What does the very small value of the ionization constant of water, k_w, indicate about the autoionization of water?

• A. Autoionization of water does not occur at all under normal conditions.
• B. Autoionization of water occurs rapidly and results in a high concentration of H_3O^+ and OH^- ions.
• C. Autoionization of water is a rare event and only a small fraction of water molecules ionize at any given time.
• D. Autoionization of water is a highly favorable process and most water molecules are ionized.

Answer: (C)

Verified step by step guidance

1. Understand that the ionization constant of water, \(K_w\), represents the equilibrium constant for the autoionization reaction of water: \(\mathrm{2\ H_2O \rightleftharpoons H_3O^+ + OH^-}\).
2. Recognize that a very small value of \(K_w\) means the equilibrium lies far to the left, favoring the reactants (water molecules) rather than the products (hydronium and hydroxide ions).
3. Interpret this small \(K_w\) value as indicating that only a tiny fraction of water molecules ionize at any given time, so the concentration of \(\mathrm{H_3O^+}\) and \(\mathrm{OH^-}\) ions is very low.
4. Conclude that the autoionization of water is a rare event under normal conditions, not a rapid or highly favorable process.
5. Therefore, the small \(K_w\) value reflects the fact that most water molecules remain in their molecular form, with only a small percentage existing as ions.