Question

Preparation of an Acetate Buffer Calculate the concentrations of acetic acid \(\left(\mathrm{p} K_{\mathrm{n}}-4.76\right)\) and sodium acetate necessary to prepare a \(0.2\) m buffer solution at pH \(5.0\).

Short answer

Acetic acid: 0.073 M, Sodium acetate: 0.127 M.

Step-by-step solution

Understand the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH, pKa, and the concentrations of an acid and its conjugate base in a buffer solution. The equation is given by: \[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \] where \([\text{A}^-]\) is the concentration of the conjugate base (sodium acetate) and \([\text{HA}]\) is the concentration of the acid (acetic acid).

Set Up the Equation Using Given Values

We are given that the desired pH is 5.0 and the pKa is 4.76. Substitute these into the Henderson-Hasselbalch equation: \[ 5.0 = 4.76 + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \] Solve for the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \).

Solve for the Ratio of Base to Acid

Rearrange the equation to solve for the ratio: \[ \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) = 5.0 - 4.76 = 0.24 \] Apply the antilog to find the ratio: \[ \frac{[\text{A}^-]}{[\text{HA}]} = 10^{0.24} \approx 1.74 \] This means the concentration of sodium acetate is 1.74 times that of acetic acid.

Determine Total Concentrations

The total concentration of the buffer is given as 0.2 M. Therefore, \([\text{A}^-] + [\text{HA}] = 0.2\) M. Let \([\text{HA}] = x\), then \([\text{A}^-] = 1.74x\). Substitute into the equation: \[ x + 1.74x = 0.2 \] Simplifying gives us \[ 2.74x = 0.2 \].

Solve for Individual Concentrations

Solve for \(x\): \[ x = \frac{0.2}{2.74} \approx 0.073 \] The concentration of acetic acid \([\text{HA}] = 0.073\) M. Then, \([\text{A}^-] = 1.74 \times 0.073 \approx 0.127 \) M. Thus, the concentrations are approximately 0.073 M for acetic acid and 0.127 M for sodium acetate.

Key concepts

Buffer Solution

A buffer solution is a special type of solution that resists significant changes in its pH level, even when small amounts of an acid or a base are added. This resistance is crucial in many chemical and biological processes that require a stable pH environment.

Buffer solutions are composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• They are often used in laboratories to maintain a steady pH during experiments.
• In biological systems, buffers help maintain homeostasis, allowing organisms to function smoothly.

Understanding how buffers work is essential when preparing experiments or interpreting their results. In the context of our problem, the buffer solution is composed of acetic acid and sodium acetate.

Acetic Acid

Acetic acid, with the chemical formula \(CH_3COOH\), is a weak acid commonly found in vinegar. As a weak acid, it does not completely dissociate in water, making it ideal for forming buffer solutions.

Acetic acid in a solution participates by partially donating protons \(\text{H}^+\) ions to the solution, maintaining equilibrium. This capability is critical in buffering systems where it can resist dramatic changes in pH.

• The acid's dissociation is represented as: \[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]
• It works in tandem with its conjugate base, acetate ion \((CH_3COO^-)\).

In our exercise, acetic acid provides the acidic component necessary for the buffer, whilst maintaining a given pH level.

Sodium Acetate

Sodium acetate, \( ext{CH}_3 ext{COONa} \), is the sodium salt of acetic acid. It acts as the conjugate base in our buffer system.

When dissolved in water, sodium acetate dissociates completely to form acetate ions \((CH_3COO^-)\) and sodium ions \((Na^+)\). The acetate ions interact with hydronium ions present in the solution to form acetic acid, thus neutralizing the added acid and stabilizing the pH.

• The dissociation is shown by the equation: \[ \text{CH}_3 ext{COONa} \rightarrow \text{CH}_3 ext{COO}^- + \text{Na}^+ \]
• The acetate ions balance any added acid with minimal change in pH.

In our buffer preparation, the concentration of sodium acetate is crucial to achieve the desired buffer strength and maintain pH at the specified level.

pH Calculation

To determine the pH of a buffer solution, we apply the Henderson-Hasselbalch equation, a fundamental equation in chemistry for calculating pH values in buffer solutions.

This equation allows us to connect pH with the ratio of the concentrations of the acid and its conjugate base. The equation is formulated as:\[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]

• \(\text{pKa}\) is the dissociation constant of the acid, giving a measure of acid strength.
• \([\text{A}^-]\) and \([\text{HA}]\) are the concentrations of the conjugate base and acid respectively.

For our buffer solution, we solve the equation step by step to find the concentrations of acetic acid and sodium acetate required to reach a pH of 5.0. Utilizing an accurate ratio of base to acid is key for the buffer to adequately resist pH changes.