Foundations — Fuel cells — H₂ - O₂ fuel cell (spacecraft relevance)

This page unpacks every symbol, arrow, and word the parent topic leans on, starting from nothing. If a symbol appears there, it is earned here first.

1. Atoms, electrons, and charge

Before any reaction, we need the actors.

Look at the figure: the small mint dot is an electron. When it leaves an atom and travels down a wire, we call that flow electric current. That is the entire product of a fuel cell — a stream of these dots doing work on the way.

2. Oxidation and reduction — the "e⁻" bookkeeping

The parent page writes things like $4e^{-}$ on one side of an arrow. Here is what that means.

The picture shows the two half-processes as two buckets connected by a pipe. Electrons pour out of the left bucket (oxidation) and can only leave if the right bucket (reduction) is ready to catch them. This is why the fuel cell has two electrodes: one where losing happens, one where gaining happens.

Reading the parent's anode equation slowly: $2{\text{H}}_2+4{\text{OH}}^{-}\to 4{\text{H}}_2\text{O}+4e^{-}$

• The $\to$ means "turns into."
• $e^{-}$ sits on the right → electrons are released → this is oxidation.
• The little "$4$" is the count: exactly four electrons leave.

3. Ions and the notation ${\text{OH}}^{-}$, ${\text{H}}^{+}$

The parent uses ${\text{OH}}^{-}$ and ${\text{H}}^{+}$ everywhere. These need building.

4. State labels $(g)$, $(l)$, $(aq)$

Tiny letters in brackets sit on almost every formula.

This is exactly why the parent's "Mistake 2" matters: the water is $(l)$, not $(g)$ — a state label, not a detail.

5. Anode, cathode, and the direction of flow

Follow the arrows in the figure: electrons leave the anode (mint arrows in the outer wire), do useful work in the lamp, arrive at the cathode. Meanwhile ${\text{OH}}^{-}$ ions (coral arrows) drift the other way through the electrolyte. This closed loop — electrons outside, ions inside — is the whole engine. See Galvanic cells and cell potential for the general version of this loop.

6. The degree circle ${}^{\circ }$ and the symbol $E_{\text{cell}}^{\circ }$

The parent writes $E_{\text{cell}}^{\circ }=1.23\text{V}$. Unpack each piece.

The double-negative is the classic trip-up: subtracting $-0.83$ adds $0.83$.

7. The energy symbols $\Delta H$, $\Delta G$, $T\Delta S$, and $\eta$

The efficiency section leans on these. Build them one at a time.

The bar in the figure is split: the whole bar is $\Delta H$ (all the energy), the mint slice is $\Delta G$ (what can become electricity), and the faded slice is $T\Delta S$ (the tax entropy takes). The theoretical efficiency is just the ratio of the useful slice to the whole bar.

Why not 100%? Because $T\Delta S$ is never zero — some energy is always paid to entropy. This is the honest ceiling before any real-world losses.

8. Reaction arrow, coefficients, and balancing

9. Catalyst and kinetics vocabulary

Prerequisite map

Each box is a symbol or idea this page built. They all feed the final node — the fuel cell itself.

Equipment checklist

Cover the right side and answer before revealing.