Editing Buffer solution (section)

==Principles of buffering==
[[File:Buffer titration graph.svg|thumb|250px|right|Figure 1. Simulated [[titration]] of an acidified solution of a weak acid ({{math|1=p''K''<sub>a</sub> = 4.7}}) with alkali]]
Buffer solutions resist  pH change because of a [[chemical equilibrium]] between the weak acid HA and its conjugate base A<sup>−</sup>:
{{block indent|em=1.5|text=HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>}}
When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, hydrogen ions (H<sup>+</sup>) are added, and 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. In Figure 1, the effect is illustrated by the simulated titration of a weak acid with [[Acid dissociation constant|p''K''<sub>a</sub>]]&nbsp;=&nbsp;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&nbsp;=&nbsp;p''K''<sub>a</sub>&nbsp;±&nbsp;1, centered at pH&nbsp;=&nbsp;4.7, where [HA]&nbsp;=&nbsp;[A<sup>−</sup>]. The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction
{{block indent|em=1.5|text=OH<sup>−</sup> + HA → H<sub>2</sub>O + A<sup>−</sup>}}
and only a little is consumed in the neutralization reaction (which is the reaction that results in an increase in pH)
{{block indent|em=1.5|text=OH<sup>−</sup> + H<sup>+</sup> → H<sub>2</sub>O.}}

Once the acid is more than 95% [[deprotonation|deprotonated]], the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.

===Buffer capacity===
Buffer capacity is a quantitative measure of the resistance to change of pH of a solution containing a buffering agent with respect to a change of acid or alkali concentration. It can be defined as follows:<ref name=Skoog/><ref name=Urbansky/>
<math display="block">\beta = \frac{dC_b}{d(\mathrm{pH})},</math>   
where <math>dC_b</math> is an infinitesimal amount of added base, or
<math display="block">\beta = -\frac{dC_a}{d(\mathrm{pH})},</math> 
where <math>dC_a</math> is an infinitesimal amount of added acid. pH is defined as −log<sub>10</sub>[H<sup>+</sup>], and ''d''(pH) is an infinitesimal change in pH. 

With either definition the buffer capacity for a weak acid HA with dissociation constant ''K''<sub>a</sub> can be expressed as<ref>{{cite book |last1=Butler |first1=J. N. |title=Ionic Equilibrium: Solubility and pH calculations |date=1998 |publisher=Wiley |pages=133–136 |isbn= 978-0-471-58526-8}}</ref><ref name=Hulanicki/><ref name=Urbansky>{{cite journal |last1=Urbansky |first1=Edward T. |last2=Schock |first2=Michael R.|title=Understanding, Deriving and Computing Buffer Capacity |journal=Journal of Chemical Education |date=2000 |volume=77 |issue=12 |pages=1640–1644 |doi=10.1021/ed077p1640 |bibcode=2000JChEd..77.1640U }}</ref>
<math chem display="block">\beta = 2.303 \left([\ce{H+}] + \frac{T_\ce{HA} K_a[\ce{H+}]}{(K_a + [\ce{H+}])^2} + \frac{K_\text{w}}{[\ce{H+}]}\right),</math>
where [H<sup>+</sup>] is the concentration of hydrogen ions, and <math>T_\text{HA}</math> is the total concentration of added acid. ''K''<sub>w</sub> is the equilibrium constant for [[self-ionization of water]], equal to 1.0{{e|−14}}. Note that in solution H<sup>+</sup> exists as the [[hydronium]] ion H<sub>3</sub>O<sup>+</sup>, and further [[aquation]] of the hydronium ion has negligible effect on the dissociation equilibrium, except at very high acid concentration. 

[[File:Buffer Capacity 2.png|thumb|250px|Figure 2. Buffer capacity ''β'' for a 0.1&nbsp;M solution of a weak acid with a p''K''<sub>a</sub>&nbsp;=&nbsp;7]]
This equation shows that there are three regions of raised buffer capacity (see figure 2).
* In the central region of the curve (colored green on the plot), the second term is dominant, and <math chem display="block">\beta \approx 2.303 \frac{T_\ce{HA} K_a[\ce{H+}]}{(K_a + [\ce{H+}])^2}.</math> Buffer capacity rises to a local maximum at pH&nbsp;=&nbsp;''pK''<sub>a</sub>. The height of this peak depends on the value of pK<sub>a</sub>. Buffer capacity is negligible when the concentration [HA] of buffering agent is very small and increases with increasing concentration of the buffering agent.<ref name=Urbansky/> Some authors show only this region in graphs of buffer capacity.<ref name=Skoog/>{{pb}} Buffer capacity falls to 33% of the maximum value at pH = p''K''<sub>a</sub> ± 1, to 10% at pH = p''K''<sub>a</sub> ± 1.5 and to 1% at pH = p''K''<sub>a</sub> ± 2. For this reason the most useful range is approximately p''K''<sub>a</sub>&nbsp;±&nbsp;1. When choosing a buffer for use at a specific pH, it should have a p''K''<sub>a</sub> value as close as possible to that pH.<ref name=Skoog>{{cite book |last1=Skoog |first1=Douglas A. |last2=West |first2=Donald M. |last3=Holler |first3=F. James |last4=Crouch |first4=Stanley R. |title=Fundamentals of Analytical Chemistry |date=2014 |publisher=Brooks/Cole |isbn=978-0-495-55828-6 |pages=226 |edition=9th}}</ref> 
* With strongly acidic solutions, pH less than about 2 (coloured red on the plot), the first term in the equation dominates, and buffer capacity rises exponentially with decreasing pH: <math display="block">\beta \approx 10^{-\mathrm{pH}}.</math> This results from the fact that the second and third terms become negligible at very low pH. This term is independent of the presence or absence of a buffering agent.
* With strongly alkaline solutions, pH more than about 12 (coloured blue on the plot), the third term in the equation dominates, and buffer capacity rises exponentially with increasing pH: <math display="block">\beta \approx 10^{\mathrm{pH} - \mathrm{p}K_\text{w}}.</math> This results from the fact that the first and second terms become negligible at very high pH. This term is also independent of the presence or absence of a buffering agent.