Explain what happens to (a) the \(\mathrm{pH}\) of a phosphoric acid solution after the addition of solid sodium dihydrogen phosphate; (b) the percentage deprotonation of HCN in a hydrocyanic acid solution after the addition of hydrobromic acid; (c) the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\)ions when pyridinium chloride is added to a pyridine solution.

In the world of chemistry, the pH is a vital measure that indicates how acidic or basic a solution is. The pH scale ranges from 0 to 14 with 7 being neutral, below 7 acidic, and above 7 basic. When it comes to understanding what happens to the pH of a phosphoric acid solution after adding a salt such as sodium dihydrogen phosphate, we encounter the common-ion effect.
In our scenario, adding sodium dihydrogen phosphate brings more dihydrogen phosphate ions into the mix, which is a common ion already present in the weak acid solution. What occurs next is guided by the principle of equilibrium: the excess common ion from the salt suppresses further ionization of phosphoric acid. This leads to fewer H+ ions being free in the solution, causing the pH to rise, making the solution less acidic. Le Chatelier's Principle helps us understand this by suggesting that the equilibrium will adjust to counteract the change introduced by the added salt. For students grappling with pH calculations, it's important to remember that these principles allow us to predict changes without complicated calculations.

The degree of deprotonation refers to the extent to which a compound loses its protons (H+ ions) in a solution, which corresponds to the percentage of a substance that is ionized. When it comes to a solution of hydrocyanic acid (HCN), adding hydrobromic acid (HBr), a strong acid, can have a noticeable impact.
Adding a strong acid like HBr increases the concentration of free H+ ions. In equilibrium terms, this supernumerary of H+ ions pushes the deprotonation of HCN to reverse, meaning it 'pushes back' the ionization of HCN. As the percentage of deprotonated HCN molecules decreases, the percentage of deprotonation drops. It's like adding more of the product of a reversed reaction—the system will adjust to produce less of it, according to Le Chatelier's principle. For chemistry students, understanding this concept is key to predicting how the addition of other substances will affect the behavior of weak acids and bases in solution.

Le Chatelier's Principle is a cornerstone concept in chemistry, providing valuable insights into how dynamic systems respond to disturbances. It posits that if a dynamic equilibrium is disturbed by changing the conditions, such as concentration, temperature, or pressure, the system will adjust or shift to counteract the disturbance and restore a new equilibrium.
For instance, when sodium dihydrogen phosphate is added to a phosphoric acid solution, the system initially contains more dihydrogen phosphate ions than at equilibrium. To reduce this stress, the system shifts left to lower the concentration of these ions by reducing their production. This shift leads to a higher pH. Such shifts in equilibrium in response to changes are imperative for students to understand the predictability and control of chemical reactions, especially in areas like pharmacology, environmental science, or any field where chemicals are in use.

The concentration of hydroxonium ions (\(\mathrm{H}_3\mathrm{O}^+\) ions) is another key factor in determining the acidity of a solution. Whenever a solution's pH decreases, it implies that the concentration of hydroxonium ions has increased. This is crucial in the context of adding pyridinium chloride to a pyridine solution.
Pyridinium chloride is the salt of pyridine, and when added to a pyridine solution, it introduces more pyridinium ions. These ions are the conjugate acids of pyridine and their presence in the solution drives the equilibrium to shift left, according to Le Chatelier's Principle, which means that fewer hydroxonium ions are consumed. Consequently, the overall concentration of hydroxonium ions rises. This is a detail that students should pay particular attention to, as it affects the pH and can be crucial for understanding the outcome of various chemical processes, such as buffering capacity in biological systems or the reactivity of substances in different pH environments.

Acid-base equilibrium is an equilibrium condition between the protonated (acidic) and deprotonated (basic) forms of a compound in solution. When acids and bases are in solution, they can donate or accept protons, reaching an equilibrium state that is represented in their acid-base or dissociation constants (\(K_a\) and \(K_b\)) respectively.
The addition of external substances can shift this equilibrium, which is seen when a common-ion or a stronger acid or base is introduced into the system. For example, with hydrocyanic acid becoming less deprotonated in the presence of hydrobromic acid, we see a classic case of acid-base equilibrium being affected. Students studying chemistry must appreciate this delicate balance in acid-base reactions to predict the outcome of mixing different chemical species and to troubleshoot when reactions don't proceed as expected.