The ionization constant for water \(\left(K_{w}\right)\) is \(9.311 \times 10^{-14}\) at \(60^{\circ} \mathrm{C}\). Calculate \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],\left[\mathrm{OH}^{-}\right], \mathrm{pH},\) and \(\mathrm{pOH}\) for pure water at \(60^{\circ} \mathrm{C}\).

The pH scale is a measure of acidity or alkalinity of a solution and is one of the most widely used chemical metrics.

It is calculated as the negative logarithm of the hydrogen ion concentration, which can be expressed in the formula: \( pH = -\text{log}_{10} [H_3O^+] \). The pH scale ranges from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and values above 7 indicating alkalinity.

In the exercise, calculating the pH involves taking the negative logarithm of the concentration of hydronium ions (\( [H_3O^+] \)) in the solution. Since we found that \( [H_3O^+] = \sqrt{9.311 \times 10^{-14}} \), the next step is just applying this value to our pH formula. For students, remembering that pH is all about the power of 10 (logarithm) can simplify the concept and streamline their calculations.

The concentration of hydrogen ions in a solution is central to several areas of chemistry, particularly acid-base chemistry. These ions are typically represented in aqueous solutions as hydronium ions, \( [H_3O^+] \).

To determine the hydrogen ion concentration in pure water, we refer to the ionization constant for water (\( K_w \)), which is the product of the concentrations of hydronium and hydroxide ions. At equilibrium in water: \( K_w = [H_3O^+][OH^-] \). Since in pure water \( [H_3O^+] = [OH^-] \), we can simplify this to \( K_w = [H_3O^+]^2 \).

This allows us to calculate \( [H_3O^+] \) by taking the square root of \( K_w \), which is crucial because understanding this concentration is not just about a number—it’s about predicting the behavior of solutions, gauging their reactivity, and applying this to real-world scenarios in the lab or industry.

The hydroxide ion concentration in a solution, denoted \( [OH^-] \), tells us how 'basic' or alkaline that solution is. It is inversely related to the hydrogen ion concentration, meaning as the concentration of hydroxide ions increases, the solution becomes more basic.

The ionization constant for water, \( K_w \), is also vital when calculating the hydroxide ion concentration. Just as with hydronium ions, in pure water at a given temperature, the ion product \( [H_3O^+][OH^-] = K_w \) allows us to express \( [OH^-] = \sqrt{K_w} \) due to the equal amounts of \( [H_3O^+] \) and \( [OH^-] \).
Understanding hydroxide ion concentration is important because it helps students grasp the nature of bases and neutralization reactions. It is a key point of knowledge for environmental science, as the alkalinity of natural waters can influence aquatic ecosystems significantly.