Autoionization of Water

Core Concept

Autoionization (or self-ionization) of water is a reaction in which two water molecules interact to produce a hydronium ion (H3O+) and a hydroxide ion (OH−).

Reaction: 2H2O(l)⇌H3O+(aq)+OH−(aq)

  • Alternatively: H2O(l)⇌H+(aq)+OH−(aq)

  • This equilibrium is fundamental to the pH scale and acid-base chemistry.

  • Always convert minutes or hours to seconds before multiplying by current.

  • 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.

Test Yourself

Assorted Multiple Choice
A constant current is passed through an electrolytic cell for 45.0 minutes, delivering a total charge of 8,100 Coulombs. How many moles of electrons were transferred during this process? (Faraday's constant = 96,485 C/mol e⁻)

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Autoionization of Water

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Calculations Involving Kw​

Calculating Ion Concentrations

  • Example: In pure water at 25°C, calculate the concentrations of $H_3O^+$ and $OH^-$.

    • Given: $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$

    • Since $[H_3O^+] = [OH^-]$, let x = [$H_3O^+$]: 2x = $1.0 \times 10^{-14}$

    • $x = [H_3O^+] = [OH^-] = 1.0 \times 10^{-7} \, \text{M}$

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

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.

Neutrality of Water

  • In pure water at $25^\circ\text{C}$: $[\text{H}_3\text{O}^+] = [\text{OH}^-] = 1.0 \times 10^{-7} \, \text{M}$.

    • The solution is neutral because the concentrations of $\text{H}_3\text{O}^+$ and $\text{OH}^-$ are equal.

Temperature Dependence

  • The autoionization constant $K_w$ increases with temperature, meaning water becomes slightly more ionized at higher temperatures.

    • At $50^\circ\text{C}$, $K_w > 1.0 \times 10^{-14}$.

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