A buffer solution is prepared by mixing \(75.0 \mathrm{~mL}\) of \(0.275 \mathrm{M}\) fluorobenzoic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{~F}\right)\) with \(55.0 \mathrm{~mL}\) of \(0.472 \mathrm{M}\) so- dium fluorobenzoate. The \(\mathrm{p} K_{\mathrm{a}}\) of this weak acid is \(2.90\). What is the \(\mathrm{pH}\) of the buffer solution?

The Henderson-Hasselbalch equation is a fundamental formula used to estimate the pH of buffer solutions. It provides a straightforward relationship between the pH of a solution, the pKa (the -log of the acid dissociation constant, Ka) of the weak acid present in the buffer, and the ratio of the concentrations of the conjugate base (\text{A}^-) to the weak acid (\text{HA}). The equation is expressed as:
\[ \text{pH} = \text{pKa} + \log\left(\frac{\text{[A}^-\text{]}}{\text{[HA]}}\right) \]
In this equation, the 'log' is the base-10 logarithm. Understanding how to apply this equation is crucial for many chemistry problems, such as calculating the pH of buffer solutions after dilution or mixing different solutions.

When a weak acid dissolves in water, it partially dissociates into its conjugate base and protons. Unlike strong acids, which dissociate completely, weak acids maintain an equilibrium between the undissociated acid and the ions in solution. This equilibrium is characterized by the acid dissociation constant, Ka, which provides a measure of the acid's strength. In contrast, the pKa is the negative logarithm of Ka and provides a more convenient term for working with acid strengths, as it offers a direct scale that corresponds to pH values. The relationship of a weak acid with its conjugate base is crucial in buffers, since they resist changes in pH upon the addition of small amounts of acid or base due to this equilibrium dynamic.

The pKa is a key chemical property that represents the strength of an acid. It's defined as the negative base-10 logarithm of the acid dissociation constant (Ka). In essence, the lower the value of pKa, the stronger the acid. For any weak acid, the pKa value is essential when using the Henderson-Hasselbalch equation to determine the pH of a buffer solution. Generally, pKa is used instead of Ka because it falls into a smaller and more manageable numerical range. Knowing the pKa allows chemists to predict how an acid will behave in a mixture and how it will influence the pH of a solution.

The molarity (M) of a solution is a measurement of the concentration of a solute in a solution, expressed as moles of solute per liter of solution. The volume (V) is simply the amount of space that the solution occupies, usually measured in liters or milliliters. For buffer solutions, the final pH depends not just on the concentrations of weak acid and conjugate base, but also on their absolute amounts, which are determined by multiplying their molarities by their volumes.
When calculating the pH of a buffer solution, the mole ratio of the weak acid to its conjugate base is particularly significant. This ratio can be found by dividing the number of moles of the weak acid by the number of moles of the conjugate base, each calculated from their respective molarity and volume. The Henderson-Hasselbalch equation uses this ratio, pKa value and allows the chemist to calculate the pH of the buffer solution.