Chapter 9 Systematic Equilibrium

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Spencer Lawrence
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1 Chapter 9 Systematic Equilibrium 1 What we Skipped Ch. 8 discussed Activity (γ) This is what should be used in equilibrium calculations rather than conc. (molarity) In Ch. 9 in later chapters, you will occasionally see examples mention activity and then now that we ve reminded you we will omit activity for the rest of the chapter. Chemistry majors will learn about activity in PChem 1

3 Systematic Treatment of Equilibrium Systematic treatment is how the process of dealing with chemical equilibria, no matter how complex There

2 Acid Rain Equilibria Marble dissolves in acid rain by two coupled equilibrium reactions: CaCO CO 3( s) Ca CO3 3 H HCO3 In the realworld chemistry is always more complex than a 1 reaction system. 3 Systematic Treatment of Equilibrium Systematic treatment is how the process of dealing with chemical equilibria, no matter how complex There are several steps in the process Write equations representing chemical species Equilibrium conditions Mass and charge balance relations Add Approximations and Conditions which ease calculations Solve mulitequation, multiunknown system

3 Charge Balance Charge balance is an algebraic statement of electroneutrality. The sum of + charges = sum of charges For H +, OH, K +, H PO, HPO, and PO 3 : H K OH H PO HPO 3 PO 3 A solution made from 0.05 mol KH PO and mol KOH in 1L: 1 H M H PO 1.3 K M HPO 3 OH 0.00 M PO 0.003M M 6 M 5 Charge Balance Example So the general form for the charge balance: n n C... m A m A... 1 C1 1 1 where [C] is the concentration of cation with charge n and [A] is the concentration of an anion with charge m Write the charge balance for a solution with: H O, H +, OH, ClO, Fe(CN) 6 3, CN, Fe 3+, Mg +, CH 3 OH, HCN, NH 3, NH + 3 H 3 Fe Mg NH OH ClO 3Fe(CN) 3 6 CN 6 3

4 Mass Balance Mass balance, also known as material balance is the statement of conservation of mass If you prepare a solution by dissolving mol acetic acid in 1 L water: CH CO H CH CO H M CH 3CO H CH 3CO The mass balance includes all the products. If you put 0.05 mol phosphoric acid in 1 L H O: H PO H PO HPO M 3 PO 3 7 Mass Balance Example (When Total Concentration is Known) Write the mass balance for K + and phosphate in solution prepared by mixing mol KH PO plus mol KOH diluted to 1 L. Potassium mass balance is easy: K 0.05 M M M For phosphate, must take dissociation into account: H PO H PO HPO M 3 PO 8

5 Mass Balance Example (When Total Concentration is Unknown) Write the mass balance for a saturated solution of the slightly soluble salt Ag 3 PO, which produces Ag + and phosphate in solution. If phosphate remained as phosphate, then: Ag 3 PO 3 But because phosphate reacts with water, so: Ag 3 H PO H PO HPO 3 3 PO 9 Systematic Treatment Process (1) Write the pertinent reactions () Write the charge balance equation (3) Write any mass balance equations () Write the equilibrium constant for each reaction (5) Count the equations and unknowns If # equations=# unknowns, go to 6, otherwise Find other equations Fix concentrations at known values (6) Solve for all of the unknowns 10 5

6 Simple Example: Water Apply the systematic treatment to find H + and OH in pure water. Step 1:Write reactions HO H OH Step : Charge balance H OH Step 3: Mass balance H OH Step : Equilibrium constants K w 1 H OH Step 5: Count, we have equations and unknowns Step 6: Solve (You ve done this already) 11 Simple Example (Solubility of Hg Cl ) Apply the systematic treatment to find Hg + in a saturated solution of Hg Cl Step 1:Write pertinent reactions HgCl Hg Cl HO H OH Step : Charge balance OH H Hg Cl Step 3: Mass balance Hg Cl H OH Step : Equilibrium constants K sp K w 18 Hg Cl H OH

Solubility of Hg Cl Example (cont) Step 5: Count the equations (5) and unknowns () Equations: Charge balance, mass balance, K equations Unknowns: [H + ], [Hg + ], [Cl ], [OH ] Step 6: Solve

We can take advantage of these to formulas: K sp K sp 18 Hg Cl 1. 10 18 Hg Hg 1. 10 7 H, OH 1.010 Hg Cl K sp 7 Hg 6.

7 Solubility of Hg Cl Example (cont) Step 5: Count the equations (5) and unknowns () Equations: Charge balance, mass balance, K equations Unknowns: [H + ], [Hg + ], [Cl ], [OH ] Step 6: Solve Since water is not interacting with Hg Cl in this system, you can essentially solve for H + and OH using water ionization: 1 H OH Of course the Hg Cl equilibrium is also of interest. We can take advantage of these to formulas: K sp K sp 18 Hg Cl Hg Hg H, OH Hg Cl K sp 7 Hg M (1/3) 13 Dependence of Solubility on ph Now we can start to deal with problems we haven t seen before. Fluorite mineral, CaF, is a cubic crystal that can change colors depending on impurities present. We will now consider the solubility of calcium fluoride in water. 1 7

8 Solubility of CaF Example Apply the systematic treatment to find Ca + in a solution of CaF. F in solution is a weak base. K sp K w Step 1:Write pertinent reactions (there are 3) HO H OH Step : Charge balance (1, as always) Step 3: Mass balance Ca F HF Step : Equilibrium constants (3 of them) 11 Ca F H OH CaF ( s) Ca F F H O HF OH H Ca OH F K b HF OH F Solubility of CaF (cont) Step 5: Count equations (5) and unknowns (5) Equations: Charge balance, mass balance, 3 K equations Unknowns: [Ca + ] (x), [HF](a), [F ](b), [H + ](c), [OH ](d) Step 6: Solve (algebraic equations) c d b d c x (1.510 d a b x x b a This is complicated! We won t go through solving it. We will keep to and 3 equation problems to actually solve. However, you should be able to setup the equations for these problems ) x 8

9 Solubility of CaF Example A little bit easier: What if ph is fixed at 3.0? Now solve: HF ph 3 F OH Ca 3 H 110 M K 11 OH w M 11 K b F HF M 1.5 HF 1.5 F F 0.80Ca 11 Ca F Ca F HF ph and Solubility If you do make an assumption and fix the ph during a calculation the charge balance equation is no longer valid. Why? You would have had to add something (ions) to the solution to fix the ph This has not been accounted for in the balance equation, so you can t use that during the calculation. 18 9

Solubility Dependence on ph Salts of basic ions (F,

10 Solubility Dependence on ph Salts of basic ions (F, OH, S, CO 3, C O, PO 3 ) have higher solubility at low ph because of connected equilibria. 19 ph Effect on Solubility ph can also have an effect on the solubility of minerals. Metals such as aluminum or lead can be freed from insoluble forms with a low enough ph. 0 10

11 ExampleBarium Oxalate Find the composition of a solution containing barium oxalate. Step 1:Write pertinent reactions Ba(C C O HO H OH Step : Charge balance Step 3: Mass balance HC O) (s) Ba C O H O HCO OH O H O HCO( aq) OH Ba H OH C O HC O Ba C O HC O H C O 1 ExampleBarium Oxalate (cont) Step : Equilibrium constants 6 Ba CO HC O OH K sp 1 10 K b C O H CO OH 13 1 Kb K w H OH 1 10 HC O Step 5: Count equations and unknowns Equations: Charge balance, mass balance, K equations Unknowns: [H + ], [Ba + ], [C O ], [HC O ], [H C O ], [OH ] Step 6: Solve 6 equations/6 unknowns Or, if you re going to fix the ph at a particular value, then you should express all of the chemical constituents as a function of H + or OH 10 11

12 ExampleBarium Oxalate (cont) K 1 OH HCO b C O Ba C O HC O H C O K sp 6 Ba C O C O H CO K b b K OH Ba CO Kb 1 Kb 1Kb 1 OH OH Ba K sp K 1 K K b1 b1 b OH OH 3 ph Effect on Barium Oxalate 1

13 Solving With a Fixed ph Step 1: Write equations systematically as normal Step : Express concentration of each protonated form [H n A] of anion in terms of [A] Step 3: Substitute expressions for [HnA] into the mass balance equation to give a relation between [M] and [A] Step : Put the [M]/[A] relation into K sp to solve for [M] Step 5: With [M] and [OH ] solve for other anions 5 Keep in Mind In solving the equilibrium system, we are limited to the reactions we have knowledge of. In the previous example Ba + reacts with OH to form BaOH + in solution At best then, our answers are an approximation if we don t have the equilibrium information for other reactions 6 13

Chapter 17 Solubility and Complex Ion Equilibria

Chem 1046 General Chemistry by Ebbing and Gammon, 8th Edition Prof George W.J. Kenney, Jr Last Update: 27Nov2008 Chapter 17 Solubility and Complex Ion Equilibria These Notes are to SUPPLIMENT the Text,