Buffers effectively "control" the pH
-- or free H+
ion concentration, [H+] -- of a solution by adsorbing H+
ionswhen acid is added to the solution, or releasing weakly bound H+
ions to neutralize hydroxyl ions (OH-) when base
is added to the solution.
For weak dissociation/association reactions, the
concentrations of products and reactants at equilibrium are all related by a fixed constant called an equilibrium constant
(K).
Buffers are like sponges,
soaking up or releasing protons as illustrated below.
Depending on its size, a sponge can soak up only so much
water, . Likewise, a buffer can only soak
up only so many H+
ions depending its molar concentration. A 1 M solution of buffer
can only bind 1 mole per liter of free H+
ion; a 0.1 M solution of buffer can only bind 0.1 mole per liter of free H+
ion.
In order to quantitate how much H+
ion is actually bound to a buffer at equilibrium it is very useful to use a parameter
called the saturation fraction (Ya).
By definition, Ya equals the fraction of buffer in solution that has bound ionizable
H+
ion at equilibrium; this fraction ranges
in value from 0 (0%) to 1.0 (100%).
The concept behind the saturation fraction
may be easier to understand by making an analogy with the properties of a
sponge. When the sponge holds all the water it can, it is
"100% saturated" (i.e., Ya = 1.0).
Conversely, if the
sponge is squeezed as hard as possible, all the water is extracted, leaving
the sponge dry, or 0% saturated (i.e., Ya = 0.0); in
this state the sponge is 100% "desaturated."
"Squeeze" the sponge above
and see what happens. Now, click the "absorb" arrow and gradually fill the sponge
with water; note the
incremental change in the saturation fraction with each click.
Alternatively, click the "extract" arrow and
note the incremental decrease in the saturation fraction.
By this analogy buffers work in the
same fashion. If you have a 2 molar solution of acetic acid, it can
only absorb a 2 molar concentration of free H+
ion to achieve full saturation (Ya = 1.0) given that 1 acetate
molecule can only bind 1 H+
ion.
Now consider what happens if hydroxyl
ion is added to fully saturated acetic acid, so that the OH-
ion concentration is initially 2 molar (e.g., by adding enough NaOH to
make the Na+
ion concentration equal to 2 molar). In this situation, all of the ionizable
acetic acid H+
ions will be stripped off in order to neutralize OH-
ions until the buffer becomes fully desaturated (i.e., Ya = 0).
Note:
The saturation fraction
is a fraction and, therefore, it is only a relative (fractional)
measure of the totalcapacity. For example, when the
saturation fraction of a sponge equals 25%, only a quarter of the
sponge's total capacity to absorb water has been achieved, independent of the sponge's size.
Likewise, when the saturation fraction of a buffer
equals 10% only a tenth of the buffer's total capacity to absorb H+
ions has been achieved, independent of the
concentration of buffer in solution.
To find out exactly how much water a
sponge holds, or how much H+
ion is bound to a buffer it is necessary to know the capacity of the
sponge or buffer. For a sponge, you
need to know the maximum amount of water (capacity) that the
sponge can soak up when fully saturated. Likewise, with a buffer you
need to know how many moles of buffer (buffercapacity)
are in the
solution.
Examples: For
a 1 M acetic acid solution you need to know the volume of the solution
in order to determine
buffer capacity. If the solution volume equals 0.5
liters, the buffer capacity equals 0.5 moles (= 1 mole/L x 0.5 L)
If Ya = 1.0, the buffer will have 0.5 moles (= 0.5 moles x 1.0) of ionizable
H+
ion bound to it. If Ya = 0.5, the buffer capacity is only at 50% capacity
with 0.25 moles (= 0.5 moles x 0.5) "saturated" and 0.25 moles
"desaturated.".
Learn
more about buffers and quantitation of their properties using the
saturation fraction with the following web pages:
.
Test your understanding of these concepts with a Practice
Quiz.