In chemistry, a weak base is a chemical base that does not ionize fully in an aqueous solution. As bases are proton acceptors, a weak base may also be defined as a chemical base in which protonation is incomplete. This results in a relatively low pH level compared to strong bases. Bases range from a pH of greater than 7 (7 is neutral, like pure water) to 14 (though some bases are greater than 14). The pH level has the formula:

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

Since bases are proton acceptors, the base receives a hydrogen ion from water, H₂O, and the remaining H⁺ concentration in the solution determines the pH level. Weak bases will have a higher H⁺ concentration because they are less completely protonated than stronger bases and, therefore, more hydrogen ions remain in the solution. If you plug in a higher H⁺ concentration into the formula, a low pH level results. However, the pH level of bases is usually calculated using the OH^- concentration to find the pOH level first. This is done because the H⁺ concentration is not a part of the reaction, while the OH^- concentration is.

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

By multiplying a conjugate acid (such as NH₄⁺) and a conjugate base (such as NH₃) the following is given:

Since $\{K\_w\}\; =**$ then, $K\_a\; \backslash times\; K\_b\; =\; K\_w$

By taking logarithms of both sides of the equation, the following is reached:

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

Finally, multipying throughout the equation by -1, the equation turns into:

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

After acquiring pOH from the previous pOH formula, pH can be calculated using the formula pH = pK_w - pOH where pK_w = 14.00.

Weak bases exist in chemical equilibrium much in the same way as weak acids do, with a Base Ionization Constant (K_b) (or the Base Dissociation Constant) indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:

$\backslash mathrm\{K\_b=\{**\backslash over*\}\}$

Bases that have a large K_b will ionize more completely and are thus stronger bases. As stated above, the pH of the solution depends on the H⁺ concentration, which is related to the OH^- concentration by the Ionic Constant of water (K_w = 1.0x10^-14) (See article Self-ionization of water.) A strong base has a lower H⁺ concentration because they are fully protonated and less hydrogen ions remain in the solution. A lower H⁺ concentration also means a higher OH^- concentration and therefore, a larger K_b.

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. 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

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As seen above, the strength of a base depends primarily on the pH level. 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 level 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.

The typical proton transfer equilibrium appears as such:

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

B represents the base.

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

In this formula, ^*_initial is the initial molar concentration of the base, assuming that no protonation has occurred.

A typical pH problem

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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.

First, write the proton transfer equilibrium:

$\backslash mathrm\{H\_2O(l)\; +\; C\_5H\_5N(aq)\; \backslash leftrightarrow\; C\_5H\_6N^+\; (aq)\; +\; OH^-\; (aq)\}$

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

	C5H5N	C5H6N+	OH-
initial normality	.20	0	0
change in normality	-x	+x	+x
equilibrium normality	.20 -x	x	x

Substitute the equilibrium molarities into the basicity constant	$K\_b=\backslash mathrm\; \{1.8\; \backslash times\; 10^\{-9\}\}\; =\; \{x\; \backslash times\; x\; \backslash over\; .20-x\}$
Assume that x << .20.	$\backslash mathrm\; \{1.8\; \backslash times\; 10^\{-9\}\}\; \backslash approx\; \{x^2\; \backslash over\; .20\}$
Solve for x.	$\backslash mathrm\; x\; \backslash approx\; \backslash sqrt\{.20\; \backslash times\; (1.8\; \backslash times\; 10^\{-9\})\}\; =\; 1.9\; \backslash times\; 10^\{-5\}$
Check the assumption that x << .20	$\backslash mathrm\; 1.9\; \backslash times\; 10^\{-5\}\; \backslash ll\; .20$; so the approximation is valid
Find pOH from pOH = -log with [OH-=x	$\backslash mathrm\; pOH\; \backslash approx\; -log(1.9\; \backslash times\; 10^\{-5\})\; =\; 4.7$
From pH = pKw - pOH,	$\backslash mathrm\; pH\; \backslash approx\; 14.00\; -\; 4.7\; =\; 9.3$
From the equation for percentage protonated with = x and [Binitial = .20,	$\backslash mathrm\; percentage\; \backslash \; protonated\; =\; \{1.9\; \backslash times\; 10^\{-5\}\; \backslash over\; .20\}\; \backslash times\; 100\backslash \%\; =\; .0095\backslash \%$

This means .0095% of the pyridine is in the protonated form of C₅H₆N⁺.

Examples

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• Alanine, C₃H₅O₂NH₂
• Ammonia, NH₃
• Magnesium hydroxide, Mg(OH)₂
• Methylamine, CH₃NH₂
• Pyridine, C₅H₅N

Other weak bases are essentially any bases not on the list of strong bases.

External links

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• http://wine1.sb.fsu.edu/chm1046/notes/AcidBase/WeakBase/WeakBase.htm
• http://www.chemguide.co.uk/physical/acidbaseeqia/bases.html
• http://bouman.chem.georgetown.edu/S02/lect16/lect16.htm
• http://www.psigate.ac.uk/newsite/reference/plambeck/chem1/p01154.htm

References

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• Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.

Bases