1. Maths and Chemistry for Biologists

2. Chemistry 3 Acids, 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  NH4+Cl-
Here hydrochloric acid is reacting with ammonia to produce ammonium chloride

4. When an acid is dissolved in water the water acts as a base
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. When a base is dissolved in water the water acts as an acid
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. Ka is called the acid dissociation constant
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 x 10-3 M x 10-8 M x 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 don’t!

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 = [H+][OH-] M2 and pKw = -log10 Kw
At 25 oC, Kw = M2 and pKw = 14

23. The pH of neutral water In neutral water [H+] = [OH-]
Since [H+][OH-] = 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 [H+][OH-] = M2 or
So [H+] = /0.1 = and pH = 13

25. Relationship between pKa and pKb
For a base
For its conjugate acid So
Hence Ka.Kb = [H+][OH-] = 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
[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 = M
pH = -log = 11