Foundations — Ionic product of water Kw = 10⁻¹⁴ at 25 °C

Before you can trust that rule, you must be able to read every symbol in it without hesitating. This page builds them one at a time, from nothing, in the order they depend on each other.

1. Concentration and the square-bracket symbol [ ]

Picture a fixed box of exactly 1 litre of water. Concentration asks: how many particles of this kind are floating inside that box?

• A crowded box (many orange dots) = high concentration = large $[\text{X}]$.
• A near-empty box (few dots) = low concentration = small $[\text{X}]$.

A mole is just a counting word, like "dozen" but enormous: one mole $=6.02\times 10^{23}$ particles. We use it because real solutions contain unimaginably many particles, and counting them one by one is hopeless.

2. The ions: H⁺ and OH⁻

The little raised + and − are the charge: a superscript sign telling you the particle is electrically unbalanced. Look at the figure: the water molecule on the left is neutral (its + and − balance). After it donates a proton (the blue H), the leftover piece keeps an extra electron and becomes negative (${\text{OH}}^{-}$); the piece that received the proton becomes positive (${\text{H}}^{+}$, shown as ${\text{H}}_3{\text{O}}^{+}$ when it lands on a water molecule).

3. Reversible reactions and the ⇌ arrow

Picture a busy doorway where people walk out (splitting into ions) at the same rate others walk back in (recombining into water). The room's population looks frozen, but every individual is still moving.

This idea of shifting the balance by adding heat or extra ions is developed fully in Le Chatelier's principle.

4. The equilibrium constant K and the Kᵢ = products / reactants form

The subscript $c$ just reminds us we are using concentrations. The exponents matter: if a substance appears twice on one side, its concentration is squared.

5. Powers of ten and scientific notation 10⁻⁷

Every extra step in the exponent moves the decimal one place:

Multiplying powers of ten just adds the exponents: $(10^{-7})\times (10^{-7})=10^{-7-7}=10^{-14}$

6. Kw itself, and its logarithm cousins pH / pOH

The letter $p$ in front of something means "take the negative logarithm (base 10) of it." A logarithm answers the question "10 to what power gives this number?" So $\log (10^{-7})=-7$, and: $\text{pH}=-\log [{\text{H}}^{+}],\text{pOH}=-\log [{\text{OH}}^{-}]$

This turns awkward tiny numbers like $10^{-7}$ into friendly ones like $7$. Because logs turn multiplication into addition, the product rule becomes a sum: $\text{pH}+\text{pOH}=14(\text{at }25{}^{\circ }\text{C})$

The full machinery lives in pH and pOH scale; here you only need to recognise the symbols.

Prerequisite map

Read it top to bottom: crowd counts and ions feed the equilibrium picture; the equilibrium constant plus the near-constant water term plus powers of ten collapse into $K_w$; logarithms then repackage $K_w$ as pH and pOH.

Equipment checklist

Test yourself — say each answer aloud before revealing.

Connections

• Yeh note Hinglish mein padho →
• pH and pOH scale — where pH and pOH come from
• Le Chatelier's principle — shifting the water equilibrium
• Strong acids and bases — flooding the crowd with extra H⁺ or OH⁻
• Arrhenius theory — defines acids/bases by their effect on these ions
• Weak acids Ka — uses the same K = products/reactants form