The #K_w-"value"# for water comes from the equilibrium expression for autoionization of water; that is,
#H_2O + H_2O# => #H_3O^+ + OH^-# (Bronsted-Lowry Proton Transfer Rxn)
The equilibrium expression for autoionization of water is ...
#K_(eq) = ([H_3O^+][OH^-])/[H_2O]^2#
#[H_2O]^2# is so large compared to the concentrations of #[H_3O^+] and [OH^-]# that it is considered constant and moved to #K_(eq)# side of the equation. That is, ...
#K_(eq)[H_2O]^2# = #[H_3O^+][OH^-]# = #K_w# (Ionization Product Constant for Water)
At #25^oC# #[H_3O^+] = [OH^-] = 1.00xx10^-7M#
Substituting into #K_w# = #[H_3O^+][OH^-]#
=>#K_w# = #(1.00xx10^-7M)(1.00xx10^-7M)# = #1.00xx10^(-14)M^2# at #25^oC#
