Question

The \(\mathrm{pH}\) of a buffer solution containing \(0.10 \mathrm{M}\) acetic acid and \(0.10 M\) sodium acetate is 4.74 . (a) Write the Henderson-Hasselbalch equation for this buffer. (b) Write the equations for reaction of this buffer with a small amount of \(\mathrm{HNO}_{3}\) and with a small amount of \(\mathrm{NaOH}\).

Short answer

(a) \(\text{pH} = \text{p}K_a + \log\left(\frac{[\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}\right)\). (b) \(\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH}\); \(\text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O}\).

Step-by-step solution

Write the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation for a buffer solution is given as follows:\[ \text{pH} = \text{p}K_a + \log\left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]Where:- \([\text{A}^-]\) is the concentration of the conjugate base (sodium acetate, \(\text{CH}_3\text{COO}^-\)).- \([\text{HA}]\) is the concentration of the weak acid (acetic acid, \(\text{CH}_3\text{COOH}\)).- \(\text{p}K_a\) is the negative logarithm of the acid dissociation constant. Plugging in the given concentrations and pH:\[ 4.74 = \text{p}K_a + \log\left( \frac{0.10}{0.10} \right) \]

Simplify the Henderson-Hasselbalch Equation

Simplifying the expression:\[ 4.74 = \text{p}K_a + \log(1) \]Since \(\log(1) = 0\), we have:\[ 4.74 = \text{p}K_a \]

Reaction with HNO3

When \(\text{HNO}_3\) is added to the buffer, it reacts with the conjugate base:\[ \text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH} \]This reaction shifts the equilibrium to consume some of the added \(\text{H}^+\) ions.

Reaction with NaOH

When \(\text{NaOH}\) is added, it reacts with the acetic acid:\[ \text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \]This reaction consumes the \(\text{OH}^-\) ions and forms more conjugate base.

Key concepts

Buffer Solution

A buffer solution is a unique mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid. Its significant role is to maintain a steady pH level in a solution, even when small amounts of acid or base are added.
This makes buffers crucial in many scientific and practical applications. Think of them as pH guardians that work to prevent drastic changes in acidity or alkalinity.
Key characteristics of buffer solutions:

• They can resist changes in pH by neutralizing added acids (H⁺) or bases (OH^-).
• Typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid, in equilibrium.
• Commonly used in biochemical processes, industrial applications, and laboratories.

The effectiveness of a buffer is determined by its capacity and range, meaning how much acid or base it can neutralize before the pH begins to change significantly.
A good buffer has both components in relatively equal concentrations, maximizing its ability to respond to pH changes effectively.

Acetic Acid

Acetic acid, a familiar chemical compound to most of us, is the primary component of vinegar that gives it the sour taste and pungent smell.
Chemically represented as \( ext{CH}_3 ext{COOH}\), it is a weak acid, and thus only partially ionizes in water.
Key characteristics of acetic acid:

• Essential component in biological and chemical buffer systems, due to its weak acidic nature.
• Functions as the weak acid component in many acetic acid-based buffer solutions.
• Its dissociation in water is represented by the equation: \( ext{CH}_3 ext{COOH} \rightleftharpoons ext{CH}_3 ext{COO}^- + ext{H}^+\).

In a buffer solution, acetic acid can donate protons (H⁺) to the solution when an alkali (like NaOH) is added, slightly increasing the concentration of its conjugate base, \( ext{CH}_3 ext{COO}^-\).
This interaction highlights its role in stabilizing the pH of the solution.

Sodium Acetate

Sodium acetate is the salt form of acetic acid and is highly soluble in water.
Its chemical formula is \( ext{CH}_3 ext{COONa}\), and in a buffer solution, it acts as the conjugate base.
Key roles of sodium acetate include:

• Serving as the conjugate base in acetic acid-sodium acetate buffer systems.
• Reacting with added acids to neutralize them, thus preventing a significant pH shift.
• Dissociates completely in water, enriching the solution with acetate ions \( ext{CH}_3 ext{COO}^-\).

When an acid like \( ext{HNO}_3\) is introduced into the buffer, the acetate ions from sodium acetate react with the added \( ext{H}^+\) ions:
\[\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH}\]
Through this reaction, the HSodium acetate stabilizes the pH by converting into acetic acid, thus maintaining the buffer balance.

Acid-Base Reaction

Acid-base reactions are fundamental processes in chemistry where an acid donates protons (H⁺ ions) and a base accepts them.
In the context of buffer solutions like the acetic acid-sodium acetate system, these reactions play a crucial role in pH regulation.
Key points about acid-base reactions:

• In a buffer, the weak acid and its conjugate base pair work together to neutralize added acids or bases.
• When an acid is added, it typically reacts with the buffer's conjugate base component.
• Conversely, added bases react with the weak acid component of the buffer.

For instance, when \(\text{HNO}_3\) is added to the buffer, the excess \(\text{H}^+\) ions are neutralized by the acetate ions, minimizing pH change:
\[\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH}\]If \(\text{NaOH}\) is added, the \(\text{OH}^-\) ions react with acetic acid, creating more acetate ions:\[\text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O}\]By managing these reactions effectively, buffer systems maintain a stable pH even under different conditions, ensuring their invaluable role in various fields of science and technology.