Weak base

In chemistry, a weak base is a base that does not ionize fully in an aqueous solution. As Brønsted–Lowry 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 compared to strong bases.

pH, K_b, and K_w

Bases range from a pH of greater than 7 (7 is neutral, like pure water) to 14 (though some bases are greater than 14). pH has the formula:

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

Since bases are proton acceptors, the base receives a hydrogen ion from water, H₂O, and the remaining H⁺ concentration in the solution determines pH. 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 results. However, pH of bases is usually calculated using the OH⁻ concentration to find the pOH first. This is done because the H⁺ concentration is not a part of the reaction, while the OH⁻ concentration is.

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

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

K_{a}\times K_{b}={[H_{3}O^{+}][NH_{3}] \over [NH_{4}^{+}]}\times {[NH_{4}^{+}][OH^{-}] \over [NH_{3}]}=[H_{3}O^{+}][OH^{-}]

Since ${K_{w}}=[H_{3}O^{+}][OH^{-}]$ then, $K_{a}\times K_{b}=K_{w}$

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

logK_{a}+logK_{b}=logK_{w}

Finally, multiplying 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 dissociation constant (K_b) indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:

{\mathrm {K_{b}={[NH_{4}^{+}][OH^{-}] \over [NH_{3}]}}}

Bases that have a large K_b will ionize more completely and are thus stronger bases. As stated above, pH of the solution depends on the H⁺ concentration, which is related to the OH⁻ concentration by the self-ionization constant (K_w = 1.0x10⁻¹⁴). 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.^[1]

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.^[2]

The typical proton transfer equilibrium appears as such:

B(aq)+H_{2}O(l)\leftrightarrow HB^{+}(aq)+OH^{-}(aq)

B represents the base.

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

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.^[3]

First, write the proton transfer equilibrium:

{\mathrm {H_{2}O(l)+C_{5}H_{5}N(aq)\leftrightarrow C_{5}H_{5}NH^{+}(aq)+OH^{-}(aq)}}

K_{b}={\mathrm {[C_{5}H_{5}NH^{+}][OH^{-}] \over [C_{5}H_{5}N]}}

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	$K_{b}={\mathrm {1.8\times 10^{{-9}}}}={x\times x \over .20-x}$
We can assume that x is so small that it will be meaningless by the time we use significant figures.	${\mathrm {1.8\times 10^{{-9}}}}\approx {x^{2} \over .20}$
Solve for x.	${\mathrm x}\approx {\sqrt {.20\times (1.8\times 10^{{-9}})}}=1.9\times 10^{{-5}}$
Check the assumption that x << .20	${\mathrm 1}.9\times 10^{{-5}}\ll .20$ ; so the approximation is valid
Find pOH from pOH = -log [OH⁻] with [OH⁻]=x	${\mathrm p}OH\approx -log(1.9\times 10^{{-5}})=4.7$
From pH = pK_w - pOH,	${\mathrm p}H\approx 14.00-4.7=9.3$
From the equation for percentage protonated with [HB⁺] = x and [B]_initial = .20,	${\mathrm p}ercentage\ protonated={1.9\times 10^{{-5}} \over .20}\times 100\%=.0095\%$

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

Examples

Alanine
Ammonia, NH₃
Methylamine, CH₃NH₂
Ammoniumhydroxide, 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.^[4]
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.^[5]
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.^[6] Weak bases tend to build up in acidic fluids.^[6] Acid gastric contains a higher concentration of weak base than plasma.^[6] Acid urine, compared to alkaline urine, excretes weak bases at a faster rate.^[6]

References

↑ "Explanation of strong and weak bases]". ChemGuide. Retrieved 2018-03-23.
↑ Howard Maskill (1985). The physical basis of organic chemistry. Oxford University Press, Incorporated. ISBN 978-0-19-855192-8.
↑ "Calculations of weak bases". Mr Kent's Chemistry Page. Retrieved 2018-03-23.
↑ Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.
↑ Clark, Jim. "Strong and Weak Bases."N.p.,2002. Web.
1 2 3 4 Milne; Scribner; Crawford. "Non-ionic Diffusion and the Excretion of Weak Acids and Bases" (PDF). Science Direct. Retrieved 19 February 2015.

External links

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[1] "Explanation of strong and weak bases]". ChemGuide. Retrieved 2018-03-23.

[Maskill1985-2] Howard Maskill (1985). The physical basis of organic chemistry. Oxford University Press, Incorporated. ISBN 978-0-19-855192-8.

[3] "Calculations of weak bases". Mr Kent's Chemistry Page. Retrieved 2018-03-23.

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

[5] Clark, Jim. "Strong and Weak Bases."N.p.,2002. Web.

[ac.els-cdn.com-6] 1 2 3 4 Milne; Scribner; Crawford. "Non-ionic Diffusion and the Excretion of Weak Acids and Bases" (PDF). Science Direct. Retrieved 19 February 2015.