How is K_w defined, and what is its numerical value at 25 °C?

Verified step by step guidance

1. K_w is the ion product constant for water, which is defined as the product of the concentrations of hydrogen ions [H^+] and hydroxide ions [OH^-] in pure water.
2. The expression for K_w is given by: K_w = [H^+][OH^-].
3. At 25 °C, the concentration of hydrogen ions [H^+] and hydroxide ions [OH^-] in pure water is equal, and each is 1.0 x 10^-7 M.
4. Substitute the concentrations into the expression: K_w = (1.0 x 10^-7 M)(1.0 x 10^-7 M).
5. This results in a numerical value for K_w at 25 °C, which is a constant value.

Key Concepts

Ion Product of Water (K_w)

K_w, or the ion product of water, is a constant that represents the equilibrium constant for the self-ionization of water. It is defined as the product of the concentrations of hydrogen ions [H⁺] and hydroxide ions [OH⁻] in pure water at a given temperature. This concept is crucial for understanding acid-base chemistry and the behavior of water in various chemical reactions.

Self-Ionization of Water

The self-ionization of water is a process where two water molecules interact to produce one hydronium ion (H₃O⁺) and one hydroxide ion (OH⁻). This reaction is reversible and occurs to a very small extent in pure water, leading to the formation of equal concentrations of H⁺ and OH⁻ ions. Understanding this process is essential for grasping the concept of K_w and its implications in acid-base equilibria.

Numerical Value of K_w at 25 °C

At 25 °C, the numerical value of K_w is 1.0 x 10⁻¹⁴. This value indicates that in pure water, the concentrations of H⁺ and OH⁻ ions are both 1.0 x 10⁻⁷ M, reflecting the neutral nature of pure water at this temperature. This constant is fundamental in calculating pH and understanding the acidity or basicity of solutions.