HS - ( aq ) + OH - ( aq ) K sp = [Ag + ] 2 [HS - ][OH - ]

19-24 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 19.2 Solubility-Product Constants (K sp ) of Selected Ionic Compounds at 25 0 C Name, FormulaK sp Aluminum hydroxide, Al(OH) 3 Cobalt ( II ) carbonate, CoCO 3 Iron ( II ) hydroxide, Fe(OH) 2 Lead ( II ) fluoride, PbF 2 Lead ( II ) sulfate, PbSO 4 Silver sulfide, Ag 2 S Zinc iodate, Zn( I O 3 ) 2 3 x x x x x x x Mercury ( I ) iodide, Hg 2 I x 10 -6

19-25 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.5Determining K sp from Solubility PROBLEM:(a) Lead ( II ) sulfate is a key component in lead-acid car batteries. Its solubility in water at 25 0 C is 4.25x10 -3 g/100mL solution. What is the K sp of PbSO 4 ? (b) When lead ( II ) fluoride (PbF 2 ) is shaken with pure water at 25 0 C, the solubility is found to be 0.64g/L. Calculate the K sp of PbF 2. PLAN:Write the dissolution equation; find moles of dissociated ions; convert solubility to M and substitute values into solubility product constant expression. K sp = [Pb 2+ ][SO 4 2- ] = 1.40x10 -4 M PbSO 4 K sp = [Pb 2+ ][SO 4 2- ] = (1.40x10 -4 ) 2 = SOLUTION:PbSO 4 ( s ) Pb 2+ ( aq ) + SO 4 2- ( aq )(a) 1000mL L 4.25x10 -3 g 100mL soln 303.3g PbSO 4 mol PbSO x10 -8

19-26 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.5Determining K sp from Solubility continued (b) PbF 2 (s) Pb 2+ (aq) + 2F - (aq) K sp = [Pb 2+ ][F - ] 2 = 2.6x10 -3 M K sp = (2.6x10 -3 )(5.2x10 -3 ) 2 = 0.64g L soln245.2g PbF 2 mol PbF 2 7.0x10 -8

19-27 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.6Determining Solubility from K sp PROBLEM:Calcium hydroxide (slaked lime) is a major component of mortar, plaster, and cement, and solutions of Ca(OH) 2 are used in industry as a cheap, strong base. Calculate the solubility of Ca(OH) 2 in water if the K sp is 6.5x PLAN:Write out a dissociation equation and K sp expression; Find the molar solubility (S) using a table. SOLUTION:Ca(OH) 2 ( s ) Ca 2+ ( aq ) + 2OH - ( aq ) K sp = [Ca 2+ ][OH - ] 2 -Initial Change Equilibrium S+ 2S S2S K sp = (S)(2S) 2 S == 1.2x10x -2 M Ca(OH) 2 ( s ) Ca 2+ ( aq ) + 2OH - ( aq )Concentration (M)

19-28 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 19.3 Relationship Between K sp and Solubility at 25 0 C No. of IonsFormulaCation:AnionK sp Solubility (M) 2MgCO 3 1:13.5 x x PbSO 4 1:11.6 x x BaCrO 4 1:12.1 x x Ca(OH) 2 1:25.5 x x BaF 2 1:21.5 x x CaF 2 1:23.2 x x Ag 2 CrO 4 2:12.6 x x 10 -5

19-29 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure The effect of a common ion on solubility. PbCrO 4 ( s ) Pb 2+ ( aq ) + CrO 4 2- ( aq ) CrO 4 2- added

19-30 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.7Calculating the Effect of a Common Ion on Solubility PROBLEM:In Sample Problem 19.6, we calculated the solubility of Ca(OH) 2 in water. What is its solubility in 0.10M Ca(NO 3 ) 2 ? K sp of Ca(OH) 2 is 6.5x PLAN:Set up a reaction equation and table for the dissolution of Ca(OH) 2. The Ca(NO 3 ) 2 will supply extra [Ca 2+ ] and will relate to the molar solubility of the ions involved. SOLUTION:Ca(OH) 2 ( s ) Ca 2+ ( aq ) + 2OH - ( aq )Concentration(M) Initial Change Equilibrium S+2S S2S K sp = 6.5x10 -6 = ( S)(2S) 2 = (0.10)(2S) 2 S << 0.10 S = = 4.0x10 -3 Check the assumption: 4.0% 0.10M 4.0x10 -3 x 100 =

19-31 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure Test for the presence of a carbonate.

19-32 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.8Predicting the Effect on Solubility of Adding Strong Acid PROBLEM:Write balanced equations to explain whether addition of H 3 O + from a strong acid affects the solubility of these ionic compounds: (a) Lead ( II ) bromide(b) Copper ( II ) hydroxide(c) Iron ( II ) sulfide PLAN:Write dissolution equations and consider how strong acid would affect the anion component. Br - is the anion of a strong acid. No effect. SOLUTION:(a) PbBr 2 ( s ) Pb 2+ ( aq ) + 2Br - ( aq ) (b) Cu(OH) 2 ( s ) Cu 2+ ( aq ) + 2OH - ( aq ) OH - is the anion of water, which is a weak acid. Therefore it will shift the solubility equation to the right and increase solubility. (c) FeS( s ) Fe 2+ ( aq ) + S 2- ( aq )S 2- is the anion of a weak acid and will react with water to produce OH -. Both weak acids serve to increase the solubility of FeS. FeS( s ) + H 2 O( l ) Fe 2+ ( aq ) + HS - ( aq ) + OH - ( aq )

19-33 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.9Predicting Whether a Precipitate Will Form PROBLEM:A common laboratory method for preparing a precipitate is to mix solutions of the component ions. Does a precipitate form when 0.100L of 0.30M Ca(NO 3 ) 2 is mixed with 0.200L of 0.060M NaF? PLAN:Write out a reaction equation to see which salt would be formed. Look up the K sp valus in a table. Treat this as a reaction quotient, Q, problem and calculate whether the concentrations of ions are > or < K sp. Remember to consider the final diluted solution when calculating concentrations. SOLUTION:CaF 2 (s) Ca 2+ (aq) + 2F - (aq) K sp = 3.2x mol Ca 2+ = 0.100L(0.30mol/L) = 0.030mol[Ca 2+ ] = 0.030mol/0.300L = 0.10M mol F - = 0.200L(0.060mol/L) = 0.012mol[F - ] = 0.012mol/0.300L = 0.040M Q = [Ca 2+ ][F - ] 2 =(0.10)(0.040) 2 = 1.6x10 -4 Q is >> K sp and the CaF 2 WILL precipitate.

19-34 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure Formation of acidic precipitation.

19-35 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure Cr(NH 3 ) 6 3+, a typical complex ion.

19-36 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure M(H 2 O) 4 2+ M(H 2 O) 3 (NH 3 ) 2+ M(NH 3 ) 4 2+ NH 3 3NH 3 The stepwise exchange of NH 3 for H 2 O in M(H 2 O) 4 2+.

19-37 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.10Calculating the Effect of Complex-Ion Formation on Solubility SOLUTION: PROBLEM:In black-and-white film developing, excess AgBr is removed from the film negative by “hypo”, an aqueous solution of sodium thiosulfate (Na 2 S 2 O 3 ), through formation of the complex ion Ag(S 2 O 3 ) Calculate the solubility of AgBr in (a) H 2 O; (b) 1.0M hypo. K f of Ag(S 2 O 3 ) 2 3- is 4.7x10 13 and K sp AgBr is 5.0x PLAN:Write equations for the reactions involved. Use K sp to find S, the molar solubility. Consider the shifts in equilibria upon the addition of the complexing agent. AgBr( s ) Ag + ( aq ) + Br - ( aq ) K sp = [Ag + ][Br - ] = 5.0x S = [AgBr] dissolved = [Ag + ] = [Br - ]K sp = S 2 = 5.0x ; S = 7.1x10 -7 M(a) (b)AgBr( s ) Ag + ( aq ) + Br - ( aq ) Ag + ( aq ) + 2S 2 O 3 2- ( aq ) Ag(S 2 O 3 ) 2 3- ( aq ) AgBr( s ) + 2S 2 O 3 2- ( aq ) Br - ( aq ) + Ag(S 2 O 3 ) 2 3- ( aq )

19-38 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 19.10Calculating the Effect of Complex-Ion Formation on Solubility continued K overall = K sp x K f = [Br - ][Ag(S 2 O 3 ] 2 3- [AgBr][S 2 O 3 2- ] 2 = (5.0x )(4.7x10 13 )= 24 AgBr( s ) + 2S 2 O 3 2- ( aq ) Br - ( aq ) + Ag(S 2 O 3 ) 2 3- ( aq )Concentration(M) Initial Change Equilibrium S 1.0-2S 00 +S SS K overall = S2S2 (1.0-2S) 2 = 24 S 1.0-2S = (24) 1/2 S = [Ag(S 2 O 3 ) 2 3- ] = 0.45M