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The Henderson-Hasselbalch equation is a handy formula used mainly in biochemistry and chemistry to calculate the pH of buffer solutions. A buffer solution contains a weak acid and its conjugate base. This equation relates the acidity (pH) to the concentration of the acid ( ext{[HA]}), its conjugate base ( ext{[A^-]}), and the acid's ionization constant (pK鈧�). The equation is expressed as follows: \[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]This comes in handy when you know the quantities of an acid and its conjugate base in a solution because it directly links these concentrations to the pH - a crucial indicator of acidity or alkalinity.
This equation assumes that the concentrations of acidic and basic components do not change significantly upon decomposition, making it perfect for buffer solutions as they resist changes in pH when small amounts of acid or base are added.

Acetic acid, also known chemically as CH鈧僀OOH, is a typical example of a weak acid. It's a colorless, pungent liquid that is present in vinegar at about 4-7% concentration. - **Weak Acid**: Acetic acid partially ionizes in a solution, meaning only some percentage of its molecules donate H鈦� ions to the solution.- **Acid Dissociation Constant \( K_a \)**: The acid dissociation constant \(K_a\) for acetic acid is a measure of its degree of ionization, which is \(1.7 \times 10^{-5}\). This relatively low \(K_a\) indicates that it is not fully energetic at ionizing, hence the classification as a weak acid.
In a buffer solution comprising acetic acid and its conjugate base, like the one described in this exercise, acetic acid plays a critical role in maintaining a stable pH by accepting H鈦� from added bases.

Sodium acetate ( ext{CH}_3 ext{COONa}) is the sodium salt of acetic acid, featuring prominently as the conjugate base. It is often found in this form: - **Conjugate Base**: In a solution, sodium acetate dissociates into sodium ions ( ext{Na}^+) and acetate ions ( ext{CH}_3 ext{COO}^-). The acetate ions are the key players here, acting as the conjugate base in our buffer solution. - **Buffer Action**: They act to neutralize added acids, combining with H鈦� ions to reform acetic acid, thus preventing any significant change in the pH.
The equilibrium between sodium acetate and acetic acid in a solution is crucial for sustaining pH levels. It provides a resistance to drastic changes by alternately accepting or donating H鈦� ions, hence facilitating the buffering action.

The process of calculating the pH of a buffer solution involves several steps but relies heavily on the use of the Henderson-Hasselbalch equation. Let's break it down:1. **Calculate Initial Concentrations**: First, determine the concentration of the weak acid (acetic acid) and the conjugate base (sodium acetate) after mixing.2. **Account for Reactions**: Consider how the addition of other substances like ext{NaOH} could affect these concentrations, as NaOH reacts with acetic acid, altering initial amounts.3. **Use the Equation**: Plug these equilibrium concentrations into the Henderson-Hasselbalch equation, alongside the ext{pK鈧恾 of acetic acid (which is calculated as \ \log(1.7 \times 10^{-5}) = 4.77).
Working through these steps for the example provided, the pH can be determined as follows:\[ \text{pH} = 4.77 + \log\left(\frac{0.0876}{0.0541}\right) = 4.98 \]This means the buffer resists significant pH changes, remaining around 4.98 even when NaOH is added.