Weak base

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• Acceptor number
• Acid
• Acid–base reaction
• Acid–base homeostasis
• Acid strength
• Acidity function
• Amphoterism
• Base
• Buffer solutions
• Dissociation constant
• Donor number
• Equilibrium chemistry
• Extraction
• Hammett acidity function
• pH
• Proton affinity
• Self-ionization of water
• Titration
• Lewis acid catalysis
• Frustrated Lewis pair
• Chiral Lewis acid
• ECW model

| heading3 = Acid types | content3 =

• Brønsted–Lowry
• Lewis
• Mineral
• Organic
• Oxide
• Strong
• Superacids
• Weak
• Solid

| heading4 = Base types | content4 =

• Brønsted–Lowry
• Lewis
• Organic
• Oxide
• Strong
• Superbases
• Non-nucleophilic
• Weak

}} 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>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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">Template:Cite book</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>{{#invoke:citation/CS1|citation |CitationClass=web }}</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

	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	<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−] with [OH−]=x	<math>\mathrm pOH \approx -log(1.9 \times 10^{-5}) = 4.7 </math>
From pH = pKw - 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">Template:Cite journal</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

External links

• Guide to Weak Bases from Georgetown course notes
• Article on Acidity of Solutions of Weak Bases from Intute