Weak base

{{Short description|Base that does not dissociate completely in water}} {{Acids and bases}} A '''weak base''' is a base that, upon dissolution in water, does not 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_b, and K_w== Bases yield solutions in which the hydrogen ion 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, H₂O, and the remaining H⁺ concentration in the solution determines pH. A weak base will have a higher H⁺ concentration than a stronger base because it is less completely protonated than a stronger base and, therefore, more hydrogen ions remain in its solution. Given its greater H⁺ concentration, the formula yields a lower pH value for the weak base. However, pH of bases is usually calculated in terms of the OH⁻ concentration. This is done because the H⁺ concentration is not a part of the reaction, whereas the OH⁻ 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 NH₄⁺) and a conjugate base (such as NH₃) 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_w = 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_b''') 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_b will ionize more completely and is thus a stronger base. As shown above, the pH of the solution, which depends on the H⁺ concentration, increases with increasing OH⁻ concentration; a greater OH⁻ concentration means a smaller H⁺ concentration, therefore a greater pH. Strong bases have smaller H⁺ concentrations because they are more fully protonated, leaving fewer hydrogen ions in the solution. A ''smaller'' H⁺ concentration means a ''greater'' OH⁻ concentration and, therefore, a greater K_b and a greater pH.

NaOH (s) (sodium hydroxide) is a stronger base than (CH₃CH₂)₂NH (l) (diethylamine) which is a stronger base than NH₃ (g) (ammonia). As the bases get weaker, the smaller the K_b 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]_initial 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, C₅H₅N. The K_b for C₅H₅N is 1.8 x 10⁻⁹.<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" ! !! C₅H₅N !! C₅H₆N⁺ !! OH⁻ |- ! initial normality | .20 || 0 || 0 |- ! change in normality | {{math|−''x''}} || {{math|+''x''}} || {{math|+''x''}} |- ! equilibrium normality | {{math|.20 − x}} || {{mvar|x}} || {{mvar|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 {{mvar|x}} is so small that it will be meaningless by the time we use significant figures. | <math> {1.8 \times 10^{-9}} \approx {x^2 \over .20}</math> |- | Solve for {{mvar|x}}. | <math> x \approx \sqrt{.20 \times (1.8 \times 10^{-9})} = 1.9 \times 10^{-5}</math> |- | Check the assumption that {{math|''x'' ≪ .20}} | <math>\mathrm 1.9 \times 10^{-5} \ll .20</math>; so the approximation is valid |- | Find pOH from pOH = −log [OH⁻] with [OH⁻] = {{mvar|x}} | <math>\mathrm{pOH} \approx -\log(1.9 \times 10^{-5}) = 4.7 </math> |- | From pH = pK_w − pOH, | <math>\mathrm{pH} \approx 14.00 - 4.7 = 9.3</math> |- | From the equation for percentage protonated with [HB⁺] = x and [B]_initial = .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 C₅H₅NH⁺.

==Examples== * Alanine * Ammonia, NH₃ * Methylamine, CH₃NH₂ * Ammonium hydroxide, NH₄OH

==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)