Question

Calculate the pH of a solution that has an acetic acid concentration of \(0.050 \mathrm{M}\) and a sodium acetate concentration of \(0.075 \mathrm{M}.\)

Short answer

The pH of the solution is approximately 4.94.

Step-by-step solution

Identify the Buffer System

The solution is a buffer system consisting of acetic acid (\( CH_3COOH \)) and its conjugate base, sodium acetate (\( CH_3COONa \)). The common ion effect will stabilize the pH.

Write the Acid Dissociation Equation

For acetic acid, the dissociation in water can be represented as: \[ CH_3COOH \rightarrow H^+ + CH_3COO^- \]

Use the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is: \[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \] where \( [\text{A}^-] \) is the concentration of acetate ion and \( [\text{HA}] \) is the concentration of acetic acid.

Find the pKa of Acetic Acid

The \( \text{pKa} \) of acetic acid is approximately 4.76.

Calculate the pH

Substitute the values into the Henderson-Hasselbalch equation: \[ \text{pH} = 4.76 + \log \left( \frac{0.075}{0.050} \right) \] Calculate the logarithm: \[ \log \left( \frac{0.075}{0.050} \right) = \log(1.5) \approx 0.176 \] Therefore, \[ \text{pH} = 4.76 + 0.176 = 4.936 \]

Verify the Calculation

Ensure the calculations and unit conversions were performed correctly and recheck the significant figures.

Key concepts

Buffer System

A buffer system is a solution that resists changes in pH when small amounts of acid or base are added. It typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.
Buffers are essential in maintaining a stable pH in various chemical and biological systems, such as human blood.

• In our exercise, the buffer system comprises acetic acid ( CH_3COOH ) and sodium acetate ( CH_3COONa ).
• The acetic acid acts as the weak acid, and sodium acetate provides the acetate ion, the conjugate base.

In this buffer system, the acetic acid can neutralize added bases by donating a proton, while acetate ions can neutralize added acids by accepting a proton.
This interplay stabilizes the pH, making buffer solutions invaluable for chemical reactions needing a constant pH environment.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a fundamental tool for calculating the pH of buffer systems. This equation relates the pH of the solution to the pKa of the acid and the ratio of the concentrations of its conjugate base and the acid.
The equation is given by:\[\text{pH} = \text{pKa} + \log \left(\frac{[\text{A}^-]}{[\text{HA}]}\right)\]

• \([\text{A}^-]\): concentration of the conjugate base (acetate ion in our example).
• \([\text{HA}]\): concentration of the weak acid (acetic acid in our example).

This equation is particularly convenient because it provides a simple way to relate directly measurable quantities (concentrations) to pH.
It allows us to efficiently calculate or adjust the pH in various buffer systems by modifying concentrations of the acid and its conjugate base.

Acetic Acid and Sodium Acetate Buffer

An acetic acid and sodium acetate buffer is a classic example of a buffer system made from a weak acid and its conjugate base. It is frequently used in laboratories due to its effectiveness in maintaining pH around 4.76, the pKa of acetic acid.
The composition:

• Acetic acid ( CH_3COOH ) - the weak acid.
• Sodium acetate ( CH_3COONa ) - provides the acetate ion, the conjugate base.

The acetic acid donates protons to neutralize added base, while the acetate ion neutralizes added acid by accepting protons.
This balance helps maintain a stable pH, even when faced with external changes. By adjusting the concentrations of acetic acid and sodium acetate, one can fine-tune the pH of the buffer, making it versatile for various experimental requirements.