Editing Weak base

{{Short description|Tiffany Sullivan Airman 2}}
{{Acids and bases}}
A '''weak base''' is a [[base (chemistry)|base]] that, upon dissolution in water, does not [[Dissociation_(chemistry)|dissociate]] completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base.

==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.-->

==Percentage protonated==
As seen above, the strength of a base depends primarily on pH. To help describe the strengths of weak bases, it is helpful to know the percentage protonated-the percentage of base molecules that have been protonated. A lower percentage will correspond with a lower pH because both numbers result from the amount of protonation. A weak base is less protonated, leading to a lower pH and a lower percentage protonated.<ref name="Maskill1985">{{cite book|author=Howard Maskill|title=The physical basis of organic chemistry|url=https://books.google.com/books?id=4AXwAAAAMAAJ|year=1985|publisher=Oxford University Press, Incorporated|isbn=978-0-19-855192-8}}</ref>

The typical proton transfer equilibrium appears as such:

:<math>B(aq) + H_2O(l) \leftrightarrow HB^+(aq) + OH^-(aq)</math>

B represents the base.

:<math>Percentage\ protonated = {molarity\ of\ HB^+ \over\ initial\ molarity\ of\ B} \times 100\% = {[{HB}^+]\over [B]_{initial}} {\times 100\%}</math>

In this formula, [B]<sub>initial</sub> is the initial molar concentration of the base, assuming that no protonation has occurred.

==A typical pH problem==
Calculate the pH and percentage protonation of a .20 M aqueous solution of pyridine, C<sub>5</sub>H<sub>5</sub>N. The K<sub>b</sub> for C<sub>5</sub>H<sub>5</sub>N is 1.8 x 10<sup>−9</sup>.<ref>{{cite web|url=http://www.kentchemistry.com/links/AcidsBases/pHWeakBases.htm|title=Calculations of weak bases|publisher=Mr Kent's Chemistry Page|access-date=2018-03-23}}</ref>

First, write the proton transfer equilibrium:

:<math>\mathrm{H_2O(l) + C_5H_5N(aq) \leftrightarrow C_5H_5NH^+ (aq) + OH^- (aq)}</math>

:<math>K_b=\mathrm{[C_5H_5NH^+] [OH^-]\over [C_5H_5N]}</math>

The equilibrium table, with all concentrations in moles per liter, is

{| width:75%; height:200px border="1"
|+
|-style="height:40px"
! !! C<sub>5</sub>H<sub>5</sub>N !! C<sub>5</sub>H<sub>6</sub>N<sup>+</sup> !! OH<sup>−</sup>
|-
! initial normality
| .20 || 0 || 0
|-
! change in normality
| -x || +x || +x
|-
! equilibrium normality
| .20 -x || x || x
|}

{| width:75%; height:200px border="1"
|-
| Substitute the equilibrium molarities into the basicity constant
| <math>K_b=\mathrm {1.8 \times 10^{-9}} = {x \times x \over .20-x}</math>
|-
| We can assume that x is so small that it will be meaningless by the time we use significant figures.
| <math>\mathrm {1.8 \times 10^{-9}} \approx {x^2 \over .20}</math>
|-
| Solve for x.
| <math>\mathrm x \approx \sqrt{.20 \times (1.8 \times 10^{-9})} = 1.9 \times 10^{-5}</math>
|-
| Check the assumption that x << .20
| <math>\mathrm 1.9 \times 10^{-5} \ll .20</math>; so the approximation is valid
|-
| Find pOH from pOH = -log [OH<sup>−</sup>] with [OH<sup>−</sup>]=x
| <math>\mathrm pOH \approx -log(1.9 \times 10^{-5}) = 4.7 </math>
|-
| From pH = pK<sub>w</sub> - pOH,
| <math>\mathrm pH \approx 14.00 - 4.7 = 9.3</math>
|-
| From the equation for percentage protonated with [HB<sup>+</sup>] = x and [B]<sub>initial</sub> = .20,
| <math>\mathrm percentage \ protonated = {1.9 \times 10^{-5} \over .20} \times 100\% = .0095\% </math>
|}

This means .0095% of the pyridine is in the protonated form of C<sub>5</sub>H<sub>5</sub>NH<sup>+</sup>.

==Examples==
* [[Alanine]]
* [[Ammonia]], NH<sub>3</sub>
* [[Methylamine]], CH<sub>3</sub>NH<sub>2</sub>
* [[Ammonium hydroxide]], NH<sub>4</sub>OH

==Simple Facts==
*An example of a weak base is ammonia. It does not contain hydroxide ions, but it reacts with water to produce ammonium ions and hydroxide ions.<ref>Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.</ref>
*The position of equilibrium varies from base to base when a weak base reacts with water. The further to the left it is, the weaker the base.<ref>Clark, Jim. "Strong and Weak Bases."N.p.,2002. Web.</ref>
*When there is a hydrogen ion gradient between two sides of the biological membrane, the concentration of some weak bases are focused on only one side of the membrane.<ref name="ac.els-cdn.com">{{Cite journal |doi = 10.1016/0002-9343(58)90376-0|title = Non-ionic diffusion and the excretion of weak acids and bases|journal = The American Journal of Medicine|volume = 24|issue = 5|pages = 709–729|year = 1958|last1 = Milne|first1 = M.D.|last2 = Scribner|first2 = B.H.|last3 = Crawford|first3 = M.A.}}</ref> Weak bases tend to build up in acidic fluids.<ref name="ac.els-cdn.com"/> Acid gastric contains a higher concentration of weak base than plasma.<ref name="ac.els-cdn.com"/> Acid urine, compared to alkaline urine, excretes weak bases at a faster rate.<ref name="ac.els-cdn.com"/>

==See also==
* [[Strong base]]
* [[Weak acid]]

==References==
{{reflist}} 

==External links==
* [http://bouman.chem.georgetown.edu/S02/lect16/lect16.htm Guide to Weak Bases from Georgetown course notes]
* [https://web.archive.org/web/20070926225948/http://www.intute.ac.uk/sciences/reference/plambeck/chem1/p01154.htm Article on Acidity of Solutions of Weak Bases] from Intute


[[Category:Bases (chemistry)]]