pH pKa2 pH pKa1

1
Acids and Bases in aqueous solution.
pKa2 2.33
pKa1 9.45
pH pKa2 pH pKa1
2
The properties of water
Water is held together by H-bonding, which gives
it its surprisingly high B.Pt. and M.Pt. for such
a small molecule. Note that the heavier H2S
molecule is a gas at room temperature. Water is
also weakly ionized into H and OH- ions, as
discussed next.
2.75 Å
H-bonds
3
The self-ionization of water

• Water ionizes weakly to produce OH- and H ions,
  where Kw is the ionization constant of water,
  according to
• H2O(l) ? H (aq) OH-(aq) Kw
  10-14
• This means that the product of the concentration
  (molarity) of H and OH- must always be
  10-14.
• Kw 10-14 H OH- 1
• Thus, for pairs of H and OH- concentrations
  in solution we have
• H 1.0 M, then OH- 10-14/1.0 10-14
  M
• H 0.01 M, then OH- 10-14/0.01 10-12
  M
• H 10-7 M, then OH- 10-14/10-7 10-7
  M
• H 10-12 M, then OH- 10-14/10-12
  10-2 M
• H 10-15 M, then OH- 10-14/10-15 10
  M

4
pH and pOH

• The concentration of H and OH- can be
  expressed as the pH and pOH (p in pH or pOH
  means potency, and means that any constant K
  or concentration with a p in front of it is
  represented as pK -log K , or pH -log H)
• pH - log H pOH - log OH-
• We can show that
• pKw 14.0 pH pOH

5

• Thus, for any solution where the pH is known,
• pH pOH 14.0, or pOH 14 pH.
• H pH pOH OH-
• 10 M -1.0 15.0 10-15 M 1 M
  0.0 14.0 10-14 M 0.01 M 2.0 12.0 10-12
  M 10-5.7 M 5.7 8.3 10-8.3 M 10-7 M 7.0
  7.0 10-7.0 M
• 10-9.3 M 9.3 4.7 10-4.7 M
• 10-12 M 12.0 2.0 10-2 M
• 10-14 M 14.0 0.0 1 M
• 10-15.09 M 15.09 -1.09 12 M

6
Acid dissociation constants (Ka)

• A weak Brønsted acid such as acetic acid
  (CH3COOH) will dissociate to give off protons in
  aqueous solution according to
• CH3COOH (aq) ? CH3COO- (aq) H (aq)
• The extent of such dissociation is controlled by
  the acid dissociation constant, Ka.
• Ka CH3COO- H
• CH3COOH

acetic acid acetate ion
conjugate acid conjugate base
proton
7
The acid dissociation constant of acetic acid

• The value of Ka for acetic acid is 10-4.84, so
  the pKa is 4.84. This gives us the expression
• 10-4.84 CH3COO- H 2
• CH3COOH
• This expression can be used to solve problems
  relating to the ionization of acetic and other
  acids. For example, what is the pH of a 0.1 M
  solution of acetic acid? Equation 2 must be
  obeyed at all times, so we have
• 10-4.84 CH3COO-H/0.1 H2/0.1
• so H (10-4.84 x 0.1)0.5 10-2.92 M, pH
  2.92.

8

• Notice that in solving the above problem,
  ionization of acetic acid produces equal
  concentrations of H and CH3COO- ions. One
  assumes that the amount of ionization is small,
  so that CH3COOH is not corrected for the small
  amount that it decreases, and we assume that
  CH3COOH is still 0.1 M.
• b) What is the pH of a 1 M solution of ammonia
  if the pKa of NH4 is 9.2?
• Note pKa of an acid plus pKb of its conjugate
  base pKw pKa(NH4) pKb(NH3) pKw 14.0.
• pKb NH3 14.0 9.2 4.8, so Kb 10-4.8.
• 10-4.8 NH4 OH- / NH3
• so again we have OH- (10-4.8 x 1)0.5,
  10-2.4.
• If OH- 10-2.4 M, then pOH 2.4, and pH
  14-2.4 11.6

9
The species distribution diagrams of acids and
bases

• We can calculate the percentage of an acid (e.g.
  CH3COOH) or its conjugate base (CH3COO-) that is
  present as the acid or the conjugate base at any
  given pH value if the pKa is known (4.84). Thus,
  for acetic acid at pH 3.7 we have
• 10-4.84 CH3COO- H / CH3COOH
• CH3COO- 10-3.7 / CH3COOH
• CH3COO- / CH3COOH 10-4.84 / 10-3.7
  10-1.14 0.072
• so percent of CH3COO- at pH 3.7
• 100 x (0.072/(10.072)) 7.2 .
• of CH3COOH 100 7.2 92.8 .

10
CH3COOH
CH3COO-
pH50 pKa
11
The relationship between pH50 and the pKa

• The pH at which the concentrations of CH3COOH
  and CH3COO- in solution are equal, i.e. both are
  50, is known as the pH50. On the previous slide
  it was indicated that the pKa of the acid equals
  pH50. This arises simply as follows
• Ka 10-4.84 CH3COO- H
• CH3COOH
• 10-4.84 H
• or pKa pH50
• Thus, we saw that for CH3COOH the crossover
  point for CH3COOH and CH3COO- occurred at pH
  4.84, which is the pKa. Similarly, on the next
  slide, we see that the crossover point for NH4
  and NH3 occurs at pH 9.22, which is the pKa of
  NH4.

CH3COO- CH3COOH at pH50, so these cancel
12
The species distribution diagram of
ammonia/ammonium ion
NH4
NH3
pH50 pKa
13
Multiprotic acids and bases

• Many acids have more than one ionizable proton,
  and many bases have more than one proton acceptor
  site. A familiar example of this is triprotic
  phosphoric acid
• H3PO4 ? H2PO4- H pKa3 2.15
• H2PO4- ? HPO42- H pKa2 7.20
• HPO42- ? PO43- H pKa1 12.38
• It can be shown that for a monoprotic acid, when
  the concentration of the acid and its conjugate
  base are equal (both 50), then pKa pH. For
  polyprotic acids the average extent of
  protonation at any pH is given by the function
  nbar. For the phosphate ion
• nbar average number of protons bound per
  phosphate

14
The relationship between nbar, pH, and the pKa
values of multiprotic acids

• On a previous slide we showed that for a
  monoprotic acid such as CH3COOH, the pKa pH50.
  At pH50 for a monoprotic acid, in fact, nbar
  0.5. This is the point at which half of the
  acetate ions have a proton on them, while half do
  not. For polyprotic acids, similar considerations
  apply. At nbar 0.5 for phosphate, we have
  HPO42- PO43-, and the pH at nbar 0.5
  pKa1. In fact the half-values of nbar give us the
  pKa values from the corresponding pH values
• nbar pH pKan
• 0.5 pH pKa1
• 1.5 pH pKa2
• 2.5 pH pKa3 etc.
• Thus from a curve of nbar versus pH for
  phosphoric acid, we can estimate the pKa values
  from the pH values corresponding to nbar
• 0.5, 1.5, and 2.5

15
Plot of nbar versus pH for phosphate
H3PO4
pKa3 2.15
H2PO4-
HPO42-
pKa2 7.20
pKa1 12.38
PO43-
pH
pH pKa3 pH pKa2
pH pKa1
16
Species distribution diagram for phosphoric acid
H3PO4 H2PO4-
HPO42- PO43-
pH
17
pKa2 2.33
pKa1 9.45
pH
pH pKa2 pH pKa1
18
NTA (nitrilo- triacetate)
pKa2 2.52 pKa1 9.46
EDTA (ethylene- diamine tetraacetate)
pKa1 9.52
pKa2 6.13
pKa3 2.69
19
Lewis acids and bases

• You will recall Brønsted acids and bases, where
  a Brønsted acid is a proton donor and a Brønsted
  base is a proton acceptor. A broader definition
  is that of Lewis Acids and Bases, where a Lewis
  Acid is an electron acceptor, and a Lewis Base is
  an electron donor.

BF3, a Lewis Acid
F-, a Lewis Base
Gilbert Newton Lewis (1875-1946)
Lewis Acid accepts electrons from the Lewis Base
to form a complex.