Question

Recognize Cause and Effect Illustrate how a buffer works using the \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}+/ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) buffer system. Show with equations how the weak base/conjugate acid system is affected when small amounts of acid and base are added to a solution containing this buffer system.

Short answer

In the \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}/ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) buffer system, when a small amount of acid (H+) is added, it reacts with the weak base (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\)) to form the conjugate acid and water, with the equation: \[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} + \mathrm{H}^{+} \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} + \mathrm{H}_{2} \mathrm{O}\] When a small amount of base (OH-) is added, it reacts with the conjugate acid (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\)) to form the weak base and water, with the equation: \[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} + \mathrm{OH}^{-} \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} + \mathrm{H}_{2} \mathrm{O}\] In both cases, the buffer system maintains a relatively stable pH in the presence of small amounts of acids and bases.

Step-by-step solution

Understanding the buffer system

A buffer is a solution containing a weak acid or base and its conjugate base or acid, which has the ability to maintain its pH within a narrow range when small amounts of acid or base are added. In our exercise, the buffer system is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}/ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\). Here, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) is the conjugate acid and \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) is the weak base.

Reaction with a small amount of acid

When a small amount of acid (usually represented as H+) is added to the buffer solution, it reacts with the weak base, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\), to form the conjugate acid and a water molecule. The chemical equation for this reaction is: \[ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} + \mathrm{H}^{+} \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} + \mathrm{H}_{2} \mathrm{O} \] Upon addition of a small amount of acid, the concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) increases, while the concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) decreases. However, since the concentrations are only marginally affected, and the reaction is reversible, the pH of the solution remains relatively constant.

Reaction with a small amount of base

When a small amount of base (usually represented as OH-) is added to the buffer solution, it reacts with the conjugate acid, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\), to form the weak base and a water molecule. The chemical equation for this reaction is: \[ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} + \mathrm{OH}^{-} \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} + \mathrm{H}_{2} \mathrm{O} \] Upon addition of a small amount of base, the concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) increases, while the concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) decreases. However, as in the case of adding acid, the concentrations are only marginally affected, and the reaction is reversible, hence the pH of the solution remains relatively constant.

Conclusion

In both cases of adding small amounts of acid and base, the buffer solution was able to maintain its pH within a narrow range, as the weak base/conjugate acid system is in a state of equilibrium. These chemical reactions demonstrate how the \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}/ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) buffer system works and maintains a relatively stable pH in the presence of small amounts of acids and bases.

Key concepts

Weak Base

A weak base is a base that does not completely dissociate in solution, meaning it does not release all of its available hydroxide ions (OH⁻) or accept protons (H⁺) completely. In the case of our buffer system, the weak base is \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2}\), known as ethylamine. This substance partially donates or accepts protons, which allows it to help neutralize added acids or bases.

When we add an acid to this system, the weak base \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2}\) reacts with the extra \(\mathrm{H}^{+}\) ions. This reaction forms the conjugate acid, \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+}\), and water. Because this reaction is incomplete, it stabilizes the pH of the solution by not allowing a large increase in free \(\mathrm{H}^{+}\) ions.

This self-regulating property is a hallmark of weak bases in buffer solutions, making them indispensable for maintaining pH stability.

Conjugate Acid

When a weak base accepts a proton, it transforms into its conjugate acid. In the case of ethylamine \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2}\), when it accepts a hydrogen ion, it converts into \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+}\), known as ethylammonium ion. This compound \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+}\) is the conjugate acid in our buffer system.

When a small amount of base is added into the buffer system, the conjugate acid \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+}\) will donate a proton to neutralize the base, converting back to \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2}\). This reversible conversion between the weak base and conjugate acid helps in resisting significant changes in pH, thus effectively stabilizing the system against additions of external H⁺ or OH⁻ ions.

The relationship between a weak base and its conjugate acid forms the backbone of buffer solutions, providing the flexibility and equilibrium required to maintain consistent pH levels.

pH Stability

The primary role of a buffer solution is to maintain pH stability. This term refers to the ability of a solution to resist significant changes in its pH level when small amounts of acids or bases are added. In other words, buffers act as shock absorbers for pH changes.

In our ethylamine/ethylammonium buffer system, the weak base and its conjugate acid work in harmony to neutralize added acids and bases. This collaboration allows the solution to absorb additions without a dramatic shift in pH.

For example:

• When acid is added, the weak base neutralizes it, slightly converting into the conjugate acid without drastically altering the pH.
• When a base is added, the conjugate acid gives up its proton to form the weak base, again buffering the change in pH.

This balance ensures that biological and chemical systems relying on a constant pH range can function properly, preventing damage that could arise from radical pH fluctuations.

Equilibrium Reaction

An equilibrium reaction in a buffer solution involves reversible reactions between the buffer's weak base and conjugate acid. This concept is central because it allows the buffer to maintain a steady pH.

Consider the buffer's reaction with an acid: \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2} + \mathrm{H}^{+} \rightleftharpoons \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+} + \mathrm{H}_{2}\mathrm{O}\). Here, the reaction can move forward or backward, responding dynamically to changes in \(\mathrm{H}^{+}\) concentration.

Similarly, when a base is added, the reaction is: \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+}\) and \(\mathrm{OH}^{-}\) undergo:\(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{3}^{+} + \mathrm{OH}^{-} \rightleftharpoons \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2} + \mathrm{H}_{2}\mathrm{O}\), which reverses as needed.

• The equilibrium shifts according to Le Chatelier's Principle, adjusting the concentrations of the buffer components to maintain a balanced pH.
• This dynamic equilibrium allows a buffer to be very effective over a specific range of pH.

Understanding these reactions is critical for appreciating the steadfast nature of buffer solutions in both chemical and biological systems.