What is auto-ionization in the context of water molecules?

How are hydronium ions (H₃O⁺) and hydroxide ions (OH^-) formed during the auto-ionization of water?

What is the equilibrium expression for the auto-ionization of water, and what does the ion product constant (K_w) represent?

How does an increase in temperature affect the ion product constant (K_w) and the equilibrium of auto-ionization?

Calculate the concentration of OH^- ions in a solution where the concentration of H⁺ ions is 1.0 x 10^-4 M at 25 degrees Celsius.