Here's a breakdown:

* Water molecules are not always stable: Water molecules (H₂O) can spontaneously dissociate into hydrogen ions (H⁺) and hydroxide ions (OH⁻):

* H₂O ⇌ H⁺ + OH⁻

* Equilibrium: This reaction is in equilibrium, meaning it's constantly going back and forth.

* Very small concentration of ions: While the auto-ionization is a very small percentage, it still creates a tiny amount of free ions. At 25°C, the concentration of H⁺ and OH⁻ ions is about 10⁻⁷ mol/L.

* Ions allow for conductivity: These free ions can carry an electrical current, making even highly purified water slightly conductive.

Factors affecting conductivity:

* Temperature: Higher temperatures increase the rate of auto-ionization, leading to higher conductivity.

* Dissolved impurities: Even trace amounts of impurities like salts or acids can significantly increase conductivity by adding more ions to the solution.

In Summary:

The auto-ionization of water, though a very small process, creates a tiny amount of ions that make purified water slightly conductive. The conductivity is still very low compared to other solutions but not completely zero.