Question

Write the chemical equations and \(K_{\mathrm{a}}\) expressions for the stepwise dissociation of \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\)

Short answer

The stepwise dissociation involves releasing \(\text{H}^+\) ions in three steps with corresponding \(K_{\text{a}}\) expressions for each step.

Step-by-step solution

Understanding Citric Acid

Citric acid, represented by the formula \( ext{H}_3 ext{C}_6 ext{H}_5 ext{O}_7\), is a triprotic acid that can dissociate in three steps, each releasing a proton (\( ext{H}^+\)). It dissociates in a stepwise manner to form an anion at each step.

First Dissociation

In the first dissociation step of citric acid, one hydrogen ion is released: \[ ext{H}_3 ext{C}_6 ext{H}_5 ext{O}_7 (aq) ightleftharpoons ext{H}_2 ext{C}_6 ext{H}_5 ext{O}_7^- (aq) + ext{H}^+ (aq)\]The equilibrium constant expression \(K_{ ext{a1}}\) for this reaction is: \[K_{ ext{a1}} = \frac{[ ext{H}_2 ext{C}_6 ext{H}_5 ext{O}_7^-][ ext{H}^+]}{[ ext{H}_3 ext{C}_6 ext{H}_5 ext{O}_7]}\]

Second Dissociation

In the second dissociation step, another hydrogen ion is released from \( ext{H}_2 ext{C}_6 ext{H}_5 ext{O}_7^-\): \[ ext{H}_2 ext{C}_6 ext{H}_5 ext{O}_7^- (aq) ightleftharpoons ext{HC}_6 ext{H}_5 ext{O}_7^{2-} (aq) + ext{H}^+ (aq)\]The equilibrium constant expression \(K_{ ext{a2}}\) for this reaction is: \[K_{ ext{a2}} = \frac{[ ext{HC}_6 ext{H}_5 ext{O}_7^{2-}][ ext{H}^+]}{[ ext{H}_2 ext{C}_6 ext{H}_5 ext{O}_7^-]}\]

Third Dissociation

In the third dissociation step, the final hydrogen ion is released from \( ext{HC}_6 ext{H}_5 ext{O}_7^{2-}\): \[ ext{HC}_6 ext{H}_5 ext{O}_7^{2-} (aq) ightleftharpoons ext{C}_6 ext{H}_5 ext{O}_7^{3-} (aq) + ext{H}^+ (aq)\]The equilibrium constant expression \(K_{ ext{a3}}\) for this reaction is: \[K_{ ext{a3}} = \frac{[ ext{C}_6 ext{H}_5 ext{O}_7^{3-}][ ext{H}^+]}{[ ext{HC}_6 ext{H}_5 ext{O}_7^{2-}]}\]

Key concepts

Citric Acid Dissociation

Citric acid is a common organic acid, scientifically represented as \( \text{H}_3\text{C}_6\text{H}_5\text{O}_7 \). It is found naturally in citrus fruits and is well-known not just for its tart flavor, but also for its role in biochemical processes like the citric acid cycle. When citric acid is in solution, it can undergo dissociation, a chemical process where molecules split into smaller particles such as atoms, ions, or radicals. For citric acid, this means losing hydrogen ions, \( \text{H}^+ \), through a process called stepwise dissociation. This stepwise dissociation leads to the formation of citrate ions and further dissociation steps result in different anions. This characteristic is crucial for understanding how citric acid behaves in various chemical reactions, especially its role as an acid in the body and industrial processes.

Equilibrium Constant

When we talk about a dissociation reaction reaching equilibrium, we refer to a state where the forward and backward reactions occur at the same rate. In this state, the concentrations of the reactants and products remain constant over time. The equilibrium constant, \( K_a \), quantifies the extent of the acid's dissociation in water. For each step of citric acid's dissociation, there is a specific \( K_a \) value indicating the strength of the acid at that stage.

• First dissociation: \( K_{a1} \) relates to the reaction of \( \text{H}_3\text{C}_6\text{H}_5\text{O}_7 \) as it releases its first proton.
• Second dissociation: \( K_{a2} \) defines the equilibrium for the deprotonation of \( \text{H}_2\text{C}_6\text{H}_5\text{O}_7^- \).
• Third dissociation: \( K_{a3} \) involves \( \text{HC}_6\text{H}_5\text{O}_7^{2-} \) losing its final proton.

A higher \( K_a \) value means a stronger acid, which more completely ionizes in solution, while lower values suggest a weaker acid.

Triprotic Acids

Citric acid is classified as a triprotic acid, meaning it can donate three protons or hydrogen ions. Each proton loss represents a different step in its dissociation process. This stepwise loss is not simultaneous but occurs in three distinct stages, each associated with its unique equilibrium state and \( K_a \).

• The first stage involves the release of one proton forming a bicarbonate ion.
• The second stage releases another proton from the resulting anion, producing a different anion.
• The final stage involves stripping the last proton away, leading to the formation of a fully deprotonated citrate ion.

Understanding that citric acid is triprotic helps chemists predict and manipulate its behavior in different chemical reactions, whether in biochemical pathways or industrial applications.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They depict the substances involved in a reaction using their chemical formulas. For the dissociation of citric acid, chemical equations provide clarity and a visual understanding of each step in the dissociation process. These equations show how each citron ion is formed as a hydrogen ion is lost.The balanced chemical equations for the dissociation of citric acid are essential for analyzing the changes in concentrations and modeling the chemical behavior in a given reaction.

• First Equation: \( \text{H}_3\text{C}_6\text{H}_5\text{O}_7 \rightleftharpoons \text{H}_2\text{C}_6\text{H}_5\text{O}_7^- + \text{H}^+ \)
• Second Equation: \( \text{H}_2\text{C}_6\text{H}_5\text{O}_7^- \rightleftharpoons \text{HC}_6\text{H}_5\text{O}_7^{2-} + \text{H}^+ \)
• Third Equation: \( \text{HC}_6\text{H}_5\text{O}_7^{2-} \rightleftharpoons \text{C}_6\text{H}_5\text{O}_7^{3-} + \text{H}^+ \)

Understanding these equations is crucial for correctly calculating the equilibrium states and the changes in concentrations of citric acid and its ions during the dissociation.