Problem 210 - Introductory Chemistry Atoms First

Question

Citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\), is a weak triprotic acid. Write equations for the three equilibrium reactions that occur during the stepwise dissociation of citric acid in water.

Step-by-Step Solution

Answer

The stepwise dissociation of citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\), in water occurs in three equilibrium reactions: 1) \[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+}(aq) + \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq)\] 2) \[\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+}(aq) + \mathrm{H} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq)\] 3) \[\mathrm{H} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+}(aq) + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}(aq)\]

Step 1: First Dissociation

In the first step, the first hydrogen ion (\(\mathrm{H}^{+}\)) is donated by citric acid, forming a hydroxonium ion and a monohydrogen citrate ion: \[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+}(aq) + \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq)\]

Step 2: Second Dissociation

In the second step, the remaining \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\) ion donates another hydrogen ion: \[\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+}(aq) + \mathrm{H} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq)\]

Step 3: Third Dissociation

Finally, in the third step, the remaining \(\mathrm{H} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}\) ion donates the last hydrogen ion: \[\mathrm{H} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+}(aq) + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}(aq)\] Now we have derived the three equilibrium reactions occurring during the stepwise dissociation of citric acid in water.

Key Concepts

Triprotic Acid

A triprotic acid is an acid that can donate three hydrogen ions (H⁺) in solution. Citric acid is a great example of a triprotic acid. Being triprotic means it goes through three stages of dissociation. Each stage represents the donation of one hydrogen ion.

The dissociation of a triprotic acid occurs stepwise:

• The first hydrogen ion is the most readily lost and significantly affects the acidity of the solution.
• The second hydrogen ion is slightly harder to lose.
• The third hydrogen ion is the least likely to be donated because it is bonded to a more negatively charged molecule.

Understanding triprotic acids helps explain how multi-stage reactions work and why some solutions have layered pH changes.

Equilibrium Reactions

Equilibrium reactions occur when the forward and reverse reactions happen at the same rate. In the context of citric acid dissociating in water, each step represents an equilibrium reaction.

There are essential characteristics of these reactions:

• They involve the continuous exchange of ions, even if the concentration of ions appears stable.
• Each reaction's progress is reversible, and the equilibrium position shifts according to changes in pressure, concentration, or temperature.
• Equilibrium constants (K) summarize the position of these reactions, showing the ratio of product to reactant concentrations.

In the real world, understanding equilibrium reactions helps predict the behavior of acids like citric acid in different environments.

Hydronium Ion Formation

Hydronium ions (\( \mathrm{H}_3\mathrm{O}^+ \)) form when hydrogen ions bond with water molecules. This is an essential part of acid dissociation. In every step of citric acid's dissociation, \( \mathrm{H}_3\mathrm{O}^+ \) ions form as a result of the released \( \mathrm{H}^+ \) ions.

Key aspects of hydronium ion formation include:

• \( \mathrm{H}_3\mathrm{O}^+ \) serves as a measure of solution acidity; the more \( \mathrm{H}_3\mathrm{O}^+ \) present, the lower the pH.
• It indicates the solution's ability to conduct electricity, as more ions increase conductivity.
• It is crucial in understanding buffer systems used to maintain pH in solutions.

Hydronium ion formation is more than just an ionic change; it's foundational to grasping acidic behavior in solutions.

Acid-Base Chemistry

Acid-base chemistry is a vital area of study involving the reactions of acids and bases. In the case of citric acid dissociation, understanding this chemistry offers insights into how acids interact with bases and affect their surrounding environment.

Important points about acid-base chemistry include:

• Acid-base reactions involve the transfer of hydrogen ions between molecules, altering the pH.
• Certain reactions result in salt and water formation, typical of neutralization.
• These reactions are crucial in numerous biological and chemical processes, from digestion to material synthesis.

Grasping acid-base chemistry enables better comprehension of pH regulation, buffer systems, and reaction mechanics in both natural and industrial processes.