Buffers Containing a Base and Conjugate Acid

A base is a substance that decreases the hydrogen ion (H⁺) concentration of a solution. In the more generalized Brønsted-Lowry definition, the hydroxide ion (OH^-) is the base because it is the substance that combines with the proton. Ammonia and some organic nitrogen compounds can combine with protons in solution and act as Brønsted-Lowry bases. These compounds are generally weaker bases than the hydroxide ion because they have less attraction for protons. For example, when ammonia competes with OH^- for protons in an aqueous solution, it is only partially successful. It can combine with only a portion of the H⁺ ions, so it will have a measurable equilibrium constant. Reactions with weak bases result in a relatively low pH compared to strong bases. Bases range from a pH of greater than 7 (7 is neutral like pure water) to 14 (though some bases are greater than 14).

An alkaline buffer can be made from a mixture of a base and its conjugate acid, similar to the way in which weak acids and their conjugate bases can be used to make a buffer.

Ammonia to ammonium ion

Two-dimensional image depicting the association of proton (H⁺) with the weak base ammonia (NH₃) to form its conjugate acid, ammonium ion (NH₄⁺).

Calculating the pH of a Base

The pH of bases is usually calculated using the OH^- concentration to find the pOH first. This is done because the H⁺ concentration is not a part of the reaction, while the OH^- concentration is. The formula for pOH is:

$pOH=-log([O{ H }^{ - }])$

By multiplying a conjugate acid (such as NH₄⁺) and a conjugate base (such as NH₃) the following is given:

${ K }_{ a }\times { K }_{ b }=\frac { [{ H }_{ 3 }{ O }^{ + }][N{ H }_{ 3 }] }{ [N{ H }_{ 4 }^{ + }] } \times \frac { [N{ H }_{ 4 }^{ + }][{ OH }^{ - }] }{ [N{ H }_{ 3 }] }$

${ K }_{ a }\times { K }_{ b }=[{ H }_{ 3 }{ O }^{ + }][{ OH }^{ - }]={ K }_{ w }$

${ log(K }_{ a })+{ log(K }_{ b })=log({ K }_{ w })$

${ pK }_{ a }+{ pK }_{ b }=p{ K }_{ w }=14.00$

The pH can be calculated using the formula:

${ pH={14}-pOH }$

Weak bases exist in chemical equilibrium much in the same way as weak acids do. A base dissociation constant (K_b) indicates the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:

$N{ H }_{ 3 }+{ H_2O}\rightleftharpoons N{ H }_{ 4 }^{ + } +{OH^-}$

${ K }_{ b }=\frac { [N{ H }_{ 4 }^{ + }][{ OH }^{ - }] }{ [N{ H }_{ 3 }] }$

Bases that have a large K_b will ionize more completely, meaning they are stronger bases. NaOH (sodium hydroxide) is a stronger base than (CH₃CH₂)₂NH (diethylamine) which is a stronger base than NH₃ (ammonia). As the bases get weaker, the K_b values get smaller.

Example:

Calculate the pH of a buffer solution consisting of 0.051 M NH₃ and 0.037 M NH₄⁺. The K_b for NH₃ = 1.8 x 10^-5.

$N{ H }_{ 3 }+{ H_2O}\rightleftharpoons N{ H }_{ 4 }^{ + } +{OH^-}$

${ K }_{ b }=\frac { [N{ H }_{ 4 }^{ + }][{ OH }^{ - }] }{ [N{ H }_{ 3 }] }$

Assuming the change (x) is negligible to 0.051 M and 0.037 M solutions:

${ K }_{ b }=\frac { [0.037][x] }{ [0.051] }$

1.8 x 10^-5$=\frac { [0.037][x] }{ [0.051] }$

x = [OH^-] = 2.48 x 10^-5

pOH = 4.61

pH = 14 - 4.61 = 9.39