Presentation on theme: "Chapter 11: Solving Equilibrium Problems for Complex Systems"— Presentation transcript:
1 Chapter 11: Solving Equilibrium Problems for Complex Systems
2 For simultaneous equilibria in aqueous solutions, BaSO4(s) in water for example, there are three equilibria:BaSO4(s) Ba2+ + SO42- (1)SO42- + H3O+ HSO4- +H2O (2)2H2O H3O+ + OH- (3)The addition of H3O+ causes:(2) shift right and (1) shift right.since Ba2+ + OAc- BaOAc+ (4)The addition of OAc- causes:(1) shift right*The introduction of a new equilibrium system into a solution does not change the equilibrium constants for any existing equilibria.
3 11 A Solving multiple-equilibrium problems using A systematic method Three types of algebraic equations are used to solve multiple-equilibrium problems:equilibrium-constant expressionsmass-balance equations(3) a single charge-balance equation
4 11 A-1 Mass-Balance Equations Mass-balance equations: The expression that relate the equilibrium concentrations of various species in a solution to one another and to the analytical concentrations of the various solutes. These equations are a direct result of the conservation of mass and moles.A weak acid HA dissolved in water for example:HA+ H2O H3O+ + A- (1)2H2O H3O+ + OH- (2)mass equation 1: cHA = [HA] + [A-]cHA is analytical concentration, [HA] and [A-] are equilibrium concentration.mass equation 2: [H3O+] = [A-] + [OH-]since [H3O+] = [H3O+]from HA + [H3O+]from H2O ,where [H3O+]from HA = [A-] , [H3O+]from H2O = [OH-]In this system, the charge-balance equation also is [H3O+] = [A-] + [OH-]
9 11A-3 Steps for solving problems with several equilibria Figure 11-1 A systematic method for solving multiple-equilibrium problems.
10 11A-4 Using Approximations to Solve Equilibrium Calculations Approximations can be made only in charge-balance and mass-balance equations, never in equilibrium-constant expressions.If the assumption leads to an intolerable error, recalculate without the faulty approximation to arrive at a tentative answer.11A-5 Use of Computer Programs to Solve Multiple-Equilibrium ProblemsSeveral software packages are available for solving multiple nonlinear simultaneous equations include Mathcad, Mathematica, Solver, MATLAB, TK, and Excel.
11 A simple example of systematic calculations Q Calculate [H3O+] and [OH-] in pure waterA Step 1: 2H2O H3O+ + OH-Step 2: [H3O+]=? and [OH-]=? unknownsStep 3: [H3O+][OH-] = 1x10-14 (1)Step 4: mass-balance equation:[H3O+]=[OH-] (2)Step 5: charge-balance equation:[H3O+]=[OH-] (3)Step 6: equations (2) and (3) are identical, omit equation (3)two unknowns two different equations (1) and (2), OKStep 7: Approximation, omitStep 8: equation (2) substitute into equation (1)[H3O+] [OH-] = [H3O+]2 = 1x10-14∴ [H3O+] = 1x10-7 and [OH-] = 1x10-7
12 11B Calculating solubilities by the systematic method 11B-1 Solubility of metal hydroxidesfor High Ksp value, pH controlled by the solubilityExample 11-5Calculate the molar solubility of Mg(OH)2 in water.Solution
18 11B-2 The Effect of pH on Solubility *The solubility of precipitates containing an anion with basic properties, a cation with acidic properties, will depend on pH. (simultaneous equilibria)Solubility Calculations When the pH Is Constant ([OH-] and [H3O+] are known)Example 11-7Calculate the molar solubility of calcium oxalate in a solution that has been buffered so that its pH is constant and equal to 4.00.Solution
22 Solubility Calculations When the pH Is Variable ([OH-] and [H3O+] are unknown) for High Ksp value (pH controlled by the solubility)omitfor Low Ksp value (pH≈7, controlled by autoprotolysis of water)
23 11B-3 The Effect of Undissociated Solutes on Precipitation Calculations For example, a saturated solution of AgCl(s) contains significant amounts of undissociated silver chloride molecules, AgCl(aq) complexs:Example 11-8Calculate the solubility of AgCl in distilled water.Solution
24 11B-4 The Solubility of Precipitates in the Presence of Complexing Agents The solubility increase in the presence of reagents that form complexes with the anion or the cation of the precipitate.Ex. F- prevent the precipitation of Al(OH)3for High stability constantomitfor Low High stability constant
25 Complex formation with a common ion to the precipitate may increase in solubility by large excesses of a common ion.ExampleWhat is the the concentration of KCl at which the solubility of AgCl is a minimum?Solutionomit
26 Figure 11-2 The effect of chloride ion concentration on the solubility of AgCl. The solid curve sows the total concentration of dissolved AgCl.The broken lines show the concentrations of the various silver-containing species.CKCl = M
27 11C Separation of ions by control of the concentration of the precipitating agent 11C-1 Calculation of the feasibility of separationsGenerally, complete precipitation is considered as 99.9% of the target ion is precipitated, i.e., 0.1% left.
28 [Fe3+][OH-]3 = 2x10-39[Mg2+][OH-]2 = 7.1x10-12Fe3+會先沈澱設剩餘 0.1% 之Fe3+為 complete precipitation for Fe(OH)3，則 [Fe3+] = 0.1x0.1% = 1x 10-4 M1 x 10-4 x [OH-]3 = 2x10-39[OH-] = 3 x M 完全沈澱Fe3+所需之[OH-]Mg(OH)2 開始沉澱之 [OH-]：0.1 x [OH-]2 = 7.1x10-12[OH-] = 8.4 x 10-6 M Mg2+開始沈澱之[OH-]控制水溶液之 [OH-] = 3 x ~ 8.4 x 10-6 M，可將 0.1 M 的 Fe3+ 與 0.1 M 的 Mg2+ 分離。
29 11C-2 Sulfide Separations Saturated H2S, [H2S](aq) = 0.1 M[S2-] in H2S saturated solution depend on the pHMetal sulfide solubility for (M2+S2-) in saturated H2S* The solubility of MS in H2S saturated solution depend on the pH
30 Homework (Due 2014/11/27) End of Chapter 11 Skoog 9th edition, Chapter 11, Questions and Problems11-5 (e) (g)11-6 (e) (g)11-7 (a)11-14End of Chapter 11