Polyprotic AcidBase Equilibria

1
Chapter 11

• Polyprotic Acid-Base Equilibria

2
Focus of Chapter

• Determination of pH of polyprotic systems
• Buffers made from polyprotic systems
• Determination of the principle species in
  solution at any given pH

3
Common Polyprotic Systems

• Diprotic
• Sulfuric Acid
• Oxalic Acid
• Triprotic
• Phosphoric Acid
• Amino Acids
• Minimum - Diprotic Systems

4
Polyprotic Systems

• Polyprotic Acids and Bases - compounds that can
  donate or accept more than one proton
• Diprotic Acids and Bases - a compound that can
  donate or accept two protons

5
Diprotic Acids and Bases

• Amino Acid Structure
• Neutral molecule is a zwitterion, a molecule that
  have both a positive and negative charge
• This form is due to the acidity of the carboxylic
  acid functional group compared to that of the
  ammonium group forcing the amino acid to
  rearrange to give the zwitterion.
• Low pH - both the ammonium and carboxyl groups
  are protonated
• High pH - neither group is protonated

6
Diprotic Acid and Base - pH Determination Example

• Calculate the pH and composition of individual
  solutions of 0.0500 M H2L, 0.0500 M HL, and
  0.0500 M L-.

7
Diprotic Acid and Base - pH Determination Example

• 0.0500 M H2L
• Diprotic system - can dissociate twice
• From pKas - K14.69 x 10-3 and K21.79 x 10-10
• H2L from K1 is a weak acid - partial
  dissociation
• HL from K2 hardly dissociates at all
• Approximation - H from H2L gtgt H from HL -
  behaves as a monoprotic acid

8
Diprotic Acid and Base - pH Determination Example

• 0.0500 M L-
• Diprotic System - hydrolyze twice
• From KaKbKw - Kb1 Kw/K25.59 x 10-5
• Kb2 Kw/K12.13 x 10-12
• L- from Kb1 is a weak base
• HL from Kb2 hardly hydrolyzes at all
• Approximation - L- behaves as a monoprotic base

9
Diprotic Acid and Base - pH Determination Example

• Diprotic System
• more complicated
• can react to give H2L or L- (amphiprotic)
• HL ? H L- Ka21.79 x 10-10
• HL H2O ? H2L OH- Kb22.13 x 10-12
• Use the systematic treatment of equilibria

10
Diprotic Acid Calculation Summary

• Solution H2A
• K1 x2 / F - x where x H HA
• H2A F - x and A2- calculated using
  K2
• Solution HA-
• H ?(K1K2F K1Kw) / (K1 F)
• should be close to 1/2(pK1 pK2)
• HA- F
• use K1, K2, H, and HA to solve for H2A
  and A2-

11
Diprotic Acid Calculation Summary

• Solution of A2-
• Kb1 x2 / F - x where x OH- HA-H2A F
  - x and A2- calculated using K2

12
Diprotic Acid and Base - pH Determination Example

• Potassium hydrogen phthalate, KHP, is a salt of
  the intermediate for of phthalic acid. Calculate
  the pH of both 0.10 M and 0.010 M KHP. (pK1
  2.950 pK2 5.408)

13
Diprotic Buffers

• Calculated the same was as for monoprotic buffers
• pH pK1 log HA- / H2A
• pH pK2 log A2- / HA-

14
Diprotic Buffer Example

• Find the pH of a solution prepared by dissolving
  1.00 g of potassium hydrogen phthalate and 1.20 g
  of disodium phthalate in 50.0 mL of water.
• How many milliliters of 0.800 M KOH should be
  added to 3.38 g of oxalic acid to give a pH of
  4.40 when diluted to 500.0 mL.

15
Polyprotic Acids and Bases

• Extension of the treatments completed for the
  diprotic systems
• Example - Triprotic System

16
Polyprotic Acids and Bases

• Triprotic System
• Equations
• H3A ? H H2A-
• H2A- ? H HA2-
• HA2- ? H A3-
• A3- H2O ? HA2- OH-
• HA2- H2O ? H2A- OH-
• H2A- H2O ? H3A OH-

17
Polyprotic Acids and Bases

• A solution of H3A
• Treat like a monoprotic weak acid
• H3A ? H H2A-
• H3A ? F(H3A)
• H H2A- x K1 x2 / (H3A - x)
• HA2- value from K2
• A3- value from K3

18
Polyprotic Acids and Bases

• A solution of H2A-
• H2A- ? H HA2-
• H2A- H2O ? H3A OH-
• H2A- ? F(H2A-)
• H ?(K1K2F K1Kw) / (K1 F)
• H3A value from K1
• HA2- value from K2
• A3- value from K3

19
Polyprotic Acids and Bases

• A solution of HA2-
• HA2- ? H A3-
• HA2- H2O ? H2A- OH-
• HA2- ? F(HA2-)
• H ?(K2K3F K2Kw) / (K2 F)
• H2A- value from K2
• A3- value from K3
• H3A value from K1

20
Polyprotic Acids and Bases

• A solution of A3-
• Treat like a monoprotic weak acid
• A3- H2O ? HA- OH-
• A3- ? F(A3-)
• OH- HA2- x Kb1 x2 / (A3- -
  x)
• H2A- value from Kb2
• H3A value from Kb3
• H Kw / OH-

21
Polyprotic Acids and Bases

• Find the pH of 0.10 M H3His2, 0.10 M H2His,
  0.10 M HHis, and 0.10 M His-, where His stands
  for the amino acid histidine.

22
Principle Species in Solution?

• How do you identify the primary species in
  solution?
• Evaluate the pKs of the system.
• If the pH lt pK1, then the most acidic species is
  the predominant species
• If the pH gt pKb1, then the species with the least
  number of protons is predominant
• If the pH resides between two pK values then the
  intermediate that lies within that region will be
  predominant

23
Principle Species in Solution?

• What is the principle species of benzoic acid at
  pH 8?
• What is the predominant form of ammonia in a
  solution of pH 7.0? Approximate what fraction is
  in this form

24
Principle Species in Solution?

• What is the principle species of oxalic acid in
  solution at a pH 4.00?
• What is the principle form of arginine at pH
  10.0? Approximately what fraction is in this
  form? What is the second most abundant form at
  this pH?

25
Principle Species in Solution?

• In the pH range 1.82 - 8.99, H2Arg is the
  principal form of arginine. Which is the second
  most prominent species at pH 6.O? at pH 5.0?