Question

Which molecules or ions are present in an aqueous solution of citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\), a triprotic acid? Which is present in the smallest concentration?

Short answer

The molecules or ions present in the solution are the undissociated citric acid, water, the hydronium ion, and the three conjugate bases of citric acid (\(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\), \(\mathrm{H}_{1} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}\), and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}\)). The ion present in the smallest concentration is the citrate ion, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}\).

Step-by-step solution

Identify the molecules in citric acid

Citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\), in its undissociated form is the first molecule present in the solution.

Identify the first proton dissociation

When citric acid is dissolved in water, it can lose its first proton to form a hydronium ion (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) and the citrate ion (\(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\)). So, the molecules or ions present after the first dissociation are \(\mathrm{H}_{3} \mathrm{O}^{+}\), \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\), and water (\(\mathrm{H}_{2} \mathrm{O}\)).

Identify the second proton dissociation

The \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\) from the first dissociation can lose a proton to water forming another hydronium ion and \(\mathrm{H}_{1} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}\). The molecules or ions now include: \(\mathrm{H}_{3} \mathrm{O}^{+}\), \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\), \(\mathrm{H}_{1} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}\), and water.

Identify the third proton dissociation

The \(\mathrm{H}_{1} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}\) from the second dissociation can lose a proton to water forming yet another hydronium ion and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}\). Therefore, the final ions present in the solution are \(\mathrm{H}_{3} \mathrm{O}^{+}\), \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}\), \(\mathrm{H}_{1} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}\), \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}\), and water.

Determining the smallest concentration

By applying the law of mass action, it can be deduced that the citrate ion, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}\), is present in the smallest concentration. This is because it is produced last in the series of reactions involving the successive loss of protons by the citric acid molecule.

Key concepts

Triprotic Acid

Citric acid is classified as a triprotic acid, a type of acid that can donate three protons or hydrogen ions. This characteristic allows citric acid to undergo three distinct dissociation steps, each involving the release of one proton.
Understanding the triprotic nature is important because it affects how citric acid behaves in solution.
The dissociation of triprotic acids occurs in a sequence, instead of all at once, which leads to varying concentrations of the dissociated ions in solution.
In practice, this means that when citric acid is dissolved in water, it will gradually lose its protons, resulting in the formation of different ions, each created at different stages of the dissociation process.

Aqueous Solution Chemistry

When we talk about acids in solution, we're often dealing with aqueous solution chemistry.
In this context, 'aqueous' simply means that water is the solvent.
When citric acid is dissolved in water, the molecules interact with water molecules, which facilitates the dissociation process.

• The initial stage involves the citric acid molecules being surrounded by water molecules.
• This interaction allows the acid to release protons into the water, forming hydronium ions (\(\mathrm{H}_{3} \mathrm{O}^{+}\)).
• The dissociated ions, such as \(\mathrm{H}_{3} \mathrm{O}^{+}\), are then dispersed throughout the solution, contributing to the solution's acidity.

This chemistry is essential for understanding how acids react in biological systems and various industrial applications where water serves as a solvent.

Proton Dissociation Steps

Citric acid, being triprotic, dissociates in three sequential steps, each releasing a proton into the solution.
Each step produces a specific ion, and understanding these steps is crucial for grasping how citric acid affects its environment.

• **First Step:** Citric acid \(\mathrm{H}_3 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7\) loses its first proton to produce \(\mathrm{H}_2 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7^{-}\) and a hydronium ion (\(\mathrm{H}_{3} \mathrm{O}^{+}\)).
• **Second Step:** The new ion \(\mathrm{H}_2 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7^{-}\) loses another proton, leading to the formation of \(\mathrm{H}_1 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7^{2-}\) and more hydronium ions.
• **Third Step:** Finally, \(\mathrm{H}_1 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7^{2-}\) loses the third proton to form \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7^{3-}\), with hydronium ions already abundant in the solution.

The concentration of each ion decreases with each step.
This sequence helps us understand which ion is in the smallest concentration, with \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7^{3-}\) being the least concentrated because it's formed last.
This aspect of dissociation is important for various scientific and industrial processes, such as buffer preparation and chemical reactions in aqueous environments.