weak base

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:

:$\backslash mbox\{pH\}\; =\; -\backslash log\_\{10\}\; \backslash left[\; \backslash mbox\{H\}^+\; \backslash right]$

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:

:$\backslash mbox\{pOH\}\; =\; -\backslash log\_\{10\}\; \backslash left[\; \backslash mbox\{OH\}^-\; \backslash right]$

If we multiply the equilibrium constants of a conjugate acid (such as NH₄⁺) and a conjugate base (such as NH₃) we obtain:

:$K\_a\; \backslash times\; K\_b\; =\; \{[H\_3O^+]\; [NH\_3]\backslash over[NH\_4^+]\}\; \backslash times\; \{[NH\_4^+]\; [OH^-]\backslash over[NH\_3]\}\; =\; [H\_3O^+]\; [OH^-]$

As $\{K\_w\}\; =\; [H\_3O^+]\; [OH^-]$ is just the self-ionization constant of water, we have $K\_a\; \backslash times\; K\_b\; =\; K\_w$

Taking the logarithm of both sides of the equation yields:

:$logK\_a\; +\; logK\_b\; =\; logK\_w$

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

:$pK\_a\; +\; pK\_b\; =\; pK\_w\; =\; 14.00$

With pOH obtained from the pOH formula given above, the pH of the base can then be calculated from $pH\; =\; pK\_w\; -\; pOH$, 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:

:$\backslash mathrm\{K\_b=\{[NH\_4^+]\; [OH^-]\backslash over[NH\_3]\}\}$

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.{{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}}

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.{{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}}

The typical proton transfer equilibrium appears as such:

:$B(aq)\; +\; H\_2O(l)\; \backslash leftrightarrow\; HB^+(aq)\; +\; OH^-(aq)$

B represents the base.

:$Percentage\backslash \; protonated\; =\; \{molarity\backslash \; of\backslash \; HB^+\; \backslash over\backslash \; initial\backslash \; molarity\backslash \; of\backslash \; B\}\; \backslash times\; 100\backslash \%\; =\; \{[\{HB\}^+]\backslash over\; [B]\_\{initial\}\}\; \{\backslash times\; 100\backslash \%\}$

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

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.{{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}}

First, write the proton transfer equilibrium:

:$\backslash mathrm\{H\_2O(l)\; +\; C\_5H\_5N(aq)\; \backslash leftrightarrow\; C\_5H\_5NH^+\; (aq)\; +\; OH^-\; (aq)\}$

:$K\_b=\backslash mathrm\{[C\_5H\_5NH^+]\; [OH^-]\backslash over\; [C\_5H\_5N]\}$

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

This means .0095% of the pyridine is in the protonated form of C₅H₅NH⁺.

• Alanine
• Ammonia, NH₃
• Methylamine, CH₃NH₂
• Ammonium hydroxide, NH₄OH

• 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.Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.
• 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.Clark, Jim. "Strong and Weak Bases."N.p.,2002. Web.
• 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.{{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.}} Weak bases tend to build up in acidic fluids. Acid gastric contains a higher concentration of weak base than plasma. Acid urine, compared to alkaline urine, excretes weak bases at a faster rate.

• Strong base
• Weak acid

{{reflist}}

• [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)