Ch' 9Systematic Equilibrium

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Ch. 9-Systematic Equilibrium
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What we Skipped

• Ch. 8 discussed Activity (?)
• 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
  weve reminded you we will omit activity for the
  rest of the chapter.
• Chemistry majors will learn about activity in
  P-Chem

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Acid Rain Equilibria
Marble dissolves in acid rain by two coupled
equilibrium reactions In the real-world
chemistry is always more complex than a 1
reaction system.
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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 mulit-equation, multi-unknown system

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Charge Balance

• Charge balance is an algebraic statement of
  electroneutrality.
• The sum of charges sum of - charges
• For H, OH-, K, H2PO4-, HPO42-, and PO43-
• A solution made from 0.025 mol KH2PO4 and 0.030
  mol KOH in 1L

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Charge Balance Example

• So the general form for the charge balance
• 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
• H2O, H, OH-, ClO4-, Fe(CN)63-, CN-, Fe3, Mg2,
  CH3OH, HCN, NH3, NH4

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Mass Balance

• Mass balance, also known as material balance is
  the statement of conservation of mass
• If you prepare a solution by dissolving 0.050 mol
  acetic acid in 1 L water
• The mass balance includes all the products. If
  you put 0.025 mol phosphoric acid in 1 L H2O

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Mass Balance Example (When Total Concentration is
Known)

• Write the mass balance for K and phosphate in
  solution prepared by mixing 0.0250 mol KH2PO4
  plus 0.030 mol KOH diluted to 1 L.
• Potassium mass balance is easy
• For phosphate, must take dissociation into
  account

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Mass Balance Example (When Total Concentration is
Unknown)

• Write the mass balance for a saturated solution
  of the slightly soluble salt Ag3PO4, which
  produces Ag and phosphate in solution.
• If phosphate remained as phosphate, then
• But because phosphate reacts with water, so

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Systematic Treatment Process

• 1) Write the pertinent reactions
• 2) Write the charge balance equation
• 3) Write any mass balance equations
• 4) 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

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Simple Example Water

• Apply the systematic treatment to find H and OH-
  in pure water.
• Step 1Write reactions
• Step 2 Charge balance
• Step 3 Mass balance
• Step 4 Equilibrium constants
• Step 5 Count, we have 2 equations and 2 unknowns
• Step 6 Solve (Youve done this already)

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Simple Example (Solubility of Hg2Cl2)

• Apply the systematic treatment to find Hg22 in a
  saturated solution of Hg2Cl2
• Step 1Write pertinent reactions
• Step 2 Charge balance
• Step 3 Mass balance
• Step 4 Equilibrium constants

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Solubility of Hg2Cl2 Example (cont)

• Step 5 Count the equations (5) and unknowns (4)
• Equations Charge balance, 2 mass balance, 2 K
  equations
• Unknowns H, Hg22, Cl-, OH-
• Step 6 Solve
• Since water is not interacting with Hg2Cl2 in
  this system, you can essentially solve for H and
  OH- using water ionization
• Of course the Hg2Cl2 equilibrium is also of
  interest. We can take advantage of these to
  formulas

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Dependence of Solubility on pH

• Now we can start to deal with problems we havent
  seen before.

Fluorite mineral, CaF2, is a cubic crystal
that can change colors depending on impurities
present. We will now consider the
solubility of calcium fluoride in water.
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Solubility of CaF2 Example

• Apply the systematic treatment to find Ca2 in a
  solution of CaF2. F- in solution is a weak base.
• Step 1Write pertinent reactions (there are 3)
• Step 2 Charge balance (1, as always)
• Step 3 Mass balance
• Step 4 Equilibrium constants (3 of them)

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Solubility of CaF2 (cont)

• Step 5 Count equations (5) and unknowns (5)
• Equations Charge balance, mass balance, 3 K
  equations
• Unknowns Ca2 (x), HF(a), F-(b), H(c),
  OH-(d)
• Step 6 Solve (algebraic equations)
• This is complicated! We wont go through solving
  it. We will keep to 2 and 3 equation problems to
  actually solve. However, you should be able to
  setup the equations for these problems.

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Solubility of CaF2 Example

• A little bit easier What if pH is fixed at 3.0?
  Now solve

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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 cant use that during the
  calculation.