Problem 23 - Chemistry The Central Science

Question

A buffer is prepared by adding \(20.0 \mathrm{~g}\) of sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) to \(500 \mathrm{~mL}\) of a \(0.150 \mathrm{M}\) acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) solution. (a) Determine the \(\mathrm{pH}\) of the buffer. (b) Write the complete ionic equation for the reaction that occurs when a few drops of hydrochloric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of sodium hydroxide solution are added to the buffer.

Step-by-Step Solution

Answer

The pH of the buffer solution is approximately 5.76. The complete ionic equation for the reaction between hydrochloric acid and buffer components is \(H^{+}(aq) + CH_3COO^{-}(aq) \rightarrow CH_3COOH(aq)\), and for the reaction between sodium hydroxide and buffer components is \(OH^{-}(aq) + CH_3COOH(aq) \rightarrow CH_3COO^{-}(aq) + H_2O(l)\).

Step 1: 1. Calculate the moles of sodium acetate and acetic acid in the buffer solution

To calculate the moles of sodium acetate, we can use the given mass and molecular weight of the substance: Moles of sodium acetate = (20.0 g) / (molecular weight of CH₃COONa) Molecular weight of CH₃COONa = (12.01 * 2) + (1.01 * 3) + (16.00 * 2) + (22.99 * 1) = 82.04 g/mol Moles of sodium acetate = 20.0 g / 82.04 g/mol ≈ 0.244 mol Now, let's calculate the moles of acetic acid: Moles of acetic acid = (0.150 mol/L) x (0.500 L) = 0.075 mol

Step 2: 2. Use the Henderson-Hasselbalch equation to determine the pH of the buffer

The Henderson-Hasselbalch equation is: pH = pKa + log ([A⁻] / [HA]) We're given that the acetic acid (CH₃COOH) has a pKa = 4.75. We have moles of sodium acetate (A⁻) and moles of acetic acid (HA), so we can calculate the pH: pH = 4.75 + log (0.244 mol / 0.075 mol) ≈ 4.75 + 1.01 ≈ 5.76 Thus, the pH of the buffer solution is approximately 5.76.

Step 3: 3. Write the complete ionic equation for the reaction between hydrochloric acid and the buffer constituents

When hydrochloric acid (HCl) is added to the buffer, it reacts with the acetate ion (CH₃COO⁻) from sodium acetate to form acetic acid: H⁺(aq) + Cl⁻(aq) + CH₃COO⁻(aq) -> CH₃COOH(aq) + Cl⁻(aq) The complete ionic equation is: H⁺(aq) + CH₃COO⁻(aq) -> CH₃COOH(aq)

Step 4: 4. Write the complete ionic equation for the effect that occurs when sodium hydroxide is added to the buffer

When sodium hydroxide (NaOH) is added to the buffer, it reacts with the undissociated acetic acid (CH₃COOH) to form sodium acetate: Na⁺(aq) + OH⁻(aq) + CH₃COOH(aq) -> CH₃COO⁻(aq) + H₂O(l) + Na⁺(aq) The complete ionic equation is: OH⁻(aq) + CH₃COOH(aq) -> CH₃COO⁻(aq) + H₂O(l) To summarize, the pH of the buffer solution is approximately 5.76. The complete ionic equation for the reaction between hydrochloric acid and buffer components is H⁺(aq) + CH₃COO⁻(aq) -> CH₃COOH(aq), and for the reaction between sodium hydroxide and buffer components is OH⁻(aq) + CH₃COOH(aq) -> CH₃COO⁻(aq) + H₂O(l).

Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is fundamental in understanding how buffer solutions work. It is a straightforward formula that relates the pH of a buffer solution to the concentration of acid and its conjugate base.
The equation is given by:\[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]Here, \(\text{pK}_a\) is the negative logarithm (base 10) of the acid dissociation constant (\(K_a\)) for the acid, \([\text{HA}]\) represents the concentration of the undissociated acid, and \([\text{A}^-]\) represents the concentration of the conjugate base.

A buffer solution consists of a weak acid and its conjugate base. In our example, the weak acid is acetic acid (CH₃COOH), and the conjugate base is acetate (CH₃COO⁻).
The Henderson-Hasselbalch equation helps in calculating the pH of the buffer by considering the relative concentrations of these two components.

Acetic Acid

Acetic acid is a common choice when creating buffer solutions due to its weak acidic properties.
It's composed of the chemical formula CH₃COOH. Among its unique characteristics, acetic acid partially dissociates in water, making it suitable as a component of buffer solutions.

In our problem scenario, acetic acid provides the proton (H⁺) in the buffer solution, interacting with acetate ions provided by sodium acetate. This interaction is crucial in maintaining the pH of the solution.
When you dissolve acetic acid in water, it establishes an equilibrium between its undissociated form (CH₃COOH) and the dissociated ions (CH₃COO⁻ and H⁺). This equilibrium is critical in its ability to resist changes in pH when acids or bases are added to the solution. The balance between these forms is what grants the buffer its effectiveness.

Ionic Equations

Writing complete ionic equations is an important step in understanding buffer reactions. These equations illustrate the species present in a reaction at the ionic level.

When hydrochloric acid (HCl) is added to a buffer solution containing acetic acid, the hydrogen ion (H⁺) from the HCl reacts with the acetate ion (CH₃COO⁻) to form more acetic acid.
The complete ionic equation simplifies this as:\[ \text{H}^+(\text{aq}) + \text{CH}_3\text{COO}^-(\text{aq}) \rightarrow \text{CH}_3\text{COOH}(\text{aq}) \]Similarly, when sodium hydroxide (NaOH) is added, the hydroxide ion (OH⁻) reacts with acetic acid to generate more acetate ions and water:\[ \text{OH}^-(\text{aq}) + \text{CH}_3\text{COOH}(\text{aq}) \rightarrow \text{CH}_3\text{COO}^-(\text{aq}) + \text{H}_2\text{O}(\text{l}) \]Understanding these ionic interactions is crucial in grasping how buffers can neutralize added acids and bases, thus maintaining a stable pH in solution.