Final answer:
The numerical value of Kw changes primarily due to temperature variations, with a higher temperature resulting in a greater Kw value due to increased water ionization.
Step-by-step explanation:
The numerical value of the ion-product constant for water (Kw) can differ primarily due to changes in temperature. Kw is the product of the molar concentrations of hydrogen ions [H3O+] and hydroxide ions [OH−] in water, and its standard value at 25°C is 1.0×10−14. Because the dissociation of water is an endothermic process, the value of Kw increases with temperature, meaning that at higher temperatures, water ionizes more, resulting in higher concentrations of hydronium and hydroxide ions. For example, at 100°C, Kw is about 5.1×10−13, which is significantly higher than the value at 25°C. Conversely, at lower temperatures, the value of Kw will be smaller. This temperature dependence shows that while Kw is constant at a given temperature, it is not a universal constant.