Given \(0.1 M\) solutions of acetic acid and sodium acetate, describe the preparation of \(1 \mathrm{L}\) of \(0.1 \mathrm{M}\) acetate buffer at a pH of 5.4.

The Henderson-Hasselbalch equation is a fundamental tool when preparing buffer solutions. This formula relates the pH of a buffer to the pKa (acid dissociation constant) of the acid and the ratio of the concentrations of its conjugate base and the acid itself. It can be expressed as:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
When preparing an acetate buffer, the equation helps us determine the necessary ratio of acetate ions (A^-) to acetic acid (HA) to achieve the desired pH. This balance is crucial, as it maintains the pH within a narrow range, buffering against changes when acids or bases are added. The calculated ratio then guides the volumes of acetic acid and sodium acetate needed to create the buffer.

The pKa value is critical for understanding acid-base chemistry and is essential in buffer preparation. It's defined as the negative logarithm of the acid dissociation constant (Ka). For acetic acid, the pKa value is commonly known to be 4.76. This value signifies the strength of the acid: the lower the pKa, the stronger the acid. In the context of the Henderson-Hasselbalch equation, the pKa allows us to calculate the pH or vice versa if the ratio of the conjugate base to acid concentrations is known. This understanding is fundamental when mixing buffer components to ensure they will maintain the pH under various conditions.

The ratio of buffer components in a solution is directly obtained from the Henderson-Hasselbalch equation. In a buffer system, this ratio dictates how the system can resist pH changes. For an acetate buffer with a desired pH of 5.4, the calculated ratio from the equation is \( \frac{[\text{A}^-]}{[\text{HA}]} = 4.37 \). This tells us that for every mole of acetic acid present, there needs to be 4.37 moles of acetate ions to maintain the desired pH. Maintaining the correct ratio is vital for the buffer's efficacy. If too much of one component is present without the correct proportion of the other, the buffer capacity to resist pH changes will be compromised.

Molarity (M) is the number of moles of a solute per liter of solution, and it is an essential concept for preparing solutions in chemistry. Understanding molarity allows us to calculate the volumes of different solutions needed to prepare a buffer with specific concentration and volume. For our 0.1 M acetate buffer, we use the molarity and the moles calculated for each component (acetic acid and sodium acetate) to find the volumes required. With the molarity being constant at 0.1 M for both the acetic acid and sodium acetate solutions, the volumes are directly proportional to the number of moles needed for each substance, allowing us to mix these volumes accurately to result in a final 1L solution of the desired concentration and pH.