Question

Mixing together solutions of acetic acid and sodium hydroxide can make a buffered solution. Explain. How does the amount of each solution added change the effectiveness of the buffer?

Short answer

When acetic acid (CH3COOH) and sodium hydroxide (NaOH) are mixed, a neutralization reaction occurs forming water and sodium acetate (CH3COONa). Sodium acetate dissociates into acetate ions (CH3COO-) and sodium ions (Na+). The presence of acetic acid and acetate ions creates a buffer system, as acetic acid is a weak acid and acetate ions act as its conjugate base. The buffer's effectiveness depends on the ratio of acetic acid to acetate ions, according to the Henderson-Hasselbalch equation: \[ pH = pK_a + \log{\frac{[conjugate\: base]}{[weak\: acid]}}\] Adding too much sodium hydroxide neutralizes the acetic acid, removing the buffering effect, while adding too little reduces the buffer's effectiveness due to a low concentration of acetate ions. Thus, the effectiveness relies on achieving an appropriate ratio between acetic acid and acetate ions.

Step-by-step solution

Understand Buffered Solutions

A buffered solution is a solution that resists significant changes in pH when a small amount of acid or base is added. It usually contains a weak acid and its conjugate base, or a weak base and its conjugate acid.

Reaction between Acetic Acid and Sodium Hydroxide

When acetic acid (CH3COOH) and sodium hydroxide (NaOH) are mixed, they undergo a neutralization reaction to form water and sodium acetate (CH3COONa). The reaction can be written as follows: \[ CH3COOH + NaOH \rightarrow CH3COONa + H2O \]

Formation of the Buffered Solution

The neutralization reaction between acetic acid and sodium hydroxide forms sodium acetate, which can dissociate into acetate ions (CH3COO-) and sodium ions (Na+). The presence of acetic acid and acetate ions creates a buffer system, as acetic acid is a weak acid and acetate ions act as its conjugate base. In this buffer system, acetic acid can donate a proton (H+) to the solution and form acetate ions, while acetate ions can capture a proton from the solution to form acetic acid. This proton-exchange equilibrium between acetic acid and acetate ions is the basis of the buffer's effectiveness.

Effects of Changing the Amount of Each Solution

The effectiveness of the buffer depends on the ratio of the concentration of the weak acid (acetic acid) to the concentration of its conjugate base (acetate ions). This ratio influences the pH of the buffered solution, as described by the Henderson-Hasselbalch equation: \[ pH = pK_a + \log{\frac{[conjugate\: base]}{[weak\: acid]}}\] By changing the amounts of acetic acid and sodium hydroxide added to the solution, we can alter the concentration ratio of acetic acid to acetate ions. However, adding too much sodium hydroxide can completely neutralize the acetic acid, at which point there will no longer be a buffering effect. Similarly, if not enough sodium hydroxide is added, the buffer's concentration of acetate ions will be low, reducing its effectiveness. Therefore, the effectiveness of the buffer depends on achieving an appropriate ratio of acetic acid and acetate ions—neither too high nor too low.

Key concepts

Acetic Acid

Acetic acid, with the formula \( \text{CH}_3\text{COOH} \), is a common component in many laboratory and household settings because of its unique properties. It is a weak acid, meaning it doesn't completely dissociate in water. Upon dissolving, only a small fraction of its molecules release hydrogen ions (H\(^+\)) into the solution.

This partial dissociation is crucial in forming buffer systems. In the context of buffer solutions, acetic acid serves as the weak acid component. When acetic acid is present in a solution, it can donate H\(^+\) ions when necessary, which helps maintain a stable pH.

Its ability to donate and accept protons in fluctuating amounts without largely affecting its concentration makes it perfect for stabilizing the pH level in buffer solutions.

Sodium Hydroxide

Sodium hydroxide, \( \text{NaOH} \), is a strong base commonly used in neutralization reactions. When dissolved in water, sodium hydroxide dissociates entirely into sodium ions (Na\(^+\)) and hydroxide ions (OH\(^-\)). This strong base is crucial when creating buffer solutions as it reacts with acids to form water and salts.

In the mixing process with acetic acid, sodium hydroxide neutralizes part of the acid, resulting in the formation of sodium acetate (\( \text{CH}_3\text{COONa} \)). The key here is that only some of the acetic acid is neutralized. This preserves enough weak acid and its conjugate base—acetate ions—in the solution, creating a buffer system.

The interaction between sodium hydroxide and acetic acid illustrates the intricate balance needed to form a buffer. The effectiveness of a buffer can depend greatly on precisely balancing the amounts of each component.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is essential for understanding how buffers work. It provides a mathematical way to calculate the pH of a buffered solution. The equation is expressed as:

\[ pH = pK_a + \log{\frac{[\text{conjugate base}]}{[\text{weak acid}]}} \]

This equation shows how the ratio of the concentration of the conjugate base (acetate ions) to the concentration of the weak acid (acetic acid in our case) determines the pH of the buffer system.

The \( pK_a \) value is a constant that represents the strength of the weak acid. When the amounts of acetic acid and its conjugate base are balanced, the solution maintains its pH effectively even when acids or bases are added.

• Increasing the concentration of the conjugate base relative to the weak acid will result in a higher pH.
• Conversely, an increase in the weak acid's concentration will lower the pH.

This ratio balance is crucial for maintaining the buffered solution's effectiveness. Any significant change in concentration can affect the buffer's ability to stabilize pH, which is why precise measurement and mixing are essential.