154 Chapter Five

Box 5.3 Worked examples of pH buffering

The principle of pH buffering can be

illustrated by considering the simple case of

acetic acid, CH 3 COOH (abbreviated here to

HA) and sodium acetate, CH 3 COONa

(abbreviated here to NaA). Acetic acid

partially dissociates in water (H 2 O) while the

sodium salt completely dissociates.

eqn. 1

eqn. 2

and

eqn. 3

Rearranging gives:

eqn. 4

For a 0.1 molar (M) solution of HA and NaA

(for simplicity we will assume that activity (a)

and concentration (c) are the same) and

assuming very little HA dissociates, then:

eqn. 5

We know that pH=-log 10 aH+(see Box 3.5),

so in our example:

eqn. 6

To illustrate the principle of buffering,

consider what happens when 0.005 moles of

NaOH (sodium hydroxide, a strong base) are

added to 1 litre of 0.1MHA and NaA. The

added base reacts with the hydrogen

ions (H+), causing an amount of the HA

equivalent to the added NaOH to dissociate

(eqn. 1); the HA concentration decreases and

the A-concentration increases by this

amount.

eqn. 7

Now pH becomes:

eqn. 8

The pH is barely altered because the excess of

undissociated HA dissociates to neutralize the

pH=-log 10 161 10. ¥ -^5 = 479.

aH+-=¥( -+ ) - -mol l

( )

10475. 01 000501 0005....=¥161 10.^51

pH=-log 1010 -^475. =4 75.

aH+-=¥= 10 01 - mol l-

01

4 75... 10 4 75 1

.

aH+-= 10 475.aaHAA-

KHA==aaHAaHA mol l

+-. --.

10475 1

NaAÆ+Na+-A

HAÆ+H+-A

added OH-. Buffering will continue if an

excess of HA is available. If acid is added to

the solution, H+will react with the excess of

A-to increase the HA and decrease the A-

concentration by an amount equivalent to

the added H+, resulting in a similar buffering

effect. The HA and NaA solution is an

effective buffer because it can react to

neutralize either added acid or base.

By contrast, if 0.005 moles of NaOH are

added to 1 litre of water, the pH will rise to

11.7, as illustrated below.

eqn. 9

Thus:

eqn. 10

and so:

eqn. 11

So, if 0.005 moles of OH-are added to 1 litre

of water (again assuming that activity and

concentration are the same), then:

eqn. 12

In natural waters the buffering system

involves the weak acid, carbonic acid (H 2 CO 3 ),

and the associated anions, bicarbonate

(HCO 3 - ) and carbonate (CO 32 - ). At pH 4–9,

HCO 3 - is the major anion. In the following

example we ignore CO 32 - (and again assume

that activity and concentration are the same).

First, we can rewrite equation 4 for the HCO 3 -

system:

eqn. 13

and define the terms used (eqns 14–17). At

25°C the equilibrium constant for equation 1

in Box 5.2 is defined as:

eqn. 14

(see also Box 3.7), whilst the relationship

between partial pressure of carbon dioxide

(pCO 2 ) and H 2 CO 3 is:

eqn. 15

Thus:

CO 22 ()gl+HO()ªHCO 23 ( )aq

KHCO HCO H

mol l

3 3 7

64 1

410

10

• 
  

  ==¥

  
  

-+ -

--

aa.

.

a a

a

H HCO

HCO HCO

+

=¥K - 3 -

23

3

pH=-log 10 ( 10 -^14 0 005. )=11 7.

pH=-log 10 aaH+-=-log 10 (Kw OH)

aKaHOH+-= w

Ka aw=◊=OH H mol l

( )

-+ 10 - 14 2 - 2

see Box 4.1

(continued)