Consider an acid HY (MM = \(100 \mathrm{~g} /\) mol [3 significant figures]). What is the \(\mathrm{pH}\) of a \(33.0 \%\) by mass solution of HY \((d=1.10 \mathrm{~g} / \mathrm{mL})\) ? The \(K_{n}\) of \(\mathrm{HY}\) is \(2.0 \times 10^{-8}\)

Acid-base equilibrium is a fundamental concept in chemistry that governs the balance between acids and bases in a solution. It is the state where the rates of the forward and reverse reactions are equal, leading to a constant composition of the solution over time. This equilibrium is key to calculating pH, which is a measure of the acidity or basicity of a solution.

For a monoprotic acid, which is an acid that donates one proton (H+ ion), like HY in our example, the acid-base equilibrium can be represented as follows: \[ \text{HY} \rightleftharpoons \text{H}^+ + \text{Y}^- \]
At equilibrium, the concentration of the products (H+ and Y-) and the reactant (HY) reaches a state where they remain constant. This state is described by an equilibrium constant known as the ionization constant, which we delve into more deeply in its own section. By understanding acid-base equilibrium, we can predict the extent of ionization of an acid in solution and therefore determine the pH.

Molarity and concentration are critical when it comes to understanding chemical solutions and calculating pH. Molarity, denoted as M, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution.\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]
The molarity tells us how 'strong' or 'concentrated' an acid or base is in a solution. In the context of pH calculation, the concentration of hydrogen ions, H+, is particularly important because the pH is the negative logarithm of the H+ concentration.\[ \text{pH} = -\text{log}_{10}[H^+] \]
In our example, the molarity of the acidic solution is directly calculated from the mass percentage and density of the solution, leading to a more accurate determination of the pH. Understanding how to convert mass percentages and densities into molarities is vital for this process.

The ionization constant, often represented by Ka or Kn for acids, is a value that indicates the strength of an acid or base in solution. It is specific to each acid or base and is a fixed value at a given temperature. The ionization constant plays a crucial role in calculating the pH of a solution because it allows us to understand the degree to which an acid or base dissociates in water.For our example, the ionization of HY in water is:\[ \text{HY} \rightleftharpoons \text{H}^+ + \text{Y}^- \]
The ionization constant expression for this reaction is:\[ K_n = \frac{[H^+][Y^-]}{[HY]} \]
When the acid dissociates, we assume that the concentration of H+ is equal to the concentration of Y- because for every molecule of HY that ionizes, one molecule of H+ and one molecule of Y- are formed. Therefore, the equilibrium expression can be simplified as follows:\[ K_n = \frac{[H^+]^2}{[HY]} \]
By knowing the Kn, the molarity of the acid solution, and doing some algebra, we are able to calculate the concentration of H+ ions. From the concentration of H+, the pH can be easily determined. The smaller the ionization constant, the weaker the acid, which leads to fewer H+ ions being produced and a higher pH (less acidic solution). Understanding the ionization constant is key to mastering pH calculations in acid-base chemistry.