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

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K_w is the ionization constant of water, which represents the equilibrium constant for the self-ionization of water. The reaction is:

H_{+} (aq) + OH (aq) \leftrightarrow H O_{2} (l)

The expression for K_w is derived from the equilibrium concentrations of the ions produced during water's self-ionization:

K_{w = [H_{+}] \times [OH]}

At 25 °C, the concentrations of

H_{+}

and

OH

in pure water are both equal to

{1.0}^{\times 10 -7}

Substitute these values into the K_w expression:

K_{w = [H_{+}] \times [OH] = {1.0}^{\times 10 -7} \times {1.0}^{\times 10 -7}}

Simplify the expression to find the numerical value of K_w at 25 °C, which is typically expressed as

{1.0}^{\times 10 -14}

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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.

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