Give a possible value of \(\left[\mathrm{OH}^{-}\right]\)and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)in a solution that is: (a) acidic (b) basic (c) neutral

The hydroxide ion concentration, denoted by \(\left[\mathrm{OH}^-\right]\), is crucial in determining whether a solution is acidic, basic, or neutral. Hydroxide ions are negatively charged and are common components of bases. In a basic solution, these ions are abundant, which means the concentration of hydroxide ions is high, typically greater than \(1 \times 10^{-7}\) M at 25 degrees Celsius.

To put this into perspective, if you have a solution with a hydroxide ion concentration of \(1 \times 10^{-4}\) M, the solution is basic because this value is significantly greater than the neutral concentration. On the other hand, in an acidic solution, hydroxide ions are sparse, and therefore, the concentration would be less than the neutral concentration. For example, a \(\left[\mathrm{OH}^-\right]\) of \(1 \times 10^{-10}\) M indicates an acidic environment, as the concentration is below that of a neutral solution. Balancing the level of hydroxide ions is important for processes such as water treatment and the proper functioning of biological systems.

Importance in Chemistry

Understanding hydroxide ion concentrations is essential for predicting the pH of a solution and for conducting titration calculations. This knowledge helps in identifying the properties of a substance and its reactivity with acids or bases, thus playing a vital role in laboratory experiments, manufacturing processes, and even in medicine.

Hydronium ion concentration, symbolized as \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\), is equally integral to characterizing the acidity of a solution. Hydronium ions, consisting of a water molecule bound to a hydrogen ion, serve as a positive indicator of the solution's acidity level. In an acidic solution, the concentration of hydronium ions is greater than that of a neutral solution, which is \(1 \times 10^{-7}\) M at 25 degrees Celsius. For instance, a solution with a hydronium ion concentration of \(1 \times 10^{-3}\) M signifies strong acidity.

In a basic or alkaline solution, however, the concentration of hydronium ions is lower than in a neutral solution because the excess hydroxide ions combine with the hydronium ions to form water, thus reducing the concentration of hydronium ions. Hence, a very low concentration like \(1 \times 10^{-11}\) M indicates a basic solution. This concept is critical for fields such as pharmacology, where the correct hydronium ion concentration can influence drug efficacy and stability.

Understanding pH

The pH scale, which ranges from 0 to 14, is a measure of the hydronium ion concentration in a solution. A pH less than 7 indicates acidity (higher \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)), a pH of 7 indicates neutrality (equal concentrations of \(\left[\mathrm{OH}^-\right]\) and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)), and a pH greater than 7 indicates basicity (lower \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)).

A fundamental concept in chemistry is the ion product of water, \(K_w\), which is the product of the molar concentrations of hydroxide ions (\(\left[\mathrm{OH}^-\right]\)) and hydronium ions (\(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)). At 25 degrees Celsius, the ion product is always \(1 \times 10^{-14}\) M^2 in pure water or any aqueous solution.

This constant value means that if the concentration of one ion increases, the other must decrease to maintain the constant product. For instance, adding an acid to water increases the \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and consequently decreases the \(\left[\mathrm{OH}^-\right]\) so that the product of their concentrations remains at \(1 \times 10^{-14}\) M^2. Similarly, adding a base increases \(\left[\mathrm{OH}^-\right]\) and decreases \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) while keeping \(K_w\) the same.

Applications in pH Calculations

Understanding the ion product of water is crucial for calculating pH and pOH, as it provides a link between the two. It allows chemists to determine the completeness of a reaction and the equilibrium constant for a given acid-base reaction. Moreover, it is important in environmental science for assessing the acidification of bodies of water and has applications in industries that require precise pH control, such as textile and food production.