Question

What is the pH of 0.15 M acetic acid to which 1.56 g of sodium acetate, \(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\) has been added?

Short answer

The pH of the solution is approximately 3.86.

Step-by-step solution

Understand the Problem

We need to calculate the pH of a buffer solution made by adding sodium acetate to acetic acid. Acetic acid is a weak acid, and sodium acetate is its conjugate base. The solution requires the application of the Henderson-Hasselbalch equation.

Write Down Known Values

Given that the concentration of acetic acid is 0.15 M and the amount of sodium acetate added is 1.56 g. The molar mass of sodium acetate (NaCH3CO2) is approximately 82.03 g/mol.

Calculate Moles of Sodium Acetate

Calculate the number of moles of sodium acetate using its mass and molar mass. \[\text{Moles of } \text{NaCH}_3\text{CO}_2 = \frac{1.56 \, \text{g}}{82.03 \, \text{g/mol}} \approx 0.0190 \, \text{mol}\]

Determine Concentration of Sodium Acetate

Assuming the solution volume remains close to 1 L, the concentration of sodium acetate is approximately equal to its moles since only a small volume change occurs by adding the solute. Therefore, the acetate concentration is 0.0190 M.

Use the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation for a buffer solution is:\[pH = pK_a + \log \left( \frac{[\text{conjugate base}]}{[\text{acid}]} \right)\]Acetic acid has a pKa of approximately 4.76.

Calculate the pH

Substitute the known values into the Henderson-Hasselbalch equation:\[pH = 4.76 + \log \left( \frac{0.0190}{0.15} \right) \approx 4.76 + \log(0.1267) \approx 4.76 - 0.8973 \approx 3.86\]

Conclusion

The pH of the buffer solution, using the calculated concentrations and the Henderson-Hasselbalch equation, is approximately 3.86.

Key concepts

pH Calculation

The pH calculation is a fundamental step in chemistry, especially when dealing with solutions. It helps determine the acidity or basicity of a solution. Calculating pH involves understanding the concentration of hydrogen ions in the solution. However, when dealing with buffer solutions, the Henderson-Hasselbalch equation simplifies this process. Let's break down its application using the given problem.
In this scenario, we have a buffer composed of acetic acid and sodium acetate. The equation used here is:\[pH = pK_a + \log \left( \frac{[\text{conjugate base}]}{[\text{acid}]} \right)\]

• pKa is the negative logarithm of the acid dissociation constant.
• The log term considers the ratio of concentrations of the conjugate base to the acid.

For acetic acid, the pKa is approximately 4.76. By plugging in the calculated concentrations into the equation, the formula allows us to find the pH without significant computation difficulty. This method is especially useful in calculating the pH of buffered solutions.

Buffer Solution

A buffer solution is a unique chemical solution that maintains a relatively constant pH when small amounts of acid or base are added. This stability is crucial in many biological and chemical processes, ensuring that pH levels remain within a range that supports active reactions. In particular, buffers are mixtures typically composed of a weak acid and its conjugate base or a weak base and its conjugate acid.
In the given exercise, acetic acid and sodium acetate form such a buffer. Here is how it works: - **Acetic Acid**: This is the weak acid, providing hydrogen ions when needed. - **Sodium Acetate**: Acts as the conjugate base, removing excess hydrogen ions to resist pH changes.
By understanding this dual action, we can appreciate how buffer solutions neutralize small additions of other acids or bases. The Henderson-Hasselbalch equation allows us to predict how these components interact to maintain the desired pH.

Acetic Acid and Sodium Acetate

Acetic acid (CH₃COOH) and sodium acetate (NaCH₃CO₂) form a classic example of a buffer solution in practice. Acetic acid is a weak acid, partially dissociating in water to donate hydrogen ions. On the other hand, sodium acetate, being a salt, dissolves and dissociates completely, providing acetate ions (\[\text{CH}_3\text{COO}^-\]) to the solution.
This combination results in:

• **Acetic Acid**: Donor of hydrogen ions, contributing to the solution's acidity but not fully ionizing like a strong acid.
• **Sodium Acetate**: Supplies acetate ions, which act as a buffer component, reacting with any added hydrogen ions.

When these components are mixed, they create a balanced solution where the acetate ions buffer against changes in hydrogen ion concentration. This action is crucial when the solution experiences addition either of a stronger acid or base, maintaining the overall pH close to the calculated 3.86. This stable property is particularly important for various chemical and biological applications where pH consistency is needed.