What is the \(\mathrm{pH}\) of a solution whose \(\mathrm{OH}\) concentration is \(2.0 \times 10^{-3} \mathrm{M}\) ? Is the solution acidic or basic?

Understanding the ion-product constant of water, denoted by the symbol Kw, is crucial when dealing with solutions and their pH levels. Kw is a fundamental property of water, representing the product of the concentrations of hydrogen ions (\text{H+}) and hydroxide ions (\text{OH-}) in pure water.

The equation can be mathematically expressed as \[K_w = [H^+][OH^-]\]
At 25°C, the value of Kw is always \(1.0 \times 10^{-14}\). This constant value is derived under the condition that water is in a state of equilibrium, meaning that the rates at which water molecules dissociate into ions and ions recombine to form water molecules are equal.

When solving pH problems, we often use Kw to relate the concentration of hydroxide ions to the concentration of hydrogen ions in the solution. It serves as an essential bridge to find one ionic concentration when the other is known, allowing us to calculate the pH, as shown in the textbook exercise solution.

The concentration of hydroxide ions, denoted by [OH-], is a vital parameter in determining the alkalinity of a solution. In the involved problem, the given \text{OH-} concentration is \(2.0 \times 10^{-3} \text{M}\). In a neutral solution, like pure water, [OH-] would equal \(1.0 \times 10^{-7} \text{M}\), since \([OH^-] = \frac{K_w}{[H^+]}\) and both [OH-] and [H+] are the same, owing to the water’s auto-dissociation equilibrium.

In this case, having [OH-] that is significantly higher than \(1.0 \times 10^{-7} \text{M}\) hints that the solution is basic. We can use this [OH-] in conjunction with Kw to find the corresponding [H+] concentration, which can then be used to calculate the pH, as highlighted in the textbook solution steps.

The concepts of acidity and basicity are paramount in understanding the nature of a solution. These are usually described in terms of pH, which is a logarithmic scale used to specify the acidity or alkalinity of an aqueous solution.

The pH scale ranges from 0 to 14:

• Solutions with a pH less than 7 are considered acidic.
• Solutions with a pH of exactly 7 are neutral.
• Solutions with a pH greater than 7 are considered basic.

In the given exercise, after calculating the pH to be approximately 11.3, we compare this value to the neutral pH of 7. Since 11.3 is greater than 7, we identify the solution as basic. The further away the pH is from 7 in either direction (lower for acids, higher for bases), the more extreme the solution's acidity or basicity. Thus, even without directly touching upon the inherent characteristics of acids and bases, pH provides a reliable measure of a solution's acid-base properties.