Editing Acid dissociation constant (section)

== Bases and basicity ==
The equilibrium constant ''K''<sub>b</sub> for a base is usually defined as the ''association'' constant for protonation of the base, B, to form the conjugate acid, {{chem2|HB+}}.
: <chem>B + H2O <=> HB+ + OH-</chem>

Using similar reasoning to that used before
: <math alt="The base association constant K b equals the concentration of the protonated form H B +, times the concentration of the hydroxyl anion O H minus, all divided by the concentration of the base B. The base power of disassociation constant p K b is defined in terms of the base association constant K b" >
\begin{align}
K_\text{b} &= \mathrm{\frac{[HB^+] [OH^-]}{[B]}} \\
\mathrm{p}K_\text{b} &= - \log_{10}\left(K_\text{b}\right)
\end{align}</math>

''K''<sub>b</sub> is related to ''K''<sub>a</sub> for the conjugate acid. In water, the concentration of the [[hydroxide]] ion, {{chem2|[OH-]}}, is related to the concentration of the hydrogen ion by {{chem2|1=''K''_{w} = [H+][OH-]}}, therefore
: <math alt="The concentration of the hydroxyl anion O H minus equals the ionization constant of water K w divided by the concentration of H +, by the definition of K w." >
\mathrm{[OH^-]} = \frac{K_\mathrm{w}}{\mathrm{[H^+]}}
</math>

Substitution of the expression for {{chem2|[OH-]}} into the expression for ''K''<sub>b</sub> gives
: <math alt="K b can be written as a ratio of four terms. The numerator holds the concentration of the protonated base H B + times the ionization constant of water K w. The denominator holds the concentration of the base B times that of H +. Using the definition for K A, K b equals K w divided by K A." >
 K_\text{b} = \frac{[\mathrm{HB^+}]K_\text{w}}{\mathrm{[B] [H^+]}} = \frac{K_\text{w}}{K_\text{a}}
</math>

When ''K''<sub>a</sub>, ''K''<sub>b</sub> and ''K''<sub>w</sub> are determined under the same conditions of temperature and ionic strength, it follows, taking [[cologarithm]]s, that p''K''<sub>b</sub>&nbsp;=&nbsp;p''K''<sub>w</sub>&nbsp;−&nbsp;p''K''<sub>a</sub>. In aqueous solutions at 25&nbsp;°C, p''K''<sub>w</sub> is 13.9965,<ref name=crc>{{cite book
| title = CRC Handbook of Chemistry and Physics, Student Edition
| last = Lide
| first = D.R.
| year = 2004
| publisher = CRC Press
| edition = 84th
| isbn = 0-8493-0597-7
}} Section D–152</ref> so
:<math>\mathrm{p}K_\text{b} \approx 14 - \mathrm{p}K_\text{a}</math>

with sufficient [[accuracy]] for most practical purposes. In effect there is no need to define p''K''<sub>b</sub> separately from p''K''<sub>a</sub>,<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=212 |edition=9th}}</ref> but it is done here as often only p''K''<sub>b</sub> values can be found in the older literature.

For an hydrolyzed metal ion, ''K''<sub>b</sub> can also be defined as a stepwise ''dissociation'' constant
: <math chem>\mathrm{M}_p(\ce{OH})_q \leftrightharpoons \mathrm{M}_p(\ce{OH})^{+}_{q-1} + \ce{OH-}</math>
: <math chem>K_\mathrm{b} = \frac{[\mathrm{M}_p(\ce{OH})^{+}_{q-1}] [\ce{OH-}]}{[\mathrm{M}_p(\ce{OH})_q]}</math>

This is the reciprocal of an [[stability constants of complexes|association constant]] for formation of the complex.

=== Basicity expressed as dissociation constant of conjugate acid ===
Because the relationship p''K''<sub>b</sub>&nbsp;=&nbsp;p''K''<sub>w</sub>&nbsp;−&nbsp;p''K''<sub>a</sub> holds only in aqueous solutions (though analogous relationships apply for other amphoteric solvents), subdisciplines of chemistry like [[organic chemistry]] that usually deal with nonaqueous solutions generally do not use p''K''<sub>b</sub> as a measure of basicity. Instead, the p''K''<sub>a</sub> of the conjugate acid, denoted by p''K''<sub>aH</sub>, is quoted when basicity needs to be quantified. For base B and its conjugate acid BH<sup>+</sup> in equilibrium, this is defined as
: <math chem>\mathrm{p}K_\mathrm{aH}(\mathrm{B})=\mathrm{p}K_\mathrm{a}(\ce{BH+})=-\log_{10}\Big(\frac{[\ce{B}][\ce{H+}]}{[\ce{BH+}]}\Big)</math>

A higher value for p''K''<sub>aH</sub> corresponds to a stronger base. For example, the values {{chem2|1=p''K''_{aH} (C5H5N) = 5.25}} and {{chem2|1=p''K''_{aH} ((CH3CH2)3N) = 10.75}} indicate that {{chem2|(CH3CH2)3N}} (triethylamine) is a stronger base than {{chem2|C5H5N}} (pyridine).