Buffers - Chemistry | Scholardog

1. Fundamental Concepts

Definition: Buffers are solutions that resist changes in pH when small amounts of acid or base are added.
Components: A buffer typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.
Henderson-Hasselbalch Equation: The equation used to calculate the pH of a buffer solution: $$ \text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) $$

2. Key Concepts

Buffer Capacity: $$\text{Buffer capacity} = \frac{\Delta \text{Base}}{\Delta \text{pH}} = \frac{\Delta \text{Acid}}{\Delta \text{pH}}$$

pH Calculation: $$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$

Application: Buffers are used in biological systems, industrial processes, and laboratory experiments to maintain a stable pH environment.

3. Examples

Example 1 (Basic)

Problem: Calculate the pH of a buffer solution containing 0.1 M acetic acid ($$ \text{CH}_3\text{COOH} $$) and 0.1 M sodium acetate ($$ \text{CH}_3\text{COONa} $$). The $$ K_a $$ for acetic acid is $$ 1.8 \times 10^{-5} $$.

Step-by-Step Solution:

Calculate $$ \text{p}K_a $$: $$ \text{p}K_a = -\log(1.8 \times 10^{-5}) = 4.74 $$
Use the Henderson-Hasselbalch equation: $$ \text{pH} = 4.74 + \log\left(\frac{0.1}{0.1}\right) $$
Simplify: $$ \text{pH} = 4.74 + \log(1) = 4.74 $$

Validation: The calculated pH is 4.74, which is consistent with the expected pH for a buffer solution with equal concentrations of the weak acid and its conjugate base.

Example 2 (Intermediate)

Problem: A buffer solution is made by mixing 0.2 M formic acid ($$ \text{HCOOH} $$) and 0.3 M sodium formate ($$ \text{HCOONa} $$). The $$ K_a $$ for formic acid is $$ 1.8 \times 10^{-4} $$. Calculate the pH of the buffer solution.

Step-by-Step Solution:

Calculate $$ \text{p}K_a $$: $$ \text{p}K_a = -\log(1.8 \times 10^{-4}) = 3.74 $$
Use the Henderson-Hasselbalch equation: $$ \text{pH} = 3.74 + \log\left(\frac{0.3}{0.2}\right) $$
Simplify: $$ \text{pH} = 3.74 + \log(1.5) = 3.74 + 0.18 = 3.92 $$

Validation: The calculated pH is 3.92, which is within the expected range for a buffer solution with the given concentrations and $$ K_a $$.

4. Problem-Solving Techniques

Identify Components: Determine the weak acid and its conjugate base, or the weak base and its conjugate acid.
Use the Henderson-Hasselbalch Equation: Apply the equation to calculate the pH of the buffer solution.
Check Concentrations: Ensure the concentrations of the weak acid and its conjugate base are known or can be determined.
Substitute and Simplify: Substitute the known values into the equation and simplify to find the pH.