What is the molecular formula representation for the water autoionization constant?

The water autoionization constant, often represented as Kw, is defined by the equilibrium constant for the following reaction:

[ 2 H_2O (l) \rightleftharpoons H_3O^+ (aq) + OH^- (aq) ]

In this reaction, two water molecules react to produce a hydronium ion (H3O+) and a hydroxide ion (OH-). The expression for the equilibrium constant (Kw) for this reaction is given by the concentrations of the products divided by the concentration of the reactants, taking into consideration their stoichiometric coefficients:

[ K_w = \frac{[H_3O^+][OH^-]}{[H_2O]^2} ]

However, since water is the solvent and its concentration remains relatively constant, it is customary to reference the autoionization constant based on the concentrations of the ions produced rather than including water in the equation. Therefore, in practical terms, the representation simplifies to:

[ K_w = [H_3O^+][OH^-] ]

When considering the available options regarding the representation of the autoionization constant, the expression [H+][OH-] directly approximates the concentration