# V. POLYPROTIC ACID IONIZATION. NOTICE: K a1 > K a2 > K a3 EQUILIBRIUM PART 2. A. Polyprotic acids are acids with two or more acidic hydrogens.

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1 EQUILIBRIUM PART 2 V. POLYPROTIC ACID IONIZATION A. Polyprotic acids are acids with two or more acidic hydrogens. monoprotic: HC 2 H 3 O 2, HCN, HNO 2, HNO 3 diprotic: H 2 SO 4, H 2 SO 3, H 2 S triprotic: H 3 PO 4, H 3 BO 3 polyprotic B. Polyprotic acids ionize in steps - one H + is removed at a time - with a different K a for each step. Examples: 1. H 3 PO 4 : Step 1: H 3 PO 4 (aq) + H 2 O(l) H 3 O + (aq) + H 2 PO 4 (aq) K a1 = 7.1 x 10 3 Step 2: H 2 PO 4 (aq) + H 2 O(l) H 3 O + (aq) + HPO 4 2 (aq) K a2 = 6.3 x 10-8 Step 3: HPO 4 2 (aq) + H 2 O(l) H 3 O + (aq) + PO 4 3 (aq) K a3 = 4.4 x NOTICE: K a1 > K a2 > K a3 2. H 2 S 3. H 2 SO 4 14

2 C. Polyprotic Acid Ionization Calculations Calculate [H 3 O + ], [H 3 PO 4 ], [H 2 PO 4 ], [HPO 4 2 ] and [PO 4 3 ] for a solution of M H 3 PO 4. Step 1: H 2 O + H 3 PO 4 H 3 O + + H 2 PO 4 K a1 = 7.1 x 10 3 I [H 3 O + ] = x -x +x +x [H 3 PO 4 ] = x [Eq] _0.2-x x x [H 2 PO 4 ] = x Step 2: H 2 O + H 2 PO 4 H 3 O + + HPO 4 2 K a2 = 6.3 x 10-8 I x x 0 -y +y +y [HPO 4 2 ] = y = K a2 [Eq] x-y x+y y Step 3: H 2 O + HPO 4 2 H 3 O + + PO 4 3 K a3 = 4.4 x I y x 0 -z +z +z _ [PO 4 3 ] = z = (K a2 K a3 ) [H 3 O + ] [Eq] y-z x+z z 15

3 VI. HYDROLYSIS A. Hydrolysis is the reaction of one or both ions of a salt with water to produce a weak base (and H 3 O + ) or a weak acid (and OH ) or both. B. Which Salts Hydrolyze? 1. Salt of a Strong Acid & Strong Base (note: of course all of these are soluble salts) example: NaCl: Does NaCl hydrolyze, and will an aqueous solution of NaCl be acidic, basic, or neutral? 1. Salt of a Weak Acid and a Strong Base example: NaCN: Does NaCN hydrolyze, and will an aqueous solution of NaCN be acidic, basic, or neutral? 3. Salt of a Strong Acid and a Weak Base example: NH 4 Br: Does NH 4 Br hydrolyze, and will an aqueous solution of NH 4 Br be acidic, basic, or neutral? 16

4 4. Salt of a Weak Acid and a Weak Base example: NH 4 F: Does NH 4 F hydrolyze, and will an aqueous solution of NH 4 F be acidic, basic, or neutral? 5. Salt of a weak polyprotic acid and a strong base example: Na 2 S: Does Na 2 S hydrolyze, and will an aqueous solution of Na 2 S be acidic, basic, or neutral? 6. Salt that contains anion from first ionization step of polyprotic weak acid example: NaHCO 3 : Does NaHCO 3 hydrolyze, and will an aqueous solution of NaHCO 3 be acidic, basic, or neutral? 17

5 C. Practice writing equations for hydrolysis of following salts: 1. KNO 2 2. N 2 H 5 Cl D. Hydrolysis Calculations 1. Calculate the ph of a M solution of NH 4 Br. (K b for NH 3 is 1.8 x 10 5 ) 2. Calculate the percent hydrolysis and the ph of a M solution of NaCN. (K a for HCN is 4.0 x ) 18

6 VII. ACID-BASE TITRATION A. Acid-Base Titration: Procedure for determining the amount of acid (or base) in solution by measuring the volume of base (or acid) solution of known concentration required to completely react with it - that is - to reach the equivalence point. Equivalence point: B. Acid-Base Titration Curve 1. Definition: A plot of the ph of a solution (of acid or base) being titrated versus the volume of titrant (base or acid solution) added. 2. Curve for Titration of a Strong Acid with a Strong Base Titration of 25.0 ml of M HCl with M NaOH. 19

7 2. Curve for Titration of a Weak Acid with a Strong Base Titration of 25.0 ml of M nicotinic acid. (K a = 1.4 x 10 5 ) with M NaOH. 20

8 VIII.SOLUBILITY EQUILIBRIA A. SOLUBILITY PRODUCT 1. In a saturated solution of a salt, equilibrium exists between the undissolved salt and its dissolved ions. For example, a saturated aqueous solution of AgBr: AgBr(s) Ag + (aq) + Br - (aq) constant expression: K = [Ag+ ][Br - ] [AgBr] K. [AgBr] = [Ag] [Br] Since [AgBr] is constant, (the concentraton in mole/liter of a solid is given by its density, which is constant, and is not dependent on the quantity of the solid) [AgBr] may be included with K. K sp = [Ag + ] [Br - ] K sp solubility product constant 2. K sp expression differs from other K expressions a. There is no denominator term. b. Concentrations are often squared or cubed, etc. examples: Fe(OH) 2 (s) Fe 2+ (aq) + 2 OH (aq) K sp = [Fe 2+ ] [OH - ] 2 Bi 2 S 3 (s) 2 Bi 3+ (aq) + 3 S 2 (aq) K sp = [Bi 3+ ] 2 [S 2 ] 3 3. K sp value depends on temperature since solubility depends on temperature 21

9 B. DISSOLVING REACTIONS 1. Simple K sp Calculations a. Calculate K sp given solubility and molar mass. PbCl 2 has a solubility of 4.43 g/l. What is its K sp? (PbCl 2 = g/mole) b. Calculate solubility given K sp and molar mass The K sp for Ag 2 CrO 4 is 1.9 x Calculate its solubility in g/l. (Ag 2 CrO 4 = g/mole) 22

10 2. Common Ion Effect on Solubility. a. The presence of a common ion will decrease the solubility of a salt. b. Example: calculate the molar solubility of PbI 2 in (a) in water (b) in a M NaI solution. (K sp of PbI 2 is 7.47 x 10-9 ) 23

11 D. PRECIPITATION REACTIONS 1. DETERMINING WHETHER A PRECIPITATE WILL FORM a. Ion Product The ion product (IP) is calculated just as the K sp is. For example: Bi 2 S 3 (s) 2 Bi 3 + (aq) + 3 S 2 (aq) K sp = [Bi 3 + ] 2 [S 2 ] 3 and IP = (M Bi 3 + ) 2 (M S 2 ) 3 However, the K sp is calculated using equilibrium concentrations only, whereas the ion product is calculated using non-equilibrium (initial) concentrations. b. Comparison of IP and K sp values to determine whether or not a precipitate will form: (1) IP = K sp (2) IP > K sp (3) IP < K sp a. Problem: NaIO 3 and Cu(C 2 H 3 O 2 ) 2 solutions are mixed. Initially, the mixture is M in NaIO 3 and M in Cu(C 2 H 3 O 2 ) 2. Will a precipitate of Cu(IO 3 ) 2 form? K sp of Cu(IO 3 ) 2 is 1.4 x

12 2. SEPARATION OF IONS BY SELECTIVE PRECIPITATION a. It is possible to separate two ions from each other when they are present together in solution, by adding an ion that will precipitate one ion but not the other. Example: a solution containing Na + and Ag + b. In the event that the added ion precipitates both ions, it is still possible to achieve some separation. Example: a solution containing Ba 2 + and Ca selective precipitation with sulfate ion Solid Na 2 SO 4 is added slowly to a solution that is M in Ba 2 + and 0.20 M in Ca 2 + ion. (1) Which sulfate will precipitate first? (2) Calculate the concentration of the ion of the less soluble sulfate at the point where the solution is saturated with respect to both salts. (That is, when the second salt is just ready to precipitate.) K sp of BaSO 4 = 1.5 x 10 9 K sp of CaSO 4 = 2.4 x

13 3. SEPARATION OF METAL IONS BY SULFIDE PRECIPITATION Consider the effect of adding a strong acid to a solution on Zn 2+ and Pb 2+ ions. Now you saturate the solution with H 2 S gas. The H 3 O + from the strong acid represses the ionization of H 2 S, giving a lower concentration of S 2- ion. By adjusting the H 3 O + concentration, you can control the S 2- concentration and therefore the ion products for ZnS and PbS. You can adjust the hydrogen ion concentration so that only PbS precipitates when the solution is saturated with H 2 S. To determine the H 3 O + concentration necessary to prevent some ions from precipitating while others form the sulfides, you need to look at the overall equation for the Ionization of H 2 S. You can determine this by adding the equations for the two steps of acid ionization: H 2 S(aq) + H 2 O(l) HS - (aq) + H 2 O(l) H 3 O + (aq) + HS (aq) H 3 O + (aq) + S 2 (aq) H 2 S(aq) + 2 H 2 O(l) 2 H 3 O + (aq) + S 2 - (aq) The equilibrium constant for the overall equation is determined by multiplying the equilibrium constants for the two reactions that were added together. K a1 K a 2 = [H 3 O + ] 2 [S 2 ] [H 2 S] K a1 = 8.9 x 10 8 K a 2 = 1.2 x Therefore, K a1 K a 2 = 1.1 x A saturated solution of hydrogen sulfide is 0.10 M H 2 S, and this is not significantly altered by changes in the hydronium ion concentration. Substitute this into the equilibrium expression: K a1 K a2 = [H 3 O + ] 2 [S 2 ] [H 2 S] 1.1 x = [H 3 O + ] 2 [S 2 ] (K a1 K a 2 = 1.1 x ) x = [H 3 O + ] 2 [S 2 ] Note that as the [H 3 O + ] increases, [S 2 ] decreases. Therefore, by adjusting the hydronium ion concentration, you can obtain any desired sulfide ion concentration. 26

14 a. Example 1: A solution that is 0.30 M in H 3 O +, M in Pb 2+, and M in Fe 2+ is saturated with H 2 S. Should PbS and/or FeS precipitate. K sp of PbS = 7 x K sp of FeS = 4 x b. Example 2: What must be the hydronium ion concentration of a solution that is M in Ni 2+ to prevent the precipitation of NiS when the solution is saturated with H 2 S. K sp of NiS =3 x

15 4. USING COMMON ION EFFECT TO PREVENT PRECIPITATION The common ion effect may be used to prevent the formation of a precipitate. precipitation of magnesium hydroxide from a solution that contains Mg 2+ ions: Consider the Mg(OH) 2 (s) Mg 2+ (aq) + 2 OH (aq) If the hydroxide ion is provided by ammonia: NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH (aq) Precipitation can be prevented by keeping the concentration of OH - low, for example by adding NH Example: What concentration of NH 4, derived from NH4 Cl, is necessary to prevent the formation of an Mg(OH) 2 precipitate in a solution that is 0.50 M in Mg 2+ and 0.50 M in NH 3? K sp of Mg(OH) 2 = 8.9 x K b of NH 3 = 1.8 x

16 IX. HETEROGENEOUS EQUILIBRIA Heterogeneous equilibria are equilibrium reactions whose reactants and products are not all in the same phase. For example: Ca(HCO 3 ) 2 (aq) CaCO 3 (s) + H 2 O(l) + CO 2 (g) K = [CaCO 3 ][H 2 O][CO 2 ] [Ca(HCO 3 ) 2 ] K = [CO 2] [CaCO 3 ][H 2 O] [Ca(HCO 3 ) 2 ] The concentrations of pure solids and pure liquids are never included in the equilibrium constant expression. K c = [CO 2 ] [Ca(HCO 3 ) 2 ] K c is a constant that depends only on temperature. 29

17 X. GASEOUS EQUILIBRIA A. EQUILIBRIUM CONSTANTS: K c and K p N 2 (g) + 3 H 2 (g) 2 NH 3 (g) 1. K c = [NH 3 ] 2 [ ] = concentration of gas in mole/liter [N 2 ][H 2 ] 3 2. K p : since partial pressures of gases are proportional to molar concentration, the K expression can be written showing partial pressures: K p = 2 NH 3 N 2 3 H 2 = partial pressure of gas 3. K p is not numerically equal to K c, but may be calculated from K c as follows: K p = K c (RT) n where n = total moles products total moles reactants (from coefficients in equation) and K c = K p (RT) n B. Review of Le Chatelier's Principle 1. Effect of concentration change 2. Effect of temperature change 3. Effect of pressure and volume changes at constant temperature. (applies only to gases since solids and liquids are not compressible.) 4. Effect of catalyst 30

18 C. GASEOUS EQUILIBRIUM CALCULATIONS 1. Consider the following equation: H 2 O(g) + CO(g) CO 2 (g) + H 2 (g) At 200 C the system is at equilibrium and there are moles H 2 O, moles CO, moles CO 2 and moles H 2 in a 2.00 liter vessel. In another experiment at 200 C, moles H 2 O and moles CO are placed in a 2.00 liter container and allowed to come to equilibrium. Calculate the equilibrium concentrations of all species. 31

19 moles N 2 and 4.00 moles H 2 are placed in a 1.00 liter reaction vessel and allowed to come to equilibrium. At equilibrium, the H 2 concentration is 3.40 M. Calculate K c N 2 (g) + 3 H 2 (g) 2 NH 3 (g) 32

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