Question

Does a mixture of carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}\), a weak acid, and sodium bicarbonate, \(\mathrm{NaHCO}_{3}\), in water constitute a buffer? If no, explain why. If yes, explain why and use chemical equations to show what happens when either \(\mathrm{OH}\) or \(\mathrm{H}_{3} \mathrm{O}^{+}\) is added to the solution.

Short answer

A mixture of carbonic acid (H₂CO₃) and sodium bicarbonate (NaHCO₃) in water constitutes a buffer because it contains a weak acid and its conjugate base. When hydroxide ions (OH⁻) are added to the solution, the bicarbonate ion (HCO₃⁻) reacts with the OH⁻ ions to form water (H₂O) and carbonate ion (CO₃²⁻), as shown by the reaction: \[HCO_{3}^{-} + OH^{-} \leftrightarrow H_{2}O + CO_{3}^{2-}\] When hydronium ions (H₃O⁺) are added to the solution, carbonic acid (H₂CO₃) reacts with the H₃O⁺ ions to form water (H₂O) and the protonated form of the carbonic acid, as shown by the reaction: \[H_{2}CO_{3} + H_{3}O^{+} \leftrightarrow H_{2}O + H_{2}CO_{3}^{+}\] Thus, the buffer neutralizes added ions to resist significant changes in pH.

Step-by-step solution

Identifying a Buffer System

A buffer system is a solution that consists of a weak acid and its conjugate base or a weak base and its conjugate acid. A buffer system can resist significant changes in pH when small amounts of acid or base are added to the solution.

Determine the acid/base nature of the given compounds

In this case, we have carbonic acid (H₂CO₃) and sodium bicarbonate (NaHCO₃). Carbonic acid is a weak acid, and sodium bicarbonate can act as the conjugate base because it can accept a proton (H⁺) from the acid. We can write the equilibrium reaction between carbonic acid and its conjugate base, bicarbonate ion (HCO₃⁻): \[H_{2}CO_{3} \leftrightarrow H^{+} + HCO_{3}^{-}\]

Confirming the Buffer System

Since the mixture of weak acid H₂CO₃ and its conjugate base HCO₃⁻ is present in the solution, the given solution constitutes a buffer.

Reactions when OH⁻ is added to the solution

The buffer can neutralize the added hydroxide ions (OH⁻) to resist pH change. The reaction that takes place when OH⁻ ions are added to the buffer is: \[HCO_{3}^{-} + OH^{-} \leftrightarrow H_{2}O + CO_{3}^{2-}\] In this reaction, the bicarbonate ion (HCO₃⁻) reacts with the added OH⁻ ions to form water (H₂O) and carbonate ion (CO₃²⁻).

Reactions when H₃O⁺ is added to the solution

The buffer can also neutralize the added hydronium ions (H₃O⁺) to resist pH change. The reaction that takes place when H₃O⁺ ions are added to the buffer is: \[H_{2}CO_{3} + H_{3}O^{+} \leftrightarrow H_{2}O + H_{2}CO_{3}^{+}\] In this reaction, the weak acid carbonic acid (H₂CO₃) reacts with the added H₃O⁺ ions to form water (H₂O) and the protonated form of the carbonic acid. In conclusion, a mixture of carbonic acid (H₂CO₃) and sodium bicarbonate (NaHCO₃) in water constitutes a buffer. When either OH⁻ or H₃O⁺ is added to the solution, the buffer neutralizes the ions to resist significant changes in pH.

Key concepts

Weak Acid

Understanding weak acids is vital for grasping the concept of buffer solutions. A weak acid only partially dissociates in water, creating a mixture of undissociated acid molecules and ions. One classic example of a weak acid is carbonic acid (\r\text{\rH\(_2\)CO\(_3\))\r}). When carbonic acid is added to water, it doesn't fully ionize. Instead, it establishes an equilibrium between the acid (\r\text{\rH\(_2\)CO\(_3\))\r} and its ions (\r\text{\rH\(^+\))\r} and \text{\rHCO\(_3^-\))\r}. \r\r
This equilibrium is crucial for the buffer's functioning, as it ensures that there are always some acid molecules ready to donate protons (H\(^+\)) when needed, which is essential for neutralizing added bases like OH\(^-\) ions.

Conjugate Base

A conjugate base is what remains after a weak acid has donated a proton. In the buffer system composed of carbonic acid and sodium bicarbonate, the bicarbonate ion (\r\text{\rHCO\(_3^-\))\r}) serves as the conjugate base. It plays a pivotal role because it can accept a proton, reverting back to the weak acid form when the solution becomes more acidic upon the addition of hydronium ions (\r\text{\rH\(_3\)O\(^+\))\r}. This ability to go back and forth between the weak acid and conjugate base forms is fundamental in maintaining pH stability, as it can neutralize excess acid or base in the solution.
\r\r

Role of Bicarbonate in Buffer Solutions

\rAs the conjugate base in the carbonic acid-bicarbonate buffer system, bicarbonate interacts with hydroxide ions (OH\(^-\)) added to the solution to form water (H\(_2\)O) and carbonate ions (CO\(_3^{2-}\)), effectively neutralizing the base without a significant shift in pH.

pH Stability

pH stability is a critical feature of buffer solutions and refers to the capacity to maintain a relatively stable pH level even when small amounts of acid or base are added. This stability is made possible by the balance between the weak acid and its conjugate base. When an acidic or basic component is introduced to the solution, the equilibrium shifts to counteract the effect of the added substance, minimizing the change in pH.
\r\r

Example Using the Carbonic Acid-Bicarbonate Buffer

\rLet's take our carbonic acid-bicarbonate buffer as an example. If a base like OH\(^-\) is introduced, it reacts with the bicarbonate ion, leaving less free OH\(^-\) and reducing the impact on pH. Conversely, if an acid like H\(_3\)O\(^+\) is added, the carbonic acid neutralizes it by reacting and forming water (H\(_2\)O) and more carbonic acid, again minimizing the pH change. These reactions attest to the effective functioning of buffer solutions in biological and chemical systems where pH stability is crucial.

Chemical Equations

Chemical equations are representations of chemical reactions using symbols and formulas. They are pivotal for understanding the changes that occur in substances during chemical processes, such as the formation of buffer solutions.
\r\rIn the context of buffer systems, the chemical equations illustrate the reactions that enable the buffer to moderate pH changes. For instance, the addition of hydroxide ions (OH\(^-\)) to the carbonic acid-bicarbonate buffer is represented by the equation:\r\text{\rHCO\(_3^-\) + OH\(^-\) \rightarrow H\(_2\)O + CO\(_3^{2-}\))\r}. This shows the neutralization of a base by the conjugate base portion of the buffer. Similarly, the addition of hydronium ions (H\(_3\)O\(^+\)) is represented by:\r\text{\rH\(_2\)CO\(_3\) + H\(_3\)O\(^+\) \rightarrow H\(_2\)O + H\(_2\)CO\(_3^+\))\r}, which depicts the neutralization of an acid by the weak acid component.
\r\rThese equations are not just symbolic; they convey the fundamental processes taking place and highlight the stoichiometry involved, enabling students and scientists alike to predict the outcomes of adding acids or bases to buffers and understand the underlying principles of chemical reactivity.