Write an equation relating \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in solution at \(25^{\circ} \mathrm{C}\).

Chemical equilibrium pertains to the balance achieved in a chemical reaction when the rates of the forward and reverse reactions are equal, causing the concentrations of the reactants and products to remain constant over time. This concept is central to understanding reactions that produce ions, such as the self-ionization of water.

At the heart of this balance is the equilibrium constant, which for the ion product of water is denoted as \( K_w \). This constant matters greatly in acid-base chemistry because it quantifies the relation between hydronium \( [H^+] \) and hydroxide \( [OH^-] \) ions in aqueous solutions. It’s critical to realize that the equilibrium concept is not static but dynamic, where reactions still occur, but the concentrations no longer change, giving the appearance of stillness.

Acid-base chemistry is a subsection of chemical equilibrium that specifically looks at the proton exchanges occurring in solution. Acids are substances that increase the concentration of hydronium ions \( [H^+] \), while bases increase the concentration of hydroxide ions \( [OH^-] \).

The relationship between these ions is profoundly tied to the ion product of water \( K_w \), which serves as a foundational point in understanding how acids and bases behave in water. The balancing act between hydronium and hydroxide concentration directly impacts the solution's acidity or basicity, a property measurable with the pH scale.

The concentration of ions in a solution is the amount of ion present in a certain volume of the solution. At any given temperature, for pure water or a neutral solution, the product of hydronium and hydroxide ion concentrations always equals the ion product constant \( K_w \).

This ion product plays an invaluable role by setting up a benchmark to determine how the addition of acids or bases will shift the balance of ion concentration. Understanding that the concentrations of ions are interconnected allows us to predict how a solution will react to changes, such as dilution or the addition of other substances, within the confines of chemical equilibrium.

pH and pOH are values that measure the acidity and basicity of aqueous solutions, respectively. The pH is a logarithmic scale based on the concentration of hydronium ions \( [H^+] \), and the pOH is similarly based on the concentration of hydroxide ions \( [OH^-] \).

These scales are inversely related, and both stem from the ion product of water. For instance, neutral water at \(25^\circ C\) has a pH of 7 which also corresponds to a pOH of 7. The sum of pH and pOH always equals 14, which is derived from the negative log of \( K_w \). This relationship is crucial for calculating either the hydronium or hydroxide ion concentration when given one or the other.