Maths and Chemistry for Biologists

1
Maths and Chemistry for Biologists
2
Chemistry 3Acids, Bases and pH

• This section of the course covers
• the nature of acids and bases
• how their strengths are defined
• the hydrogen ion concentrations of solutions of
  acids and bases
• the pH scale

3
What are acids and bases?

• Acids are molecules that can donate protons to
  other substances. The substances that accept the
  proton are called bases.
• If we represent the acid by HA and the base by B
  then the reaction is
• HA B ? A- BH
• The product of this reaction is a salt. For
  example
• HCl NH3 ? NH4Cl-
• Here hydrochloric acid is reacting with ammonia
  to produce ammonium chloride

4
Acids in water

• When an acid is dissolved in water the water acts
  as a base
• HA H2O ? A-
  H3O
• acid base conjugate base
  conjugate acid
• The ion A- is called the conjugate base of the
  acid because it is capable of reacting with some
  other acid to go back to HA
• H3O, which is called the hydroxonium ion, is
  the conjugate acid of water because it can donate
  a proton to some other base and go back to H2O

5
Bases in water

• When a base is dissolved in water the water acts
  as an acid
• B H2O ? BH
  OH-
• base acid conjugate acid conjugate
  base
• The reasons why BH is called the conjugate acid
  of B and OH- is called the conjugate base of H2O
  are just the same as in the previous slide
• OH- is called the hydroxide ion and occurs in
  substances such as NaOH which react with acids to
  form salts plus water
• NaOH HCl ? NaCl H2O

6
Important facts

• Water acts as an acid or a base depending on what
  is dissolved in it
• An acid/base reaction is always of the form
• Acid Base ? Conjugate base Conjugate
  acid
• of the acid
  of the base

7
Acids in biology

• These are of two main types -
• Carboxylic acids where the
• -O-H is the acidic group. R means
• any other chemical group.
• (NB alcohols, R-OH, are not acidic)
• Phosphates. Here one or both
• of the Rs can be H so there can be
• two or even three acid groups

8
Bases in biology

• One main type amines
• These can be primary (one R group), secondary
  (two R groups) or tertiary (three R groups)
• (NB amides are not basic)

9
Amino acids

• A very important group
• of biomolecules are the
• amino acids. They have both a carboxylic acid
  and an amine group. So they are both acids and
  bases. The structure shown is glycine. In water
  the molecule is ionised as shown in the lower
  structure.

10
Strengths of acids
Measured by the extent to which they dissociate
in water that is, for the process below (now
shown as an equilibrium), what fraction of HA
dissociates to A- HA H2O
A- H3O
For strong acids such as HCl, H2SO4 and HNO3 the
process is essentially complete So in a 0.1 M
solution of HCl H3O 0.1 M (note that the
indicate the concentration of H30)
11
Strengths of weak acids
Weak acids dissociate only partially. For the
process HA H2O A-
H3O we can write an equilibrium expression
where K is the equilibrium constant and the
concentrations are those at equilibrium (for more
details about equilibria see section Chem
6) contd
12
We can simplify this by noting that the
concentration of water is very high (55.6 M) and
effectively constant so the it can be included in
K to give Ka (Ka 55.6 x K). In addition it
is usual to write H as a shorthand for H3O so
the equation becomes
Ka is called the acid dissociation
constant (1,000 g of H2O is 1000/18 55.6 mol)
13
Meaning of Ka
The bigger is Ka then the stronger is the acid
that is, the more H there will be in the
solution What sort of values does Ka have? For
CH3COOH, Ka 1.74 x 10-5 M For HCOOH, Ka 1.78
x 10-4 M So formic acid is about 10 x stronger
than acetic acid These numbers are inconvenient
and there is a better way of doing it
14
pKa
We DEFINE a quantity called pKa as pKa -log10
Ka Then for acetic acid pKa 4.76 and for
formic acid pKa 3.75 This gives us a scale of
acid strength where the numbers are small and
positive and where the value changes by 1 as the
acid strength changes 10x The SMALLER the pKa the
STRONGER the acid
15
One for you to do
Phosphoric acid, H3PO4, has three dissociable
hydrogens with the Ka values shown. Calculate
the pKa values H3PO4 ? H2PO4- ?
HPO42- ? PO43- Ka 7.08 x 10-3 M 6.31
x 10-8 M 4.68 x 10-13 M
16
Answer
pKa1 2.15, pKa2 7.20, pKa3
12.33 Note that the species are progressively
weaker acids. HPO42- is 1010 x weaker than is
H3PO4. In fact PO43- is quite a strong base
17
What about bases?
We could write an equation B H20
BH OH- and then an equilibrium
expression
or
and then define pKb -log10 Kb - but we usually
dont!
18
The pKa of the conjugate acid
Instead we talk about the pKa of the conjugate
acid. That is, we consider the process BH
H2O B H3O
from which
e.g. for ammonia (NH3) we quote the pKa of the
conjugate acid (NH4, pKa 9.2) as a measure of
base strength
19
The hydrogen ion concentration
The hydrogen ion concentration (or more properly
H3O) is of crucial importance in biology For a
strong acid it is equal to the concentration 0.1
M HCl, H 0.1 M, 0.1 M H2SO4, H 0.2
M For weak acids it depends on both the
concentration and the pKa 0.1 M acetic acid, H
1.32 x 10-3 M or 1.32 mM
20
The pH
Again, these numbers are not convenient so we
DEFINE the quantity pH -log10 H For H
1.32 x 10-3 M, pH 2.88 NB the HIGER the H
the LOWER is the pH H 10-4 M, pH 4, H
10-3 M, pH 3
21
Calculation of H for weak acids
Suppose we make a 0.1 M solution of acetic acid
and that some of it dissociates to give x M of
H CH3COOH
CH3COO- H At equilibrium (0.1 x) M
x M x M
We know that Ka 1.74 x 10-5 M so we can solve
for x
22
Water is both an acid and a base
Water undergoes self-dissociation 2 H2O
H3O OH- Or, in shorthand, H2O
H OH- The ionic product of water Kw is
DEFINED as Kw HOH- M2 and pKw
-log10 Kw At 25 oC, Kw 10-14 M2 and pKw 14
23
The pH of neutral water
In neutral water H OH- Since HOH-
10-14 M2 then H 10-7 M so the pH 7 So a
solution with a pH less than 7 is acidic and a
solution with a pH greater than 7 is basic
24
pH of solutions of strong bases
We can calculate these using the value of Kw For
example in 0.1 M NaOH, OH- 0.1 M But
HOH- 10-14 M2 or So H
10-14/0.1 10-13 and pH 13
25
Relationship between pKa and pKb
For a base
For its conjugate acid
So
Hence Ka.Kb HOH- Kw or pKa pKb pKw
26
Ones for you to do
What is the pH of a solution with H of a) 5
mM, b) 50 mM? What is the H of a solution of
pH 6? What is the pH of a 1mM solution of NaOH?
27
Answers
5 mM is 5 x 10-3 M so pH -log (5 x 10-3)
2.30 50 mM is 5 x 10-2 M so pH -log (5 x 10-2)
1.30 H antilog (-pH) so if pH 6.0,
H antilog -6 10-6 M or 1 ?M OH-
10-3 M so H 10-14/10-3 M 10-11 M pH -log
10-11 11