Acid Base Equilibria

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Acid Base Equilibria

• Chapter 17

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Topics of Discussion

• Solutions of a weak acid and base
• Acid-Ionization Equilibria
• Polyprotic Acids
• Base-Ionization Equilibria
• Acid-base Properties of Salt Solutions
• Solutions of Weak Acid/Base with Another Solute
• Common-Ion Effect
• Buffers
• Acid-Base Titration Curves

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Weak acid

• HA H2O ? H3O A-
• Ka is acid dissociation constant
• HA ? H A-

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Some weak acids
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Weak Base

• B H20 ? BH OH-
• NH3 H2O ? NH4 OH-

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Some weak bases
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Equilibrium calculations

• Ka and Kb from percentage ionization
• ionization (amount ionized)/(amount
  available)x100
• Example
• In a 0.01 M solution of butyric acid the acid is
  4 ionized at 20 0C. Calculate Ka and pKa for
  butyric acid at this temperature.

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Solution

• HBu H2O ? H3O Bu-

• Ka (0.0004)2/(0.00996)
• 1.6x10-5
• pKa 4.8

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Equilibrium calculations

• Ka and Kb from initial concentrations and pH
• Example
• In a 0.1 M solution of formic acid, the pH is
  2.38 at 25 0C. Calculate the Ka and pKa for
  formic acid at this temperature.
• HCOOH H2O ? HCOO- H3O

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Solution

• H3O 10-2.38 0.0042 M

Ka 1.84x10-4
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Simplifying assumption

• HA ? H A-
• Accuracy of calculations may be set within 5
• H/HAinitial lt 0.05
• H2/HAinitial Ka
• HAinitial gt Ka 400
• HAequilibrium HAinitial - x (x is
  negligible)
• HAequilibrium HAinitial

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Example

• What is the pH of 0.010 M solution of dimethyl
  amine, (CH3)2NH? Kb 9.6x10-4
• (CH3)2NH H2O ? (CH3)2NH2 OH-
• Is simplification possible?
• (CH3)2NHinitial gt 400 Kb
• 0.01 gt (400)(9.6x10-4) 0.384
• No simplification. Quadratic solution.

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Solution

• x2 9.6x10-4x - 9.6x10-6 0
• x 2.65x10-3
• pOH -log(2.65x10-3) 2.58
• pH 11.42

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Polyprotic Acids

• Acids with two or more acidic protons
• H2SO3(aq) ? HSO3-(aq) H(aq) Ka1 1.3x10-2
• HSO3-(aq) ? SO32-(aq) H(aq) Ka2 6.3x10-8
• For polyprotic acids Ka1gt Ka2gt Ka3
• Number of protons to be dissociated are larger.
• First proton separates from singly negative
  charged ion.
• For 0.25 M sulfuroz acid pH?, ?SO32-??

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Polyprotic Acids-II

• xapp 0.06, quadratic equation is needed to
  obtain x.
• ?SO32-??

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Acid-base Properties of Salt Solutions

• Ionization of formic acid
• HCOOH H2O ? H3O HCOO-
• Hydrolysis of formate ion
• HCOO- H2O ? HCOOH OH-

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For any acid-base conjugate pairs

• Ka x Kb KW
• pKa pKb pKW 14
• The value of Ka 1.8x10-5 for CH3COOH. What is
  the value of Kb for CH3COO-?
• Solution

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Solutions of salts of weak acids and bases

• HCOOH H2O ? HCOO- H3O
• Strong acid ? weak conjugate base
• HCl ? H Cl-
• H2O ? H OH-

acid
conjugate base
Very strong acid
Very weak base
Very weak acid
Very strong base
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Example

• What is the pH of 0.1 M solution of NaOCl?
• Ka 3.0x10-8
• Solution
• OCl- H2O ? HOCl OH-

(x2/0.1) 3.3x10-7 HOCl OH- x
1.8x10-4 pOH -log(1.8x10-4) 3.74 pH 14.00 -
3.74 10.26
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Ammonia and its conjugate acid ammonium ion

• NH3 H2O ? NH4 OH-
• NH4 H20 ? NH3 H3O

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Examples of some weak acids and bases

• Metal ions with high charge densities are weak
  acids
• Al(H2O)63 H2O ? Al(H2O)5OH2 H3O
• Metal ions with small charges are nonacids
• Aquous ions of Gr IA Li, Na, K, Rb, or Cs
  (except Be2) and Gr IIA Mg2, Ca2, Sr2, and
  Ba2 do not affect pH of solution.

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Acid-base properties of a salt

• If only the cation of salt is acidic, the
  solution will be acidic.
• If only the anion of the salt is basic, the
  solution will be basic.
• If a salt has a cation that is acidic and an
  anion that is basic, the pH of the solution is
  determined by the relative strength of the acid
  or base.

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Example

• Predict whether the following salts are acidic,
  basic or neutral.
• NaOCl
• NaNO2
• KCl
• NH4Br
• NaOCl ? Na OCl-
• OCl- H2O ? HOCl OH- (basic)
• NaNO2 (basic)
• KCl (neutral)
• NH4Br (acidic)

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Common-Ion Effect

• The common-ion effect is the shift in an ionic
  equilibrium cause by the addition of a solute
  that provides an ion that takes part in the
  equilibrium.
• What is the degree of ionization of 0.10 M formic
  acid, HCOOH, solution? Ka 1.84x10-4
• a. When it is together with 0.20 M HCl. b.When
  it is pure.

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Buffers

• Buffer solutions are used to keep the pH
  constant. Dilution of solution, addition of acid
  or base to buffer solution affects the pH very
  little.
• Buffer consists of a weak Bronsted acid and its
  conjugate base or vice versa.
• Examples
• NH3 and NH4Cl (NH3 / NH4)
• CH3COOH and CH3COONa (CH3COOH / CH3COO-)

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How a buffer work?

• Buffer HA ? H A-
• If extra acid is added
• H A- ? HA (extra acid is neutralized by
  conjugate base A-)
• If extra base is added
• OH- HA ? H2O A- (extra base is neutralized
  by acid HA)

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Acetic acid / acetate buffer

• What is the pH of a buffered solution made up
  0.015 M sodium acetate and 0.10 M acetic acid? Ka
  1.8x10-5

• H x 1.2x10-4
• pH 3.92

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Ammonia / ammonium ion buffer

• Calculate the pH of a buffer solution prepared by
  dissolving 0.10 mol NH3 and 0.2 mol NH4Cl in 1 L
  water. Kb 1.8x10-5

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Henderson-Hasselbalch Equation

• HA ? H A-
• -logKa logHA - logH - logA-

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Preparation of a buffer solution with a given pH

• How do you prepare an acetate/acetic acid buffer
  solution with a pH 5.0? (Ka 1.8x10-5)
• Solution
• pH pKa log(A-/HA)
• 5.0 -log(1.8x10-5) log(A-/HA)
• 10(5.00 - 4.74) A-/HA
• A-/HA 1.82

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Selecting a weak acid for the preparation of a
buffer solution

• A buffer solution is effective if
• 0.1 lt HA / A- lt 10
• pH pKa log(A-/HA)
• pH pKa 1

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Example

• How a buffer solution with pH 8.00 be prepared?
• Solution
• pH pKa log(A-/HA)
• Hypochlorous acid, HOCl Ka 3.0x10-8
• pKa 7.52
• 8.00 7.52 log(OCl-/HOCl)
• OCl-/HOCl 3.02

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Buffer capacity

• The ratio A-/HA defines the pH of buffer
  solution.
• The magnitude of concentrations A- and HA
  defines the buffer capacity.
• It is the ability of a buffer solution to
  compensate extra added acid or base.

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Example (Buffer capacity)

• A 1 L buffer solution is prepared using 1.00 M
  acetic acid, HA, and 1.00 M NaAc. In an
  experiment 0.11 mol of hydroxide ion is generated
  without any volume change. Can the buffer
  solution handle this without a pH change of 0.1
  unit?
• Ka 1.8x10-5

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Solution
HA H2O ? H3O A-

• pH 4.84 (buffer solution just tolerates excess
  base)

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Acid-base titrations

• The pH of an unknown acid may be found by
  titrating it with a standard base solution until
  the end point is reached.
• The equivalence point occurs when
  stoichiometrically equivalent acid and base
  reacts.
• Titration curves are drawn, pH vs added reagent,
  and equivalence point is determined.

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Titration of 25 mL of 0.2 M HCl with 0.2 M NaOH
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Titration curve
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Titration of weak acid by strong base

• CH3COOH OH- ? CH3COO- H2O
• Before the titration begins
• Dissociation of weak acid
• During the titration but before the equivalence
  point
• Formation of a buffer solution
• At the equivalence point
• Hydrolysis of conjugate base
• After the equivalence point
• Concentration of OH-

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Before the titration begins

• What is the pH of 0.2 M CH3COOH?
• Ka 1.8x10-5
• CH3COOH H2O ? CH3COO- H3O
• Solution

H3O 1.9x10-3 M pH 2.72
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Before the equivalence point...

• Adding 10 mL 0.2 M NaOH to 25 mL 0.2 M CH3COOH.

CH3COOH (3 mmol)/(35 mL) 0.0857 M CH3COO-
(2 mmol)/(35 mL) 0.0571 M
H 2.7x10-5 M pH 4.57
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At the equivalence point

• 25 mL 0.2 M NaOH is added to 25 mL 0.2 M CH3COOH.
  What is the pH of solution?
• Acetic acid is converted to acetate ion
  completely.
• CH3COO- H2O ? CH3COOH OH-

• OH- 7.5x10-6 M
• pOH 5.12 pH 14.00 - 5.12 8.88

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After the equivalence point

• 35 mL 0.2 M NaOH is added to 25 mL 0.2 M CH3COOH.
  What is the pH of solution?
• OH- neutralizes CH3COOH. Excess OH- defines the
  pH.
• OH- (35x0.2-25x0.2 mmol)/(60 mL) 0.033M
• pOH 1.48 pH 12.5

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pH 8.88 at equivalence pt
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Titration of a weak base by strong acid

• NH3 H2O ? NH4 OH-
• Before the titration begins
• Dissociation of weak base
• During the titration but before the equivalence
  point
• Formation of a buffer solution
• At the equivalence point
• Hydrolysis of conjugate acid
• After the equivalence point
• Concentration of H

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Acid-base indicators

• HIn(aq) ? H(aq) In-(aq)
• pH pKa log(In-/HIn)
• pH gt pKa 1 (In-/HIn 10, base color)
• pH lt pKa - 1 (In-/HIn 0.1, acid color)

Acid form color1
Base form color2