# Buffer Solutions

A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small or moderate amount of strong acid or base is added to it and thus it is used to prevent changes in the pH of a solution. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications.

## Principles of buffering

Buffer solutions achieve their resistance to pH change because of the presence of an equilibrium between the acid HA and its conjugate base A$^-$:
HA ⇌ H$^+$ + A$^-$
When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, the equilibrium is shifted to the left, in accordance with Le Chatelier's principle. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added. Similarly, if strong alkali is added to the mixture the hydrogen ion concentration decreases by less than the amount expected for the quantity of alkali added. The effect is illustrated by the simulated titration of a weak acid with pK$_a$ = 4.7. The relative concentration of undissociated acid is shown in blue and of its conjugate base in red. The pH changes relatively slowly in the buffer region, pH = pK$_a$ ± 1, centered at pH = 4.7 where [HA] = [A$^-$]. The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction
OH$^-$ + HA → H$_2$O + A$^-$
and only a little is consumed in the neutralization reaction which results in an increase in pH.
OH$^-$ + H$^+$ → H$_2$O
Once the acid is more than 95% deprotonated the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.

## Estimating the pH

The Henderson–Hasselbalch equation describes the derivation of pH as a measure of acidity in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions.
The equation is given by:
* ${\mathit {pH}}={\mathit {pK}}_{a}+{\log }_{10}\left({\frac {\left\lbrack {\mathit {Base}}\right\rbrack }{\left\lbrack {\mathit {Acid}}\right\rbrack }}\right)$
There are some significant approximations implicit in the Henderson–Hasselbalch equation. The most significant is the assumption that the concentration of the acid and its conjugate base at equilibrium will remain the same as the formal concentration. This neglects the dissociation of the acid and the binding of H$^+$ to the base. The dissociation of water and relative water concentration itself is neglected as well. These approximations will fail when dealing with relatively strong acids or bases (pKa more than a couple units away from 7), dilute or very concentrated solutions (less than 1 mM or greater than 1M), or heavily skewed acid/base ratios (more than 100 to 1). In high buffer dilutions, where the concentration of protons arising from water become equally or more prevalent than the buffer species themselves (at pH 7, this means buffer component concentrations of <10$^{−5}$ M formally, but practically much higher), the pK$_a$ of the 'buffer' system will tend towards neutrality.

## Common buffer solutions

* Phosphate buffered saline (PBS) is a buffer solution commonly used in biological research. It is a water-based salt solution containing sodium phosphate, sodium chloride and, in some formulations, potassium chloride and potassium phosphate. The osmolarity and ion concentrations of the solutions match those of the human body (isotonic). PBS has many uses because it is isotonic and non-toxic to most cells. These uses include substance dilution and cell container rinsing. PBS with EDTA is also used to disengage attached and clumped cells. Divalent metals such as zinc, however, cannot be added as this will result in precipitation. For these types of applications, Good's buffers are recommended.
* Tris, also known as THAM (the shorter names being abbreviations of tris(hydroxymethyl)aminomethane), is an organic compound with the formula (HOCH$_2$)$_3$CNH$_2$. Tris is extensively used in biochemistry and molecular biology. In biochemistry, Tris is widely used as a component of buffer solutions, such as in TAE and TBE buffer, especially for solutions of nucleic acids. It contains a primary amine and thus undergoes the reactions associated with typical amines, e.g. condensations with aldehydes. Tris has a pK$_a$ of 8.07 at 25 °C, which implies that the buffer has an effective pH range between 7.07 and 9.07. Tris inhibits a number of enzymes, and therefore it should be used with care when studying proteins.