Overview of the Saturation Fraction, Ya

Overview of Buffers and the Saturation Fraction, Ya
Go back

Buffers effectively "control" the pH -- or free H⁺ ion concentration, [H⁺] -- of a solution by adsorbing H⁺ ions when 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 total capacity. 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 (buffer capacity) 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.

©	Duane W. Sears Revised: October 07, 2010