Problem 126 - A Complete Resource Book in Chemistry for JEE Main

Question

The species present in solution when \(\mathrm{CO}_{2}\) is dissolved in water are (a) \(\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{HCO}_{3}^{-}, \mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\) (b) \(\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{CO}_{3}^{2-}\) (c) \(\mathrm{CO}_{3}^{2-}, \mathrm{HCO}_{3}^{-}\) (d) \(\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{CO}_{3}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{CO}_2, \mathrm{H}_2\mathrm{CO}_3, \mathrm{HCO}_3^-, \mathrm{CO}_3^{2-}\)

Step 1: Understanding the reaction

When \( \mathrm{CO}_2 \) is dissolved in water, it reacts with the water to form carbonic acid. The chemical reaction can be written as: \[ \mathrm{CO}_2 + \mathrm{H}_2O \rightleftharpoons \mathrm{H}_2\mathrm{CO}_3 \] This shows that liquid water and carbon dioxide directly produce another species, \( \mathrm{H}_2\mathrm{CO}_3 \).

Step 2: Carbonic acid equilibrium

Carbonic acid, \( \mathrm{H}_2\mathrm{CO}_3 \), is a weak acid and can dissociate in an aqueous solution to form bicarbonate ions and hydrogen ions: \[ \mathrm{H}_2\mathrm{CO}_3 \rightleftharpoons \mathrm{HCO}_3^- + \mathrm{H}^+ \] This reaction produces \( \mathrm{HCO}_3^- \).

Step 3: Bicarbonate ion equilibrium

The bicarbonate ion can further dissociate at a lesser extent producing carbonate ions: \[ \mathrm{HCO}_3^- \rightleftharpoons \mathrm{CO}_3^{2-} + \mathrm{H}^+ \] This results in the presence of \( \mathrm{CO}_3^{2-} \) in the solution.

Step 4: Identifying all species

From the above steps, we know that the species present in the solution are \( \mathrm{CO}_2 \), \( \mathrm{H}_2\mathrm{CO}_3 \), \( \mathrm{HCO}_3^- \), and \( \mathrm{CO}_3^{2-} \) as they all result from the equilibrium processes of dissolved \( \mathrm{CO}_2 \) in water.

Key Concepts

Chemical Equilibrium

When substances are mixed, they often reach a state known as chemical equilibrium. It's a delicate balance where the rate of the forward reaction equals the rate of the reverse reaction. In simple terms, the substances transform back and forth, but the overall concentrations of each component stay constant over time.

When carbon dioxide \( (\mathrm{CO}_2) \) is dissolved in water, it forms carbonic acid \( (\mathrm{H}_2 \mathrm{CO}_3) \). This is a reversible reaction, represented by an equilibrium where both the reactants and products exist together:

• The forward reaction: \( \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_2\mathrm{CO}_3 \)
• The backward reaction: \( \mathrm{H}_2\mathrm{CO}_3 \rightleftharpoons \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \)

This equilibrium ensures that no matter how much \( \mathrm{CO}_2 \) you start with, the balance of these reactions will always produce both \( \mathrm{CO}_2 \) and \( \mathrm{H}_2 \mathrm{CO}_3 \) in specific ratios.

Carbonic Acid

When \( \mathrm{CO}_2 \) dissolves in water, the carbonic acid \( (\mathrm{H}_2 \mathrm{CO}_3) \) produced is crucial for the stability of the resulting solution. It's a weak acid, meaning it does not fully dissociate in water.

The reaction forming carbonic acid is reversible and tends to favor the dissolved carbon dioxide and water at equilibrium:

• Weak acids like \( \mathrm{H}_2 \mathrm{CO}_3 \) only partially dissociate, contributing to the presence of hydrogen ions \( (\mathrm{H}^+) \) in the solution.
• As \( \mathrm{H}_2 \mathrm{CO}_3 \) breaks down, it forms bicarbonate ions \( (\mathrm{HCO}_3^-) \) and hydrogen ions \( (\mathrm{H}^+) \).

Understanding carbonic acid's behavior helps us grasp its central role in processes like regulating pH in natural waters and biological systems.

Bicarbonate Ion

The bicarbonate ion \( (\mathrm{HCO}_3^-) \) emerges when carbonic acid dissociates. It's an intermediate form that plays a dynamic role in the system. Its existence is a perfect example of how equilibrium is maintained:

• As part of the weak acid dissociation, bicarbonate ions result from carbonic acid's partial dissociation.
• This ion can further dissociate, producing carbonate ions \( (\mathrm{CO}_3^{2-}) \) and releasing more hydrogen ions \( (\mathrm{H}^+) \).

Bicarbonate ions are adaptable and crucial for buffering systems in biological environments, helping maintain pH within narrow limits. Its reactivity makes it central in many biogeochemical cycles.

Carbonate Ion

Carbonate ions \( (\mathrm{CO}_3^{2-}) \) are the result of further dissociation of the bicarbonate ion. In aqueous solutions, reaching this form indicates that the substance has passed through multiple stages of dissociation:

• Although present in lower concentrations than bicarbonate ions, carbonates are essential for acid-base balance.
• The reaction: \( \mathrm{HCO}_3^- \rightleftharpoons \mathrm{CO}_3^{2-} + \mathrm{H}^+ \) showcases the transition from a singly charged ion to a doubly charged ion.

Carbonate ions are significant within geological processes like sediment formation and dissolution, and they play a critical role in ocean chemistry.

Weak Acid Dissociation

Weak acids like carbonic acid dissociate incompletely, meaning not all acid molecules donate a proton \( (\mathrm{H}^+) \). This partial dissociation is what defines it as a weak acid. It governs the formation of bicarbonate and carbonate ions in likely proportions:

• Weak acid dissociation is expressed as \( \mathrm{H}_2\mathrm{CO}_3 \rightleftharpoons \mathrm{HCO}_3^- + \mathrm{H}^+ \).
• The low dissociation constant \( K_a \) of carbonic acid illustrates its tendency to remain mostly undissociated.

This property of weak acids contributes to buffering capacity, allowing solutions to resist changes in pH when small amounts of acids or bases are added. Understanding this concept is key to grasping how many natural and biological systems achieve stability.