9.8 Buffer Solutions and Their Applications

A buffer solution is a solution that resists significant changes in pH upon the addition of a small amount of acid or base. Such solutions maintain a relatively constant pH, even over long periods.

9.8.1 Types of Buffer Solutions

There are two primary types of buffer solutions:

1. Acidic Buffers: Formed by mixing a weak acid with a salt of that acid and a strong base. These buffers have a pH value of less than 7.

   • Example: A solution of acetic acid ($\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$) and sodium acetate ($\mathrm{C}{\mathrm{H}}_3\mathrm{COONa}$).

2. Basic Buffers: Formed by mixing a weak base with a salt of that base and a strong acid. These buffers have a pH value greater than 7.

   • Example: A solution of ammonium hydroxide ($\mathrm{N}{\mathrm{H}}_4\mathrm{OH}$) and ammonium chloride ($\mathrm{N}{\mathrm{H}}_4\mathrm{Cl}$).

9.8.2 Buffer Action

A buffer resists pH change by neutralising any added acid or base using its components.

Acidic Buffer Action (e.g., CH₃COOH / CH₃COONa)

When a small amount of strong acid (H⁺) is added: The conjugate base (acetate ion) from the salt reacts with the added H⁺: $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}+{\mathrm{H}}^{+}\to \mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ The H⁺ is consumed, so the pH decreases only slightly.

When a small amount of strong base (OH⁻) is added: The weak acid component reacts with the added OH⁻: $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}+\mathrm{O}{\mathrm{H}}^{-}\to \mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}+{\mathrm{H}}_2\mathrm{O}$ The OH⁻ is consumed, so the pH increases only slightly.

9.8.3 Calculation of pH of Buffer Solutions

The pH of a buffer solution is calculated using the Henderson-Hasselbalch equation, which relates pH (or pOH) to the $p{K}_a$ (or $p{K}_b$) and the ratio of the concentrations of the conjugate acid-base pair.

Since the salt is a strong electrolyte, the concentration of the conjugate species is approximated as equal to the concentration of the salt.

For Acidic Buffers

$\text{pH}={\text{pK}}_{\text{a}}+\log \frac{[\text{salt}]}{[\text{acid}]}$

For Basic Buffers

$\text{pOH}={\text{pK}}_{\text{b}}+\log \frac{[\text{salt}]}{[\text{base}]}$

Worked Examples

Example 9.6

What is the pH of a buffer if the concentration of $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ is 0.1 M and $\mathrm{C}{\mathrm{H}}_3\mathrm{COONa}$ is 1.0 M? The $p{K}_a$ for $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ is 4.76.

Solution

1. Given:

   • $[\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}]=0.1\text{M}$
   • $[\mathrm{C}{\mathrm{H}}_3\mathrm{COONa}]=1.0\text{M}$
   • $p{K}_a=4.76$

2. Apply the Henderson-Hasselbalch equation: $\text{pH}={\text{pK}}_{\text{a}}+\log \frac{[\text{salt}]}{[\text{acid}]}$

3. Calculate: $\text{pH}=4.76+\log \frac{1.0}{0.1}=4.76+\log (10)=4.76+1.00=5.76$

Example 9.7

Calculate the pH of a buffer solution containing 0.11 M $\mathrm{C}{\mathrm{H}}_3\mathrm{COONa}$ and 0.09 M $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$. The $K_a$ for $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ is $1.8\times 10^{-5}$.

Solution

1. Given:

   • $[\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}]=0.09\text{M}$
   • $[\mathrm{C}{\mathrm{H}}_3\mathrm{COONa}]=0.11\text{M}$
   • $K_a=1.8\times 10^{-5}$

2. Calculate $p{K}_a$: $p{K}_a=-\log (1.8\times 10^{-5})=4.74$

3. Apply Henderson-Hasselbalch: $\text{pH}=4.74+\log \frac{0.11}{0.09}=4.74+\log (1.222)=4.74+0.087\approx 4.83$

9.8.4 Buffers in Biological Systems

Buffers are crucial for maintaining stable pH levels in biological systems, which is essential for the proper functioning of enzymes and other biochemical processes.

The primary buffer system in human blood is the carbonic acid–bicarbonate system (${\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_3$ / $\mathrm{HC}{\mathrm{O}}_3^{-}$), which maintains blood pH between 7.35 and 7.45. Deviation from this range causes acidosis (pH < 7.35) or alkalosis (pH > 7.45).

Other applications of buffers include:

• Electroplating: Maintaining consistent pH for uniform metal deposition.
• Bacteriological culture media: Maintaining optimal pH for microbial growth.
• Pharmaceutical formulations: Ensuring drug stability and efficacy.