Equilibrium constant for water (Kw)

1. Definition of $K_w$

• $K_w$ is the ionisation constant (or equilibrium constant) for the self-ionisation of water.
• It represents the equilibrium between hydronium ions $(H₃O⁺)$ and hydroxide ions $(OH⁻)$in water.

2. Auto-ionisation Reaction of Water

• Water undergoes auto-ionisation, forming hydronium and hydroxide ions: $H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$

• The equilibrium constant expression is: $K_w = [H_3O^+][OH^-]$

• Since $H⁺$ is often used instead of $H₃O⁺$, the equation can also be written as: $K_w = [H^+][OH^-]$

3. Value of Kw

• At 25°C, the value of Kw is: $K_w = :highlight[1.0 \times 10^{-14}]$

• This means that the concentrations of $H₃O⁺$ and $OH⁻$ in pure water are each: $[H_3O^+] = [OH^-] = :highlight[1.0 \times 10^{-7}] \text{ M}$

4. Importance of Kw

• Kw helps determine the pH of solutions.

• Since: $pH + pOH = :highlight[14]$ knowing $K_w$ allows us to calculate $pH$ or $pOH$ if one of the ion concentrations is known.

• Kw changes with temperature, affecting the $pH$ of water.

5. Key Takeaways

• $K_w = [H₃O⁺][OH⁻] = :highlight[1.0 × 10^{-14}]$ at 25°C.
• In neutral water, $[H_3O^+] = [OH^-]$ , so $pH = :highlight[7].$
• The $pH$ scale is based on $K_w$, making it essential in acid-base chemistry.