Problem 106 - Chemistry An Atoms First Approach

Question

Write out the stepwise \(K_{\mathrm{a}}\) reactions for citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) a triprotic acid.

Step-by-Step Solution

Answer

The stepwise $K_{a}$ reactions for citric acid (H3C6H5O7) are as follows: 1. \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq)\) 2. \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq) \) 3. \(\mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}(aq) \)

Step 1: First Dissociation Reaction

In the first dissociation reaction, citric acid donates its first acidic proton (H+). The equation for this step can be written as follows: \[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq)\]

Step 2: Second Dissociation Reaction

In the second dissociation reaction, the resulting ion from the first step, H2C6H5O7-, donates its second acidic proton (H+). The equation for this step can be written as follows: \[ \mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq) \]

Step 3: Third Dissociation Reaction

In the third dissociation reaction, the resulting ion from the second step, HC6H5O7²-, donates its third and final acidic proton (H+). The equation for this step can be written as follows: \[ \mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{2-}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{3-}(aq) \]

Key Concepts

Triprotic Acid

A triprotic acid is a type of acid that has three available protons (or hydrogen ions) that can dissociate, or detach, during reactions in solution. These acids undergo three steps of dissociation, with each step releasing one proton. Citric acid is a prime example of a triprotic acid, as it has the potential to donate three protons in a stepwise manner.

In general, the dissociation of a triprotic acid can be represented by three distinct reactions. The overall ability of an acid to donate protons in water is quantified using the acid dissociation constant, represented as \(K_a\).

• The first dissociation step typically has the highest \(K_a\) value because protons are more readily available when the acid is fully protonated.
• Subsequent dissociation steps usually have lower \(K_a\) values, indicating less readiness to give up a proton.

The behavior of triprotic acids often depends significantly on the pH of the surrounding environment, which influences how many protons are readily dissociable.

Dissociation Reaction

Dissociation reactions describe the process in which molecules separate into two or more substances when dissolved in water. For acids, this means splitting into protons \((H^+)\) and conjugate base ions. In terms of citric acid, which is triprotic, it can dissociate in three distinct stages, each releasing one proton.

Let's look into these stepwise reactions for citric acid:

• First dissociation: Citric acid releases its first proton, forming \(H_2C_6H_5O_7^-\).
• Second dissociation: The ion \(H_2C_6H_5O_7^-\) releases a second proton to become \(HC_6H_5O_7^{2-}\).
• Third dissociation: The ion \(HC_6H_5O_7^{2-}\) releases the third proton, resulting in \(C_6H_5O_7^{3-}\).

The stepwise nature of these reactions is crucial because each step involves the release of one proton, demonstrating the acid's complete dissociation potential depending on how the environmental conditions, like pH, guide the reactions.

Acid-Base Chemistry

Acid-base chemistry is a field that focuses on the behaviors and reactions of acids and bases. Understanding this field is crucial to comprehend how substances like citric acid interact when dissolved. In an aqueous solution, an acid will dissociate to release \(H^+\) ions, while a base will accept these protons or produce \(OH^-\) ions.

The stepwise dissociation reactions of a triprotic acid like citric acid are excellent examples of these principles. Acid-base chemistry describes how:

• Acids are defined either by their ability to donate protons (Bronsted-Lowry) or by increasing the concentration of \(H^+\) in solution (Arrhenius).
• In reversible reactions, such as those of dissociation, equilibrium is reached when the rate of the forward reaction equals that of the reverse.
• The pH of the solution affects the extent of dissociation; at higher pH levels, dissociation is more extensive because of decreased \(H^+\) concentration.

Citric acid's triprotic nature makes it a versatile and informative subject for demonstrating key principles in acid-base chemistry, helping students explore how proton donation influences the characteristics and reactivity of molecules in solutions.