Autoionization of Water
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Topic Summary & Highlights
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Core Concept
Autoionization (or self-ionization) of water is a reaction in which two water molecules interact to produce a hydronium ion ($H_3O^+$) and a hydroxide ion ($OH^−$).
Reaction: $2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$
Alternatively: $H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)$
This equilibrium is fundamental to the pH scale and acid-base chemistry.
Practice Tips
Water is Always Ionized: Even pure water contains $H_3O^+$ and $OH^-$ due to autoionization.
pH and Kw: The pH scale is derived from the autoionization of water, with $K_w$ determining the relationship between [$H_3O^+$] and [$OH^-$].
Neutrality is Temperature-Dependent: At higher temperatures, water is neutral at a pH lower than 7 because $K_w$ increases.
Calculations Involving Kw
1. Calculating Ion Concentrations
Example: In pure water at 25°C, calculate the concentrations of H3O+H_3O^+H3O+ and OH−OH^-OH−.
Given: $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$
Since $[H_3O^+] = [OH^-]$, let x = [$H_3O^+$]: 2x = $1.0 \times 10^{-14}$
$x = [H_3O^+] = [OH^-] = 1.0 \times 10^{-7} \, \text{M}$
2. Non-Neutral Solutions
For a solution with $[H_3O^+] = 1.0 \times 10^{-3} \, \text{M}$:
$[OH^-] = \frac{K_w}{[H_3O^+]} = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-3}} = 1.0 \times 10^{-11} \, \text{M}$
Key Concepts
1. Equilibrium Constant ($K_w$)
The equilibrium constant for the autoionization of water is denoted as $K_w$.
At 25°C: $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$
This value varies with temperature, increasing as the temperature rises.
2. Neutrality of Water
In pure water at 25°C: [H3O+]=[OH−]=1.0×10−7 M[H_3O^+] = [OH^-] = 1.0 \times 10^{-7} \, \text{M}[H3O+]=[OH−]=1.0×10−7M
The solution is neutral because the concentrations of H3O+H_3O^+H3O+ and OH−OH^-OH− are equal.
3. Temperature Dependence
The autoionization constant KwK_wKw increases with temperature, meaning water becomes slightly more ionized at higher temperatures.
At 50∘C50^\circ C50∘C, Kw>1.0×10−14K_w > 1.0 \times 10^{-14}Kw>1.0×10−14.