Citric acid, a tricarboxylic acid important in intermediary metabolism, can be symbolized as \(\mathrm{H}_{3} \mathrm{A}\). Its dissociation reactions are \\[\begin{array}{ll}\mathrm{H}_{3} \mathrm{A} \rightleftharpoons \mathrm{H}^{+}+\mathrm{H}_{2} \mathrm{A}^{-} & \mathrm{p} K_{1}=3.13 \\\\\mathrm{H}_{2} \mathrm{A}^{-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{HA}^{2-} & \mathrm{p} K_{2}=4.76 \\\\\mathrm{HA}^{2-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{A}^{3-} & \mathrm{p} K_{3}=6.40 \end{array}\\] If the total concentration of the acid and its anion forms is \(0.02 \mathrm{M}\) what are the individual concentrations of \(\mathrm{H}_{3} \mathrm{A}, \mathrm{H}_{2} \mathrm{A}^{-}, \mathrm{HA}^{2-},\) and \(\mathrm{A}^{3-}\) at pH \(5.2 ?\)

Understanding the dissociation of acids is crucial in chemistry, and the acid dissociation constant (\( K_a \) or pKa) provides scientists with a measure of an acid's strength. Citric acid, which is a key metabolite in the energy-producing citric acid cycle, has three acidic protons and thus three dissociation steps, each with its own dissociation constant.

The lower the pKa value, the stronger the acid. This means that at the first dissociation (with the lowest pKa), citric acid donates a proton more readily than in the subsequent steps. When calculating the dissociation stages of citric acid, you must take into account these constants to understand the balance between different ionic species of citric acid in a solution, which directly impacts the pH levels and the biological function of this molecule in intermediary metabolism.

The pH is a logarithmic measure of the hydrogen ion concentration in a solution and is a crucial parameter in chemistry, biology, and environmental science. pH calculation is often required to find out the acidity or basicity of a solution. Since pH is related to the concentrations of various ionic species in a solution, it can be calculated using the acid dissociation constants and the equilibrium concentrations of these species.

As we see in the exercise with citric acid, once we know the total concentration and the dissociation constants, we can use the pH value to calculate the individual concentrations of citric acid and its dissociated forms. This understanding is essential, especially in biological systems where the proper pH is crucial for enzyme activity and metabolic pathways.

Intermediary metabolism refers to the array of biochemical processes that occur within cells, involving the synthesis, breakdown, and transformation of biomolecules essential for life. In this complex web, citric acid plays a pivotal role as a metabolite in the citric acid cycle (also known as the Krebs cycle or TCA cycle), which is a fundamental pathway for energy production in aerobic organisms.

The dissociation behavior of citric acid in physiological conditions affects how it is utilized in metabolic pathways. An understanding of its dissociation constants and their influence on the acid's ionization at different pH levels provides insight into how citric acid behaves in the highly regulated environment of the cell.

In a chemical reaction set in a closed system, the equilibrium concentrations are the amounts of reactants and products present when the reaction has reached a state where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations remain constant over time.

In the dissociation of citric acid, we aim to find out the equilibrium concentrations of citric acid and its various dissociated forms in solution. By setting up the total concentration equation that includes all species in the equilibrium and using the provided pH, one can deduce the concentration of undissociated acid (in this case, \(H_3A\)) and, from that, calculate the concentrations of all dissociated species. These calculations are pivotal in making conclusions about the system's chemical behavior and preparing solutions with desired properties in laboratory and industrial applications.