BioMath: Quadratic Functions Applications

The Biology Project > Biomath > Quadratic Functions > Applications > Acid/Base Equilibria

Quadratic Functions- Applications

Acid/Base Equilibria

Weak acids react with water in a process known as acid ionization. The ionization of a weak monoprotic acid (denoted as HA) in water occurs by the following equilibrium,

The acid-ionization constant (K_a) is the equilibrium constant for the ionization of a weak acid. The value of K_a tells you how much a weak acid dissociates in water, thus indicating how much H⁺ is formed. The acid ionization constant is defined as,

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In the case of a diprotic acid, an acid that loses two protons in aqueous solution, working with the ionization constant involves the use of quadratic functions. Take oxalic acid, H₂C₂O₄ is a diprotic organic acid found in many plants, notably rhubarb leaves. In humans, oxalic acid can be poisonous, causing skin and mouth irritation, nausea, vomiting, diarrhea, kidney stones, and, rarely, death.

Oxalic acid has the following simultaneous acid-ionization equilibria

with the following acid-ionization constants at 25 °C,

Notice that oxalic acid has two ionization constants, K_a₁ and K_a₂, because it is a diprotic acid.

Use the information provided to answer the following questions:

Determine the equilibrium concentration of H⁺.

Determine the equilibrium concentration of C₂O₄^2-.

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The Biology Project > Biomath > Quadratic Functions > Applications > Acid/Base Equilibria

The Biology Project
Department of Biochemistry and Molecular Biophysics
The University of Arizona
May 2006
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