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

Verified step by step guidance

1. K_w is the ionization constant of water, which represents the equilibrium constant for the self-ionization of water. The reaction is: $H_{+}(aq)+{\mathrm{OH}}_{}(aq)\leftrightarrow H_{}{O}_2(l)$.
2. The expression for K_w is derived from the equilibrium concentrations of the ions produced during water's self-ionization: $K_w$.
3. At 25 °C, the concentrations of $H_{+}$ and ${\mathrm{OH}}_{}$ in pure water are both equal to ${1.0}^{\times }$ M.
4. Substitute these values into the K_w expression: $K_w$.
5. Simplify the expression to find the numerical value of K_w at 25 °C, which is typically expressed as ${1.0}^{\times }$.

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 hydroxide ion (OH⁻) and one hydronium ion (H₃O⁺). 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 pH and the neutrality of water.

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 water at this temperature. This constant is fundamental in calculations involving pH, pOH, and the acidity or basicity of solutions.