Solubility and Complex Ion. Equilibria

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1 Solubility and Complex Ion a mineral formed by marine organisms through biological precipitation CALCITE Equilibria CaCO 3(s) Ca 2+ (aq) + CO 3 2- (aq) K = K sp = [Ca 2+ ][CO 3 2- ] = 2.8 x 10-9 K sp = solubility product constant Chapter 19: 4, 5, 7a-c, 10, 11a,b, 14, 47, 53, 58, 62, 64

2 K sp describes equilibrium between a solid and dissolved ions. If no solid is present, there is no equilibrium! K sp =[Al 3+ ][OH - ] 3 K sp =[Ca 2+ ][SO 4 2- ] K sp =[Mg 2+ ] 3 [PO 4 3- ] 2

3 Solubility The concentration of the solid that can dissolve in solution (expressed in moles per L) when in equilibrium with an excess amount of solid. Expressed another way, Solubility is the maximum concentration (in terms of the solid) of a substance that can exist in solution before precipitation begins if sufficiently seeded. CaCO 3 K sp = [Ca 2+ ][CO 3 2- ] = 2.8 x 10-9

4 Problems i) We can determine the solubility from K sp. ii) We can determine K sp from solubilities. Example: What is the solubility of AgCl in water at 25 o C? K sp = 1.8 x Let us define, solubility = S AgCl (s) Ag + (aq) + Cl - (aq) DEFINE! S = [Ag + ] = [Cl - ] I solid 0 0 C -x +x +x E solid-x S S K sp = [Ag + ][Cl - ] = S * S = S 2 = = =

5 Example 1 Example: What is the solubility of Mg 3 (AsO 4 ) 2 at 25 o C? K sp = 2.0 x Mg 3 (AsO 4 ) 2 3 Mg 2+ (aq) + 2 AsO 4 3- (aq) DEFINE 2+ 3 [Mg ] [AsO 4 ] S = = 3 2 K sp = [Mg 2+ ] 3 [AsO 4 3- ] 2 = (3S) 3 (2S) 2 = 27S 3 x 4S 2 = 108 S 5 20 Ksp 2x10 5 S = 5 = 5 = 4.5x10 M Molar solubility: 4.5x10-5 moles/l of Mg 3 (AsO 4 ) 2. Mass solubility: (equivalent to molar solubility X molar mass) 4.5x10-5 moles/l x g/mole = g/l

6 Example 2 Determine the K sp of Bi 2 S 3 if the solubility is 1.0 x M. Bi 2 S 3(s) 2 Bi 3+ (aq) + 3 S2- (aq) K sp = [Bi 3+ ] 2 [S 2- ] 3 =? DEFINE 3+ 2 [Bi ] [S ] 15 S = = = 1x10 M [Bi ] 2 [S ] = 2S = 3S K sp = [Bi 3+ ] 2 [S 2- ] 3 = (2S) 2 (3S) 3 = 108 S 5 = 108 (1.0 x ) 5 = 1.1 x 10-73

7 Factors influencing solubility Common ion and salt effects As with other equilibria we ve discussed, adding a common ion will result in a shift of a solubility equilibrium. For example, AgCl (s) Ag + (aq) + Cl - (aq) K sp = [Ag + ] [Cl - ] Adding either Ag + or Cl - to our equilibrium system will result in driving it to the left, precipitating out more AgCl, and lowering the solubility of AgCl.

8 Example 3 a) What is the solubility of CaF 2? K sp = 5.3x10-9 CaF 2(s) Ca 2+ (aq) + 2 F - (aq) S = [F - ]/2 = [Ca 2+ ] K sp = [Ca 2+ ][F - ] 2 = S(2S) 2 = 4S 3-9 K 3 sp S = = = M 4 4 b) What is the solubility of CaF 2 in M CaCl 2? S = [F - ]/2 [Ca 2+ ] = M K sp = [Ca 2+ ][F - ] 2 = (0.1)(2S) 2 = 0.1x4S 2 S = 2 K sp 4(0.1) = 2 5.3x10 4(0.1) 9 = 1.2X10 Notice that the common ion, Ca 2+, decreases the solubility of CaF 2 by a factor of M

9 Uncommon Ion (Salt) Effect Observation: If NaNO 3 salt is added to AgCl precipitate, it s solubility can be increased dramatically. There is no chemical reaction with the NaNO 3, so what is going on? Thus far we have used molar concentrations in K sp and other equilibrium expressions, but this is an approximation of the exact solution - we should use activities instead! (recall earlier discussion on activities in section on chemical equilibrium) K sp = a Ag+ a Cl-

10 Uncommon vs Common ion effect: The influence of KNO 3 and K 2 CrO 4 on the solubility of AgCrO 4

11 What is activity? Activities are effective concentrations. The effective concentrations are equal to the real concentrations of species when the species behave under ideal conditions. For ionic species, ideal conditions are dilute conditions, where each molecule or ion behaves independently. At higher concentrations, the species in solution do not necessarily behave independently. The ions can be stabilized in solution through electrostatic forces with other ions in solution.

12 Mathematical description of Activity For ions in solution, the effective concentration is lower than the true concentration (usually) due to electrostatic interactions (stabilization). a i = γ i [ I ] where a i is the activity of the species γ i is the activity coefficient of species i [ I ] is the true concentration of species i Activities (effective concentrations) are frequently less than true concentrations. γ values are frequently less than 1. Activity coefficients can be predicted using Debye-Huckel theory.

13 Criteria for Precipitation Ion Product - used to decide if something will precipitate Q = [Ca 2+ ] exp [CO 3 2- ] exp If Q > K sp, the solution is supersaturated. In this case, a precipitate will form. Sufficient material will precipitate until solution becomes saturated. If Q < K sp, precipitate will not form at equilibrium, solution is unsaturated. If solid exists, it will dissolve. If Q = K sp, solution is saturated and no net change is expected.

14 ph effects Hydrolysis If the anion of a weak acid, or cation of a weak base, is part of a K sp, solubilities will be greater than expected and will also be dependent upon ph. AgCN(s) Ag + (aq) + CN - + (aq) K sp = [Ag ][CN ] + H 2 O(l) The The formation of of HCN reduces the the free free [CN [CN - ], - ], thus thus increasing the the solubility of of AgCN. HCN(aq) + OH - (aq) K b = [HCN][OH [CN ] - ] Conjugate base of a weak acid

15 ph effects: dissolution of limestone CaCO 3(s) Dissolution of of limestone, CaCO 3, 3, is is increased through addition of of acid. Ca 2+ (aq) + CO 3 2- (aq) H + HCO 3 - (aq) H + H 2 CO 3 (aq) H 2 O + CO 2(g)

16 ph effects: quantitative example What is the solubility of CaF 2 in a solution that is buffered at ph = 1? K sp (CaF 2 ) = 5.3 x 10-9, K a (HF) = 6.6 X 10-4, pk a = 3.18 CaF 2(s) Ca 2+ (aq) + 2 F - (aq) K = K sp 2F - + 2H 3 O + 2HF + 2H 2 O K = 1/K 2 a CaF 2(s) + 2H 3 O + Ca 2+ (aq) + 2HF + 2H 2 O K = K sp /K 2 a K = K K sp 2 a = 2+ [Ca ][HF] + 2 [H O ] 3 2 = Since the ph is much lower than the pk a, fluoride will exist predominantly in the HF form, we can presume that [F - ] << [HF]. 2

17 Cont d CaF 2(s) + 2H 3 O + Ca 2+ (aq) + 2HF + 2H 2 O x = S I 0.1M 0 0 C -2x x 2x E ~0.1M x 2x Remember - solution is buffered! K = (x)(2x) [H O ] 3 2 = + 2 4x [H O ] 2 1.2X K[H O ] (1.2X10 )(0.1) 2 x = = = 3.1X10 M 4 4 The solubility of CaF 2 in a ph=1 solution is 3.1x10-2 M. We can compare this to a solubility of 1.7x10-3 M in neutral solution determined previously. Solubility goes up by 18x!!

18 Solubility of Hydroxides The solubility of hydroxides, Me(OH) n, is very high in acids due to OH - reacting with H 3 O +. Example: Zn( OH ) ( s) Zn ( aq) + 2 OH ( aq) K = sp 2 OH ( aq) + 2 H O ( aq) 2 H O( l) + 2 H O( l) K = 1/ K = w Zn( OH ) ( s) + 2 H O ( aq) 4 H O( l) K = K / K = sp 2 12 w Large value of K indicates that the overall reaction goes to completions. It means that the stoichiometry of the overall reaction defines the solubility of Zn(OH) 2. In this example S = [H 3 O] + /2

19 Complex Ion Formation The solubility of slightly soluble salts is increased by the formation of complex ions. Example: addition of excess Cl - to solution of AgCl AgCl(s) Ag + (aq) + Cl - (aq) K sp = + [Ag ][Cl ] add large } + excess of 2Cl - [AgCl (aq) 2 ] Kform = + 2 [Ag ][Cl ] chloride A large excess of of chloride results in in the the formation of of the the complex. More AgCl will will dissolve as as a result. AgCl 2- (aq)

20 Fractional Precipitation A method used for: a) quantitative analysis using precipitation titrations b) separation and/or purification Textbook example: 0.01M CrO 4 2- & 0.01 M Br - Both form insoluble precipitates with Ag + Ag 2 CrO 4 (s) 2Ag + (aq) + CrO 4 2- (aq) K sp = 1.1x10-12 AgBr (s) Ag + (aq) + Br - (aq) K sp = 5.0x10-13 Can we separate the chromate and bromide by fractional precipitation with AgNO 3?

21 example, cont d Which precipitates first, Br - or CrO 4 2-? Calculate [Ag + ] necessary to just start precipitating each - whichever needs the smaller amount, precipitates first. Br - Q sp = K sp = [Ag + ][Br - ] = [Ag + ](0.01M ) = 5.0x10-13 [Ag + ] = 5.0x10-13 /0.01 CrO 4 2- = 5.0x10-11 M K sp = [Ag + ] 2 [CrO 4 2- ] = [Ag + ] 2 (0.01M ) + [Ag ] = 1.1x10-12 Ksp 1.1x10 = = = 1.0x10-5 M 12

22 cont d Br - precipitates first. As it continues to precipitate, [Br - ] drops and [Ag + ] increases until it reaches a point where Ag 2 CrO 4 just starts to precipitate. When Ag 2 CrO 4 just starts to precipitate, what is [Br - ]? [CrO 4 2- ] = 0.01M, [Ag + ] = 1.0x10-5 (calculated previously) K sp = [Ag + ][Br - ] = (1.0x10-5 M)[Br - ] = 5.0x10-13 [Br - ] = 5.0x10-8 M So if we stop the addition of AgNO 3 just before Ag 2 CrO 4 starts to precipitate... [Br - ] drops from 0.01M to 5.0x10-8 M. What % of Br - is left? 5.0x10-8 M / 1.0x10-2 M *100% =0.0005% Good separation!!

23 Solubility in General Solubility of solid in liquid requires solvation of molecules of the solid (S) by those of the liquid (L) L L L L S L L L Solvation requires that interaction between S and L be stronger than that between S and S Molecules of water are highly polar; therefore they solvate polar hydrophilic molecules. Ions are highly hydrophilic Organic solvents are non-polar and they better solvate non-polar hydrophobic molecules.

24 Solubility of proteins in aqueous solutions Proteins contain ionizable groups, amino-groups (R -- NH 2 ) and carboxyl-groups (R - COOH). The solubility will increase with increasing level of ionization of these groups. Amino groups will ionize at acidic ph: R -- NH 2 + H 3 O + R NH 3+ + H 2 O Carboxyl-groups will ionize in basis solutions: R -- COOH + OH - R COO - + H 2 O Conclusion: if the protein has more amino-groups, it will better dissolved in acidic solutions, it it has more carboxyl-groups it will be better dissolved in basic solutions.

25 Effect of ph on Proteins + H3 N- NH 2 0 COOH raise ph -COO - -NH + 3 -COOH lower ph + H 3 N- NH 2 - OOC- / H 2 N charge HOOC- / H 2 N charge +2 -COOH COOH -NH 3 + -COOH H2N- NH OOC- charge -2 / H 2 N COO - -COO - -NH 2 -COOH Better solubility at high and low ph

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