Use the value of \(K_{\mathrm{w}}\) to calculate the hydronium ion concentration and the hydroxide ion concentration in pure water.

Water, H₂O, a seemingly simple liquid, has a unique property called autoionization. It is a process where water molecules interact with each other to form hydronium ions (H₃O⁺) and hydroxide ions (OH^-). Imagine each water molecule as both a potential acid and base; they can donate and accept a hydrogen ion, respectively. This behavior can be expressed by the reversible chemical reaction:
\[2H₂O \leftrightarrow H₃O^+ + OH^-\]
This is a crucial concept to grasp, as it sets the stage for understanding the intrinsic nature of water's ionization. The dissociation doesn't significantly alter the concentration of the water itself, because the ratio of dissociated molecules is exceedingly small compared to the total number of water molecules. Consequently, even though this reaction is continually occurring, pure water is still electrically neutral, with the concentrations of positive and negative ions balanced.

The concentration of hydronium ions in water is a telltale sign of the solution's acidity. In pure water at 25°C, due to the autoionization process mentioned earlier, the concentration of hydronium ions, represented by \[\text{[H₃O⁺]}\], is in a delicate equilibrium with the concentration of hydroxide ions. According to the dissociation constant (\(K_{\mathrm{w}}\)), which is \(1.0 \times 10^{-14}\) at this temperature, the concentration of hydronium ions can be mathematically calculated. By taking the square root of \(K_{\mathrm{w}}\), one finds that \[\text{[H₃O⁺]} = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7}\] M. This reveals a neutral pH, showing that pure water isn't inherently acidic or basic. Moreover, any change in hydronium ion concentration is reflected in the acidity or basicity of the solution, making it an important indicator in chemistry.

Equally important as its counterpart, the hydroxide ion concentration in water gives insight into the solution's basicity. For pure water, the concentration of hydroxide ions, denoted by \[\text{[OH^-]}\], also equals \(1.0 \times 10^{-7}\) M at 25°C. This is because the autoionization of water produces hydronium and hydroxide ions in a 1:1 ratio. The formula for the water dissociation constant, \(K_{\mathrm{w}}\), encapsulates this relationship: \[[H₃O⁺][OH^-] = K_{\mathrm{w}}\]. Here, any shift in \(K_{\mathrm{w}}\) due to temperature changes can alter the concentrations of both ions. Understanding the hydroxide ion concentration is fundamental for studying chemical reactions in aqueous solutions, especially when identifying basic or neutral environments.