Chemistry 232

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Chemistry 232

• Applications of Aqueous Equilbria

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The Brønsted Definitions

• Brønsted Acid proton donor
• Brønsted Base proton acceptor
• Conjugate acid - base pair an acid and its
  conjugate base or a base and its conjugate acid

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Example Acid-Base Reactions

• Look at acetic acid dissociating
• CH3COOH(aq) ? CH3COO-(aq) H(aq)
• ?
• Brønsted acid Conjugate base
• Look at NH3(aq) in water
• NH3(aq) H2O(l) ? NH4(aq) OH-(aq)
• ? ?
• Brønsted base conjugate acid

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Representing Protons in Aqueous Solution

• CH3COOH(aq) ? CH3COO-(aq) H(aq)
• CH3COOH(aq) H2O(l) ? CH3COO-(aq) H3O(aq)
• HCl (aq) ? Cl-(aq) H(aq)
• HCl(aq) H2O(l) ? Cl-(aq) H3O(aq)

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What is H (aq)?

H3O
H
H5O2
H9O4
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Representing Protons

• Both representations of the proton are
  equivalent.
• H5O2 (aq), H7O3 (aq), H9O4 (aq) have been
  observed.
• We will use H(aq)!

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The Autoionization of Water

• Water autoionizes (self-dissociates) to a small
  extent
• 2H2O(l) ? H3O(aq) OH-(aq)
• H2O(l) ? H(aq) OH-(aq)
• These are both equivalent definitions of the
  autoionization reaction. Water is acting as a
  base and an acid in the above reaction ? water is
  amphoteric.

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The Autoionization Equilibrium

• From the equilibrium chapter

• But we know a(H2O) is 1.00!

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The Defination of Kw

• Kw a(H) a(OH-)
• Ion product constant for water, Kw, is the
  product of the activities of the H and OH- ions
  in pure water at a temperature of 298.15 K
• Kw a(H) a(OH-) 1.0x10-14 at 298.2 K

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The pH scale

• Attributed to Sørenson in 1909
• We should define the pH of the solution in terms
  of the hydrogen ion activity in solution
• pH -log a(H)
• Single ion activities and activity coefficients
  cant be measured

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Determination of pH

• What are we really measuring when we measure the
  pH?
• pH -log a?(H)
• a? (H) is the best approximation to the hydrogen
  ion activity in solution.
• How do we measure a?(H)?

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• For the dissociation of HCl in water
• HCl (aq) ? Cl-(aq) H(aq)
• We measure the mean activity of the acid
• a(HCl) a(H) a(Cl-)
• a(H) a(Cl-) (a?(HCl))2

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• Under the assumption
• a(H) a(Cl-)
• We obtain
• a(H) (a(HCl))1/2 a?(HCl)

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Equilibria in Aqueous Solutions of Weak Acids/
Weak Bases

• By definition, a weak acid or a weak base does
  not ionize completely in water (? ltlt100). How
  would we calculate the pH of a solution of a weak
  acid or a weak base in water?
• To obtain the pH of a weak acid solution, we must
  apply the principles of chemical equilibrium.

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Equilibria of Weak Acids in Water The Ka Value

• Define the acid dissociation constant Ka
• For a general weak acid reaction
• HA (aq) ? H (aq) A- (aq)

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Equilibria of Weak Acids in Water

• For the dissolution of HF(aq) in water.
• HF (aq) ? H (aq) F- (aq)

• The small value of Ka indicates that this acid is
  only ionized to a small extent at equilibrium.

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The Nonelectrolyte Activity

• HF (aq) ? H (aq) F- (aq)
• The undissociated HF is a nonelectrolyte
• ? a(HF) ?(HF) mHF ? mHF
• ?(HF) ? 1

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Equilibria of Weak Bases in Water

• To calculate the percentage dissociation of a
  weak base in water (and the pH of the solutions)
  
• CH3NH2 (aq) H2O ? CH3NH3(aq) OH- (aq)
• We approach the problem as in the case of the
  weak acid above, i.e., from the chemical
  equilibrium viewpoint.

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The Kb Value

• Define the base dissociation constant Kb
• For a general weak base reaction with water
• B (aq) H2O (aq) ? B (aq) OH- (aq)

• For the above system

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Examples of Acid-Base Calculations

• Determining the pH of a strong acid (or base
  solution).

• Determining the pH of a weak acid (or base
  solution).

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Calculating the pH of Solutions of Strong Acids

• For the dissolution of HCl, HI, or any of the
  other seven strong acids in water
• HCl (aq) ? H (aq) Cl- (aq)
• HI (aq) ? H (aq) I- (aq)

?eq 100

• The pH of these solutions can be estimated from
  the molality and the mean activity coefficient
  of the dissolved acid
• pH -log (?? (acid) mH)

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Calculating the pH of Solution of Strong Bases

• For the dissolution of NaOH, Ba(OH)2, or any of
  the other strong bases in water
• NaOH (aq) ? Na (aq) OH- (aq)
• Ba(OH)2 (aq) ? Ba2 (aq) 2OH- (aq)

?eq 100
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• The pH of these solutions is obtained by first
  estimating the pOH from the molality and mean
  activity coefficient of the dissolved base
• pOH -log (?? (NaOH) mOH-)
• pOH -log?? (Ba(OH)2) 2 mBa(OH)2
• pH 14.00 - pOH

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Calculating the pH of a Weak Acid Solution

• The pH of a weak acid solution is obtained via an
  iterative procedure.
• We begin by making the assumption that the mean
  activity coefficient of the dissociated acid is
  1.00.
• We correct the value of ?(H) by calculating
  the mean activity coefficient of the dissociated
  acid.
• Repeat the procedure until ?(H) converges.

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Measuring the pH of Solutions

• Because the activity of a single ion cannot be
  measured, we can only measure our best
  approximation to the hydrogen ion activity.
• Lets assume that we are going to couple a
  hydrogen electrode with another reference
  electrode, e.g., a calomel reference electrode.

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A Cell for Measuring the pH
Pt H2 (g), f1 H (aq) HgCl2 Hg Cl- (aq),
3.5 M Pt

• Half-cell reactions.
• HgCl2 (s) 2e- ? Hg (l) 2 Cl- (aq)
• E?(SCE) 0.2415 V
• 2 H (aq) 2e- ? H2 (g)
• E? (H/H2) 0.000 V
• Cell Reaction
• HgCl2 (s) H2 (g) ? Hg (l) 2 H (aq) 2Cl-
  (aq)
• E?cell (0.2415 - 0.0000 V) 0.2415 V

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The Nernst Equation

• For the above cell

• Note since the concentration of the KCl on one
  side of the liquid junction is so large, the
  magnitude of the junction potential should be
  small!

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The Practical Problem

• The activity of the Cl- ion in the cell is not
  accurately known.
• We try to place the cell in a reference solution
  with an accurately known pH (solution I).
• Next place the solution whose pH we are
  attempting to measure into the cell (solution
  II).

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• Assuming that the ELJ and the a(Cl-) are the same
  in both cases,

• Substituting the definition of the pH into the
  above expression,

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Standard Solutions

• Generally, two solutions are used as references.
• Saturated aqueous solution of sodium hydrogen
  tartarate, pH 3.557 at 25?C.
• 0.0100 mol/kg disodium tetraborate, pH 9.180 at
  25?C.

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The Glass Electrode

• The glass electrode has replaced the hydrogen
  electrode in the operational definition of the
  pH.

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Glass Electrodes

• Measuring the pH the glass electrode is
  immersed in the solution of interest.
• Inner solution solution is generally a
  phosphate buffer with a sufficient quantity of
  Cl- (aq).
• Silver-silver chloride electrode is sealed within
  the cell and a calomel electrode is used as the
  reference electrode.

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Glass Electrodes and pH

• The potential difference across the special glass
  membrane arises to equilibrate the hydronium ions
  inside the membrane with those outside the
  membrane.

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The Definition of a Buffer

• Buffer ? a reasonably concentrated solution of a
  weak acid and its conjugate base that resists
  changes in the pH when an additional amount of
  strong acid or strong base is added to the
  solutions.

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• How would we calculate the pH of a buffer
  solution?

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note pH -log a(H)
Define pKa -log (Ka )
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The Buffer Equation

• Substituting and rearranging

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The Generalized Buffer Equation

• The pH of the solution determined by the ratio of
  the weak acid to the conjugate base. This
  equation (the Henderson-Hasselbalch equation) is
  often used by chemists, biochemists, and
  biologists for calculating the pH of a solution
  of a weak acid and its conjugate base!

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• Note The Henderson-Hasselbalch equation is
  really only valid for pH ranges near the pKa of
  the weak acid!

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• Buffer ? CH3COONa (aq) and CH3COOH (aq))
• CH3COOH (aq) ? CH3COO- (aq) H (aq)
• The Equilibrium Data Table

n(CH3COOH) n(H) n(CH3COO-)
Start A 0 B
Change -?eq ?eq ?eq
? m (A-?eq) (?eq) (B ?eq)
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• The pH of the solution will be almost entirely
  due to the original molalities of acid and base!!

• This ratio will be practically unchanged in the
  presence of a small amount of added strong acid
  or base
• The pH of the solution changes very little after
  adding strong acid or base (i.e., it is buffered)

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Example of Buffer Calculations

• How do we calculate the pH of a buffer solution?

• How does the pH change after the addition of
  strong acid or base?

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The pH of a Buffer Solution

• The major task in almost all buffer calculations
  is to obtain the ratio of the concentrations of
  conjugate base to weak acid!
• Using the Ka of the appropriate acid, the pH of
  the solution is obtained from the
  Henderson-Hasselbalch equation.

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Adding Strong Acid or Base to Buffer Solutions

• To obtain the pH after the addition of a strong
  acid or base, we must calculate the new amount
  of weak acid and conjugate base from the reaction
  of the strong acid (or base) to the buffer
  system.
• The pH of the solution may again be calculated
  with the Henderson-Hasselbalch equation.

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Solubility Equilibria

• Examine the following systems
• AgCl (s) ? Ag (aq) Cl- (aq)
• BaF2 (s) ? Ba2 (aq) 2 F- (aq)
• Using the principles of chemical equilibrium, we
  write the equilibrium constant expressions as
  follows

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Examples of Ksp Calculations

• Calculate the solubility of a sparingly soluble
  solid in water.

• Calculate the solubility of a solid in the
  presence of a common ion.

• Calculate the solubility of a solid in the
  presence of an inert electrolyte.

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Solubility of Sparingly Soluble Solids in Water

• AgCl (s) ? Ag (aq) Cl- (aq)
• We approach this using the principles of chemical
  equilibrium. We set up the equilibrium data
  table, and calculate the numerical value of the
  activity of the dissolved ions in solution.

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The Common Ion Effect

• What about the solubility of AgCl in solution
  containing NaCl (aq)?
• AgCl (s) ? Ag (aq) Cl- (aq)
• NaCl (aq) ? Na (aq) Cl- (aq)
• AgCl (s) ? Ag (aq) Cl- (aq)

Equilibrium is displaced to the left by
LeChateliers principle (an example of the common
ion effect).
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Solubility in the Presence of an Inert Electrolyte

• What happens when we try to dissolve a solid like
  AgCl in solutions of an inert electrolyte (e.g.,
  KNO3 (aq))?
• We must now take into account of the effect of
  the ionic strength on the mean activity
  coefficient!

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The Salting-In Effect

• AgCl (s) ? Ag (aq) Cl- (aq).
• We designate the solubility of the salt in the
  absence of the inert electrolyte as so m(Ag)
  m(Cl-) at equilibrium.

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• For a dilute solution

• Designate s as the solubility of the salt in the
  presence of varying concentrations of inert
  electrolyte.