11 Solving Equilibrium Problems for Complex Systems

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1 11 Solving Equilibrium Problems for Complex Systems When water is saturate with sparingly soluble BaS : BaS (s) Ba S (111) S H HS H (11) H H H (11) 1. if ae [H : 11 shifte to the right, [S, solubility of BaS. if ae acetate ions Ba Ac BaAc (11) [Ba, solubility of BaS 11A Solving MultipleEquilibrium Problems by a Systematic Metho a. equilibrium constant expressions b. massbalance equations c. a single chargebalance equation 11A1 MassBalance Equation Ex Write massbalance expressions for a 0.00 M soln of HCl that is in equilibrium with an excess of soli BaS. BaS (s) Ba S S H HS H H H H [Ba [S [HS [ H CHCl [H 0.00 [H Ex. 11. Write massbalance expressions for the system forme when a 0.0 M NH solution is saturate with AgBr. AgBr(s) Ag Br Ag NH Ag(NH ) NH H NH H [Ag [Ag(NH ) [Br CNH [NH [NH [Ag(NH ) A ChargeBalance Equation no. mol/l positive charge no. mol /L negative charge 5

2 Ex. 11. Write a chargebalance equation for the system in Ex.. [Ag [Ag(NH ) [H [NH [H [Br Ex. 11. Neglecting the issociation of water, write a chargebalance equation for a soln that contains NaCl, Ba(Cl ) & Al (S ). [Na [Ba [Al [Cl [Cl [S 11A Steps for solving problems involving several equilibria 1. Write balance chemical equations. Set up equation for unknown quantity *Approximations. Write equilibrium constant expressions (never). Write mass balance expressions (can be mae) 5. Write charge balance expression (can be mae) 6. Count no. of equations an no. of unknowns Is no. equations no. unknowns Yes No STP problem unsolvable 7. Make suitable approximation Try 8. Solve equations for unknow again 9. Were approximations vali? If no Yes Problem solve *Approximations can be mae only in chargebalance an massbalance equations, never in equilibriumconstant expressions. 11B Calculating solubilities by the systematic metho 11B1 Solubility calculations 5

3 Ex Calculate the molar solubility of Mg(H) in water. Mg(H) (s) Mg H [Mg [H sp H (aq) H H [H [H w solubility Mg(H) [Mg, [H [Mg [H assume that [H << [Mg [H [Mg [Mg ([Mg ) 7.1 1, [Mg 1.78 [Mg solubility M Check of Assumptions: 1 [H 1.1. M, 1.00 [H.1. The assumption that.1 11 << 1.6 is certainly vali M Ex Calculate the solubility of Fe(H) in water. Proceeing by the systematic approach use in Ex. 5 gives. Fe(H) (s) Fe H sp [Fe [H 9 H H H w [H [H solubility [Fe, [H [Fe [H assume that [H << [Fe [H [Fe, [Fe ([Fe ) 9 solubility [Fe Step 9. Check of Assumptions: [H [Fe 9 11 M [H M >> [Fe The assumption that [H << [Fe, was invali an the provisional values for [Fe, [H an [H are all significantly in error. assume that [Fe << [H, [H [Fe [H [H 9 [H [Fe M 7 (1 ) [Fe << [H or 18 << 7, the assumption is vali solubility [Fe 18 M M 5

4 11B The Effect of ph on Solubility All ppts that contain an anion that is the conjugate base of a weak aci are more soluble at low ph than at high ph. Solubility Calculations When the ph Is Constant Ex Calculate the molar solubility of calcium oxalate in a soln that has been buffere so that its ph is constant an equal to.00. CaC (s) Ca C H C H H HC HC H H C H H H solubility [Ca sp [Ca [C (1) [H [ H [HC [HC () [ H [C 5. () [HC w [H [H [Ca [C [HC [H C () [H 1.00 ; [H 1.00 Unknown [Ca, [C, [HC an [H C [H [C 1.00 [C [HC 1.85[C 5. C [H [C [C [Ca [C 1.85 [C.0 [C.85 [C [Ca [Ca [Ca [C ; [Ca solubility M [C 55

5 11B The Effect of Unissociate Solutes on Precipitation Calculations AgCl(s) AgCl(aq) [AgCl(aq), [AgCl(aq) [AgCl(s) s.6 7 [AgCl(s) AgCl(aq) Ag Cl [Ag [Cl 5.0 [AgCl(aq) sp s [Ag [Cl Ex Calculate the solubility of AgCl in istille water. solubility S [AgCl(aq) [Ag [Ag [Cl sp 1.8 [Ag S [AgCl(aq) [Ag M M 11B The solubility of Precipitates in the presence of complexing agent Al(H) (s) Al H 6 F AlF 6 Complex Formation with a common ion solubility AgCl(s) Cl AgCl Cl AgCl Ex. 119 Derive an equation that escribes the effect of the analytical concentration of on the solubility of AgCl in an aqueous solution. Calculate the concentration of at which the solubility is a minimum. AgCl(s) AgCl(aq) [Ag [Cl sp 1.8 AgCl(aq) Ag Cl [Ag [Cl.9 [AgCl(aq) AgCl(s ) Cl AgCl [AgCl.0 [AgCl(aq)[Cl [AgCl AgCl Cl AgCl 1 [AgCl [Cl 56

6 [Cl c [Ag [AgCl [AgCl Assumption: c >> [Ag [AgCl [AgCl [Cl c [AgCl [Cl [AgCl( aq ).0 SP SP sp SP sp S [Cl [Cl c [Cl c S c (.0 sp 0 c c c sp c 5 7 ) c (.0 ) c [Cl c Check: [Ag (1.8 )/ M << c 8 [AgCl M << c [AgCl M << c S M c 0 Fig. 11 The Effect of [Cl on the solubility of AgCl. The soli curve shows the total concentration of issolve AgCl. The broken lines show the concentration of the various silvercontaining species. Zn H Zn(H) (s) Zn(H) (s) H Zn(H) 57

7 11C Separation of Ions by Control of the Concentration of the Precipitating Agent 11C1 Calculation of the Feasibility of Separations Ex. 11 Can Fe an Mg be separate quantitatively as hyroxie from a solution that is 0. M in each cation? If the separation is possible, what range of [H is permissible? [Fe [H 9 [Mg [H Quantitative separation: (1) 99.9% Fe will be precipitate an () Mg not precipitate. quantitative: > 99% precipitation < 0.1% remaine [Fe << 1.0 M 9 1. (1.0 )[H 9 [H 1 M [H [H 8. M 0.1 By maintaining [H between 1 M an 8. 6 M. In practice, [H is kept as low as practicaloften about M 11C Sulfie Separations Solubility ifferences : control ph control active reagent conc. reagents in which the anion is the conjugate base of a weak aci Ex: S (conjugate base of H S), H (conjugate base of H ) an the anions of several organic weak acis. MS :(sp: 50 or small) [S : 0.1 M MS(s) M S, [M [S sp H S H H HS, [H [HS [H S HS H H S, [H [S 1 1. [HS Solubility [M The [H S in a saturate soln is 0.1 M [S [HS [H S 0.1 assuming that ([S [HS ) << [H S [H S 0. M 58

8 H S H H S [H [S 1 1. [H S [H [S [S sp 1. [H 1. [H [S [M 1. [H [M solubility 1 [H 1. sp 1 ph Fig.11 [H S as a function of ph in a saturate H S solution. Ex CS is less soluble than Tl S. Fin the conitions uner which C an Tl can, in theory, be separate quantitatively with H S from a solution that is 0.1 M in each cation. CS(s) C S, [C [S 1 7 Tl S(s) Tl S, [Tl [S 6 Consier a separation to be quantitative when all but 1 part in 00 of the C has been remove, or, when the conc. of the cation has been reuce to 1.00 M [S > 1 7, [S > 1 (Min) (0.1) [S < 6, [S < 6 0 (Max) 1. [H < 1, [H <.5 M (Max) 1 1. [H >.0, [H > 0.05 M (Min) 0 6 maintaining [H between 0.05 an.5 M 59