Calculate The Ph of Each of The Following Buffered Solutions.

Calculating the pH of buffered solutions is essential in chemistry, biology, and environmental science. A buffer solution resists changes in pH when small amounts of acid or base are added. The Henderson-Hasselbalch equation is the standard method for calculating the pH of buffered solutions.

Introduction to Buffered Solutions

A buffered solution consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. These components work together to maintain a relatively constant pH, even when small amounts of acid or base are added.

Buffered solutions are widely used in laboratory settings, medical applications, and industrial processes. Understanding how to calculate the pH of buffered solutions is crucial for scientists and researchers working with chemical equilibria.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to calculate the pH of a buffered solution. The equation is derived from the definition of pH and the equilibrium constant for the dissociation of a weak acid.

Formula

pH = pKa + log₁₀([A^-]/[HA])

Where:

pH is the negative logarithm of the hydrogen ion concentration
pKa is the negative logarithm of the acid dissociation constant
[A^-] is the concentration of the conjugate base
[HA] is the concentration of the weak acid

The Henderson-Hasselbalch equation shows that the pH of a buffered solution depends on the ratio of the concentrations of the conjugate base to the weak acid. When the concentrations are equal, the pH equals the pKa of the weak acid.

Worked Examples

Let's look at two examples to illustrate how to calculate the pH of buffered solutions.

Example 1: Acetic Acid Buffer

Consider a buffer solution containing 0.1 M acetic acid (CH₃COOH) and 0.1 M sodium acetate (CH₃COONa). The pKa of acetic acid is 4.76.

Using the Henderson-Hasselbalch equation:

pH = pKa + log₁₀([CH₃COONa]/[CH₃COOH])

pH = 4.76 + log₁₀(0.1/0.1)

pH = 4.76 + log₁₀(1)

pH = 4.76 + 0 = 4.76

The pH of this buffer solution is 4.76, which matches the pKa of acetic acid.

Example 2: Phosphate Buffer

Now consider a buffer solution containing 0.05 M sodium dihydrogen phosphate (NaH₂PO₄) and 0.05 M disodium phosphate (Na₂HPO₄). The pKa of the phosphate buffer is 7.2.

Using the Henderson-Hasselbalch equation:

pH = pKa + log₁₀([Na₂HPO₄]/[NaH₂PO₄])

pH = 7.2 + log₁₀(0.05/0.05)

pH = 7.2 + log₁₀(1)

pH = 7.2 + 0 = 7.2

The pH of this buffer solution is 7.2, which matches the pKa of the phosphate buffer.

Frequently Asked Questions

What is the Henderson-Hasselbalch equation used for?

The Henderson-Hasselbalch equation is used to calculate the pH of buffered solutions. It shows the relationship between the pH, the pKa of the weak acid, and the ratio of the concentrations of the conjugate base to the weak acid.

When is the pH of a buffered solution equal to its pKa?

The pH of a buffered solution is equal to its pKa when the concentrations of the conjugate base and the weak acid are equal. This occurs when the ratio [A^-]/[HA] equals 1.

What are some common buffer systems?

Common buffer systems include acetic acid/acetate, phosphate, and carbonate/bicarbonate. Each of these systems has a specific pKa range and is suitable for different applications in chemistry and biology.

How do you prepare a buffered solution?

To prepare a buffered solution, you need to mix a weak acid with its conjugate base or a weak base with its conjugate acid. The concentrations of the components should be equal to achieve the desired pH.

What factors affect the pH of a buffered solution?

The pH of a buffered solution is affected by the ratio of the concentrations of the conjugate base to the weak acid, the pKa of the weak acid, and the total concentration of the buffer components.