Editing Weak base (section)

==pH, K<sub>b</sub>, and K<sub>w</sub>==
Bases yield solutions in which the hydrogen ion [[Activity (chemistry)|activity]] is lower than it is in pure water, i.e., the solution is said to have a [[pH]] greater than 7.0 at standard conditions, potentially as high as 14 (and even greater than 14 for some bases). The formula for pH is:
:<math>\mbox{pH} = -\log_{10} \left[ \mbox{H}^+ \right]</math>
Bases are [[proton]] acceptors; a base will receive a hydrogen ion from water, H<sub>2</sub>O, and the remaining H<sup>+</sup> [[concentration]] in the solution determines pH. A weak base will have a higher H<sup>+</sup> concentration than a stronger base because it is less completely [[protonation|protonated]] than a stronger base and, therefore, more hydrogen ions remain in its solution. Given its greater H<sup>+</sup> concentration, the formula yields a lower pH value for the weak base. However, pH of bases is usually calculated in terms of the OH<sup>−</sup> concentration. This is done because the H<sup>+</sup> concentration is not a part of the reaction, whereas the OH<sup>−</sup> concentration is. The pOH is defined as:

:<math>\mbox{pOH} = -\log_{10} \left[ \mbox{OH}^- \right]</math>

If we multiply the equilibrium constants of a [[conjugate acid]] (such as NH<sub>4</sub><sup>+</sup>) and a conjugate base (such as NH<sub>3</sub>) we obtain:

:<math> K_a \times K_b = {[H_3O^+] [NH_3]\over[NH_4^+]} \times {[NH_4^+] [OH^-]\over[NH_3]} = [H_3O^+] [OH^-]</math>

As <math>{K_w} = [H_3O^+] [OH^-]</math> is just the [[self-ionization constant]] of water, we have '''''<math>K_a \times K_b = K_w</math>'''''

Taking the logarithm of both sides of the equation yields:

:<math>logK_a + logK_b = logK_w</math>

Finally, multiplying both sides by -1, we obtain:

:<math>pK_a + pK_b = pK_w = 14.00</math>

With pOH obtained from the pOH formula given above, the pH of the base can then be calculated from <math>pH = pK_w - pOH</math>, where pK<sub>w</sub> = 14.00.

A weak base persists in [[chemical equilibrium]] in much the same way as a [[weak acid]] does, with a [[base dissociation constant]] ('''K<sub>b</sub>''') indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:

:<math>\mathrm{K_b={[NH_4^+] [OH^-]\over[NH_3]}}</math>

A base that has a large K<sub>b</sub> will ionize more completely and is thus a stronger base. As shown above, the pH of the solution, which depends on the H<sup>+</sup> concentration, increases with increasing OH<sup>−</sup> concentration; a greater OH<sup>−</sup> concentration means a smaller H<sup>+</sup> concentration, therefore a greater pH. Strong bases have smaller H<sup>+</sup> concentrations because they are more fully protonated, leaving fewer hydrogen ions in the solution. A ''smaller'' H<sup>+</sup> concentration means a ''greater'' OH<sup>−</sup> concentration and, therefore, a greater K<sub>b</sub> and a greater pH.

NaOH (s) (sodium hydroxide) is a stronger base than (CH<sub>3</sub>CH<sub>2</sub>)<sub>2</sub>NH (l) ([[diethylamine]]) which is a stronger base than NH<sub>3</sub> (g) (ammonia). As the bases get weaker, the smaller the K<sub>b</sub> values become.<ref>{{cite web|url=http://www.chemguide.co.uk/physical/acidbaseeqia/bases.html|title=Explanation of strong and weak bases]|publisher=ChemGuide|access-date=2018-03-23}}</ref>
<!-- The pie-chart representation is as follows:
* purple areas represent the fraction of OH- ions formed
* red areas represent the cation remaining after ionization
* yellow areas represent dissolved but non-ionized molecules.-->