Explain the self-ionisation of water, define and use the ionic product Kw, and relate pH, pOH and temperature

What this dot point is asking

Pure water conducts electricity very slightly, which shows it contains a small concentration of ions. This is because water undergoes self-ionisation (also called autoionisation):

often written more simply as $\text{H}_2\text{O}(l) \rightleftharpoons \text{H}^+(aq) + \text{OH}^-(aq)$. One water molecule acts as a Bronsted-Lowry acid and another as a base, transferring a proton.

Relating pH and pOH

Taking the negative logarithm of the $K_w$ expression gives a relationship you use constantly:

In pure water $[\text{H}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}$ mol L$^{-1}$, so pH $= 7$ and the water is neutral. Adding an acid raises $[\text{H}^+]$ above $10^{-7}$; because the product must stay equal to $K_w$, $[\text{OH}^-]$ falls below $10^{-7}$. The two concentrations are inversely linked through $K_w$ at all times.

The temperature dependence of Kw

Self-ionisation is an endothermic process (it requires energy to break the O-H bond). By Le Chatelier's principle, raising the temperature shifts the equilibrium to the right, increasing both $[\text{H}^+]$ and $[\text{OH}^-]$, so $K_w$ increases. For example, at 50 degrees Celsius $K_w$ is larger than $10^{-14}$.

This has an important consequence: neutral water at a higher temperature still has $[\text{H}^+] = [\text{OH}^-]$, but both are greater than $10^{-7}$, so its pH is below 7. The water is still neutral; only at exactly 25 degrees does neutral equal pH 7. This is a common point of confusion that examiners like to test.

Why this matters

$K_w$ is the bridge between the acid and base sides of any aqueous system. It lets you calculate the pH of bases (which directly supply $\text{OH}^-$), underpins the relationship between $K_a$ and $K_b$ for a conjugate pair, and explains why pH measurements must specify temperature.