The pH of Solutions of Weak Bases

What weak bases are present in these foods?

Mackerel

Emmentaler cheese

Red wine

How are they formed and why are they important?

Ammonia is one of the most common examples of weak bases. In water, ammonia forms ammonium hydroxide with K_b= 1.81 x 10^-5. The replacement of hydrogen atoms in ammonia with other elements produces inorganic amines (NCl₃). The replacement of hydrogen atoms with other functional groups such as alkyl and aryl groups generates organic amines which can be primary (one hydrogen atom replaced), secondary (two hydrogen atoms replaced) and tertiary (three hydrogen atoms replaced). Amines are weak bases and their basicities depend on their electronic and steric nature ^[1].

The amines present in food are biogenic amines, which are formed mainly by decarboxilation of amino acids or by amination or transamination of aldehydes and ketones. They are products of the metabolism of microbes, vegetables, and animals. In food and beverages, biogenic amines are formed by the enzymes of raw material or are generated by microbial decarboxilation of amino acids ^[2].

Biogenic Amines in Food ^{[3] [4]}

Amine	pKb1; pKb2	Food
Phenylethylamine	4.17	Ripened cheeses, cocoa beans, wine, and banana.
Tyramine	4.26	Ripened cheeses, lemon, pineaple, avocado, banana, wine, and meat.
Tryptamine	3.8	Ripened cheeses, banana, kiwi, pineapple, tomato, and meat.
Histamine	7.96; 4.25	Ripened cheeses. It is produced from histidine due to bacterial decomposition of fish. Also found in banana, meat, and wine.
Putrescine	3.2; 4.37	Ripened cheeses, wine, and meat.
Cadaverine	3.95; 3.07	Ripened cheeses, wine, and meat.
Trimethylamine oxide	9.35	Regulation of osmotic pressure in fish.
Trimethylamine	4.2	Found in small amounts in fresh-water fish. Responsible for the "fishy" aroma in dead fish, it is produced from the reduction of trimethylamnie oxide.
Serotonin	4.2; 2.9	Pinneaple, banana, kiwi, and walnut.
Dopamine	5.1; 3.4	Plum/prune, avocado, and banana.
Octylamine	3.35	Apple

The presence of biogenic amines in some foods is a sign of microbial activity. In some cases, such activity is desired, for example, in the fermentation of wine and vegetables. Other times, the presence of biogenic amines implies microbial activity related to spoilage of fruits and vegetables. Biogenic amines contribute to the aroma and flavor of foods and their concentration can make the difference between a desirable flavor note or a completely disgusting one. Histamine and tyramine are associated to food poisoning and toxic reactions (cheese and fish). Secondary amines are substrates for the formation of nitrosamines associated with carcinogenic activity (meat and meat products).

On the other hand, many biogenic amines are extremely important to neurological activity: epinephrine, norepinephrine, dopamine, serotonin, and histamine are neurotransmitters. The huge industry of psychotherapeutic drugs is based on the synthesis of compounds able to either mimic, block, or modulate the activity of these neurotransmitters in the brain ^[5]. Poly- and di-amines such as putrescine, spermidine, spermine, and cadaverine are crucial components of living cells and are important in the regulation of nucleic acid function, protein synthesis, and the stabilization of membranes ^{[6] [7] [8]}.

Figure \(\PageIndex{1}\) Biogenic amines: Histamine, Putrescine, and Dopamine

The pH of a solution of a weak base, such as the amines presented above, can be calculated in a very similar way to that used for a weak acid. Instead of an acid constant K_a, a base constant K_b must be used. If a weak base B accepts protons from water according to the equation

\[\text{B} + \text{ H}_{\text{2}}\text{O}\rightleftharpoons\text{BH}^{+} + \text{OH}^{-} \label{1}\]

then, the base constant is defined by the expression

\[K_{b}=\dfrac{\text{ }\!\![\!\!\text{ BH}^{\text{+}}\text{ }\!\!]\!\!\text{ }\!\![\!\!\text{ OH}^{-}\text{ }\!\!]\!\!\text{ }}{\text{ }\!\![\!\!\text{ B }\!\!]\!\!\text{ }} \label{2}\]

A list of K_b values for selected bases can be found in our collection of acid-base resources.

To find the pH we follow the same general procedure as in the case of a weak acid. If the stoichiometric concentration of the base is indicated by c_b, the result is entirely analogous to equation 4 in the section on the pH of weak acids; namely,

\[K_{b}=\dfrac{\text{ }\!\![\!\!\text{ OH}^{-}\text{ }\!\!]\!\!\text{ }^{\text{2}}}{c_{b}-\text{ }\!\![\!\!\text{ OH}^{-}\text{ }\!\!]\!\!\text{ }} \label{3}\]

Under most circumstances we can make the approximation

\(\text{c}_b - [\text{OH}^{-}] \approx \text{c}_b\)

in which case Equation \(\ref{3}\) reduces to the approximation

\[[OH^–] ≈ \sqrt{K_{b}c_{b}} \label{4}\]

which is identical to the expression obtained in the acid case (approximation shown in equation 6 in the section on the pH of weak acids) except that OH^– replaces H₃O⁺ and b replaces a. Once we have found the hydroxide-ion concentration from this approximation, we can then easily find the pOH, and from it the pH.

Example \(\PageIndex{1}\) pH of Trimethyl Amine

Using the value for pK_b listed in the table of Biogenic Amines in Food, find the pH of 0.100 M trimethyl amine, N(CH₃)₃. Where is this compound found?

Solution It is not a bad idea to guess an approximate pH before embarking on the calculation. Since we have a dilute solution of a weak base, we expect the solution to be only mildly basic. A pH of 13 or 14 would be too basic, while a pH of 8 or 9 is too close to neutral. A pH of 10 or 11 seems reasonable. Using Eq. (4) we have

The pK_b of trimethylamine is 4.2 and its K_b is

\(\text{K}_b = \text{10}^{-pK_b} = \text{10}^{-4.2} = \text{6.3} \times \text{10}^{-5}\)

With this K_b the concentration of hydroxide ions becomes

\(\text{ OH}^{-} \approx \sqrt{K_{b}c_{b}} \)

\(\approx \sqrt { \text{6.3} \times \text{10}^{-5} \text{mol dm}^{-3} \times \text{0.100} \text{mol dm}^{-3}}\)

\(\approx \sqrt { \text{6.3} \times \text{10}^{-6} \text{mol}^{2} \text{ dm}^{-6}}\)

\(\approx \text{2.51} \times \text{10}^{-3} \text{mol dm}^{-3}\)

Checking the accuracy of the approximation, we find

\(\dfrac{\text{OH}^{-}}{c_{\text{b}}}=\dfrac{\text{2}\text{.51 }\times \text{ 10}^{-\text{3}}}{\text{0}\text{.1}}\approx \text{2 percent}\)

The approximation is valid, and we thus proceed to find the pOH.

\(\text{pOH}=-\text{log} \dfrac{\text{OH}^{-}}{\text{mol dm}^{-3}}=-\text{log} (\text{2.51 }\times \text{ 10}^{-\text{3}}\text{)}=\text{2.6}\)

From which

\(\text{pH} = \text{14 - pOH} = \text{14} - \text{(2.6)} = \text{11.4}\)

This calculated value checks well with our initial guess.

Occasionally, we will find that the approximation

\(\text{c}_b - [\text{OH}^{-}] \approx \text{c}_b\)

is not valid, in which case we must use a series of successive approximations similar to that outlined in the page for acids. The appropriate formula can be derived from Eq. \(\ref{3}\) and reads

\([\text{OH}^-] ≈ \sqrt{K_{b}(c_{b} - [\text{OH}^{-}]} \)

Note

Trimethylamine is responsible for the "fishy" smell in fish. This compound is found in small amounts in fresh water fish ( 0-5 mg/kg ) and in dead fish is produced in higher amounts by bacteria capable of reducing trimethylamine oxide, compound involved in the regulation of osmotic pressure in fish.

Figure \(\PageIndex{2}\) Cocoa pods

Processing of chocolate

The processing of chocolate involves an alkalization step in which the cocoa nib or cocoa mass is treated with a base. This process mellows the flavor by partial neutralization of free acids, improves the color, and enhances the ability of cocoa powder to become wet, form dispersions, and remain in suspension. This modification prevents the formation of sediment in cocoa drinks.

The process, called "Dutch cocoa process" was introduced by C.I. van Houten in 1828. The roasted cocoa nibs are treated with a dilute 2-2.5% alkali solution at 75-100^oC. The treated nibs are then neutralized if necessary with tartaric acid and dried to a moisture content of 2% in a vacuum dryer or by further kneading of the mass at a temperature above 100^oC. This treatment also causes swelling of the starch producing a spongy porous cell structure of the cocoa mass.

Figure \(\PageIndex{3\) The Dutch process develops smooth flavor and texture of cocoa.

 

Example \(\PageIndex{2}\) pOH and pH of Cocoa

One of the bases employed in the Dutch cocoa process is the ion carbonate in the form sodium carbonate, Na₂CO₃. a) Calculate the concentration of hydroxide ions in a 2.25% (m/v%) sodium bicarbonate solution. b) Calculate the pOH and the pH of this solution.

Solution Sodium carbonate is soluble in water and will dissociate into sodium and carbonate ions. The carbonate ion accepts one proton from water producing hydroxide and bicarbonate ions.

\(\text{CO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{OH}^- \)

a) If the solution contains 2.25% (m/v%) of sodium carbonate, we have 2.25 g Na₂CO₃ in 100 mL of solution. The number of moles of Na₂CO₃, whose molar mass is 105.99 g/mol (in anhydrous form), equals then

\( n_{Na_{2}CO_{3}} = \dfrac{\text{2.25} \text{ g} \text{Na}_2 \text{CO}_3}{\text{105.99} \text{g mol}^{-1}} \)

\(= \text{2.12} \times \text{10}^{-2} \text{mol} \text{Na}_2\text{CO}_3\)

Since 1 mol of sodium carbonate produces 1 mol of carbonate ion in solution, 2.12 x 10^-1 mol of sodium bicarbonate will produce 2.12 x 10^-1 moles of carbonate ions. The concentration of carbonate ion is then

\([\text{CO}_3^{2-}] = \dfrac{n_{CO_3^{2-}}}{\text{V}_solution} = \dfrac{\text{2.12}\times\text{10}^{-2} \text{mol}}{\text{1.0}\times \text{10}^{-1} \text{dm}^3} = \text{2.12} \times \text{10}^{-2} \text{mol} \text{Na}_2 \text{CO}_3\)

Using equation \(\ref{4}\) and a K_b=2.1 x 10^–4 mol dm^–3 for the carbonate ion, taken from our collection of acid-base resources, the concentration of hydroxide ions is

\([OH^–] \approx \sqrt{K_{b}c_{b}} \)

\(\approx \sqrt { \text{2.1} \times \text{10}^{-4} \text{mol dm}^{-3} \times \text{0.212} \text{mol dm}^{-3}}\)

\(\approx \sqrt { \text{4.45} \times \text{10}^{-5} \text{mol}^{2} \text{ dm}^{-6}}\)

\(\approx \text{6.67} \times \text{10}^{-3} \text{mol dm}^{-3}\)

Checking the accuracy of the approximation, we find

\(\dfrac{\text{OH}^{-}}{c_{\text{b}}}=\dfrac{\text{6}\text{.67 }\times \text{ 10}^{-\text{3}}}{\text{0}\text{.212}}\approx \text{3 percent}\)

The approximation is then valid.

b) The pOH of this solutions is

\(\text{pOH}=-\text{log} \dfrac{\text{OH}^{-}}{\text{mol dm}^{-3}}=-\text{log} (\text{6.67 }\times \text{ 10}^{-\text{3}}\text{)}=\text{2.17}\)

and the pH

\(\text{pH} = \text{14 - pOH} = \text{14} - \text{(2.17)} = \text{11.83}\)

Again, notice how the pH of this weak base solution remains under 13.

From CoreChem: 14.4: The pH of Solutions of Weak Bases

References

1. ↑ Amines. 2004. Lawrence, S. A.
2. ↑ Silla-Santos, M.H. 1996. Biogenic amines: their importance in foods. Int. J. Food Microbiol. 29:213-231.
3. ↑ Food Chemistry, 3rd Ed. 2004 Belitz, et al.
4. ↑ Smit, A.Y., du Toit, W.J., du Toit, M. 2008. Biogenic amines in wine: understanding the headache. S. Afr. J. Enol. Vitic. 29:2:109-127
5. ↑ Neuroscience, 3rd Ed. 2001 Purves, D. et al.
6. ↑ Bardocz, S, Grant, G., Brow, D.S., Ralph, A., and Pusztai, A. 1993. Polyamines in food - implications for growth and health. J. Nutr. Biochem. 4:66-71
7. ↑ Maijala, R.L., Eerola, S.H., Aho, M.A., and Hirn, J.A. 1993. The effect of GDL-induced pH decrease on the formation of bigenic amines in meat. J. Food Prot. 50, 125-129
8. ↑ Halasz, A. Barath, A., Simon-Sarkadi, L. and Holzapfel, W. 1994. Biogenic amines and their production by microorganisms in food. Trends Food Sci. Technol. 5:42-48

Contributors and Attributions

• Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.