Problem 109 - Chemistry Matter and Change

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.

Step-by-Step Solution

Answer

The buffer system neutralizes added acids and bases, keeping pH stable.

Step 1: Understand the Buffer System

A buffer system is a solution that resists changes in pH when small amounts of acid or base are added. In this exercise, the buffer system is composed of a weak base, ethylamine \( \mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2 \), and its conjugate acid, ethylammonium ion \( \mathrm{C}_2\mathrm{H}_5\mathrm{NH}_3^+ \). This system will resist pH changes upon addition of \(\mathrm{H}^+\) ions or \(\mathrm{OH}^-\) ions.

Step 2: Identify Reaction with Added Acid

When a small amount of acid (\(\mathrm{H}^+\)) is added to the buffer, the ethylamine will react with the \(\mathrm{H}^+\) ions:\[ \mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2 + \mathrm{H}^+ \rightarrow \mathrm{C}_2\mathrm{H}_5\mathrm{NH}_3^+ \]The \(\mathrm{H}^+\) ions are consumed by the reaction with the weak base, and the concentration of \(\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2\) decreases slightly while \(\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_3^+\) increases slightly. The pH remains nearly constant.

Step 3: Identify Reaction with Added Base

When a small amount of base (\(\mathrm{OH}^-\)) is added, the conjugate acid \(\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_3^+\) will react with the \(\mathrm{OH}^-\) ions:\[ \mathrm{C}_2\mathrm{H}_5\mathrm{NH}_3^+ + \mathrm{OH}^- \rightarrow \mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2 + \mathrm{H}_2\mathrm{O} \]The \(\mathrm{OH}^-\) ions are consumed in this reaction, converting \(\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_3^+\) back to \(\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2\), and the pH remains relatively stable due to the consumption of the base.

Step 4: Conclude Buffer Functionality

The buffer system resists changes in pH by converting added acids to the conjugate base and added bases to the weak acid. In this way, small additions of acids or bases are neutralized, maintaining the equilibrium and resisting drastic changes in pH.

Key Concepts

Weak Base

In the context of the buffer system, a weak base plays a crucial role. A weak base is a chemical species that does not fully ionize in a solution. Instead, it partially accepts protons (\({H}^+\)), making it less reactive compared to strong bases. Ethylamine (\({C}_2{H}_5{NH}_2\)) is an example of a weak base.

• A weak base like ethylamine partially ionizes in water, leading to an equilibrium between the unionized base and its conjugate acid.
• This partial ionization is what allows the buffer system to be effective, as it provides a "reservoir" of base prepared to react when acids are added.

When a small amount of acid is introduced, this weak base steps in, reacting with the acid, and thus reduces the amount of free \({H}^+\) ions. This is crucial because fewer free \({H}^+\) ions means minimal change in pH. In this way, the weak base maintains the equilibrium within the buffer system.

Conjugate Acid

The conjugate acid is the counterpart to the weak base in a buffer system. It is formed when the weak base accepts a proton. For the ethylamine buffer system:

• The conjugate acid is the ethylammonium ion (\({C}_2{H}_5{NH}_3^+\)), which forms when ethylamine (\({C}_2{H}_5{NH}_2\)) gains a proton.
• This ion plays a pivotal role when a basic substance, such as \({OH}^-\), is added to the solution.

Upon addition of a base, the conjugate acid gives up its proton, neutralizing the base. This reaction mitigates the increase of \({OH}^-\) ions, preventing significant shifts in the pH level. The interactions between the weak base and its conjugate acid allow the buffer system to effectively handle small additions of either acid or base, making them indispensable partners in maintaining pH stability.

pH Stability

Achieving pH stability is the primary goal of a buffer system. This stability ensures that the environment within the solution remains optimal for various biochemical reactions. The buffer's capacity to maintain a stable pH results from the dynamic equilibrium established between the weak base and its conjugate acid. Here’s how the system works:

• When an acid is added, the weak base absorbs the added protons, stabilizing the pH.
• Conversely, when a base is added, the conjugate acid releases a proton, counteracting the effect of the base.

This balance is vital in biological and chemical processes where even minor pH changes can have significant consequences. The buffer’s ability to neutralize additions and maintain an almost constant pH is what makes it invaluable. Remember, the effectiveness of a buffer also depends on the concentration ratio of the weak base to its conjugate acid. For best results, these concentrations should be relatively high and closely matched, thus enhancing the buffer capacity and ensuring superior pH stability.