Q.If we use pentane as fuel in a fuel cell, what relationship will represent the change in Gibbs free energy? (E deg = 1.23 V)

The Apollo space programme was powered by the H$_2$–O$_2$ fuel cell.

Fuel cells work at about 70% efficiency, versus about 40% for thermal plants.

A fuel cell (e.g. the H2-O2 fuel cell) converts the chemical energy of a fuel directly into electrical energy through controlled electrochemical reactions, avoiding the wasteful heat-to-work steps of a thermal plant. Its efficiency is therefore high, a …

A fuel cell directly converts the chemical energy from the combustion of a fuel (like hydrogen) into electrical energy, without burning the fuel in a flame. The correct answer is (B).

A fuel cell is a galvanic cell fed continuously with fuel and oxidant to give a steady electric current.

A fuel cell is a galvanic (voltaic) cell in which the chemical energy of combustion of a fuel (such as $H_2$, $CH_4$, $CH_3OH$) is converted directly into electrical energy. Fuel (at the anode) and oxygen/air (at the cathode) are fed continuously, and the products are removed continuously, so the cell keeps working as long as the reactants are supplied. Example: the $H_2$–$O_2$ fuel cell, where

Anode: $2H_2 + 4OH^- \to 4H_2O + 4e^-$

Cathode: $O_2 + 2H_2O + 4e^- \to 4OH^-$

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Fuel cells can run on other combustible fuels besides hydrogen, with methanol being a commonly cited practical alternative.

A fuel cell converts the chemical energy of a continuously supplied fuel directly into electrical energy through controlled electrochemical oxidation at the anode (paired with reduction of an oxidant, usually oxygen, at the cathode). While hydrogen is the most common fuel used (as in the $H_2$–$O_2$ fuel cell), other fuels can also be oxidised electrochemically at a fuel cell's anode, such as:

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A fuel cell oxidises a fuel like $H_2$ or $CH_4$ at one electrode and reduces $O_2$ at the other, converting combustion chemical energy directly into electrical energy.

In a fuel cell (e.g. the $H_2$–$O_2$ fuel cell used in spacecraft), hydrogen is oxidised at the anode and oxygen is reduced at the cathode, with an electrolyte (often aqueous KOH) between them:

Anode: $2H_2(g) + 4OH^-(aq) \rightarrow 4H_2O(l) + 4e^-$

Cathode: $O_2(g) + 2H_2O(l) + 4e^- \rightarrow 4OH^-(aq)$

Overall: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$

This is exactly the combustion reaction of hydrogen, but instead of releasing the energy as heat, the electron transfer is forced through an external circuit, generating electricity directly and with high efficiency (no Carnot-limited heat-engine step) and no pollution (only water is produced).

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The cathode is where reduction happens; in a hydrogen–oxygen fuel cell, oxygen is reduced there, matching option (a).

In a fuel cell, the cathode is always the electrode where reduction occurs (the electrode that accepts electrons from the external circuit). In an $H_2$–$O_2$ fuel cell operating in an acidic medium, oxygen gas is reduced at the cathode:

$O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(g) \quad \text{(cathode, reduction)}$

Checking the other options: …

The hydrogen-oxygen cell is a fuel cell: it produces electricity from a continuously supplied fuel (H2) and oxidant (O2).

A fuel cell is a galvanic cell in which the reactants (a fuel and an oxidiser) are fed continuously to the electrodes, converting the energy of combustion directly into electrical energy.

Electrode reactions (in KOH):

• Anode: H2 + 2OH- -> 2H2O + 2e-
• Cathode: O2 + 2H2O + 4e- -> 4OH- …

Galvanic cells that convert the energy of combustion of fuels like H2, CH4 etc directly into electrical energy are called fuel cells.

In a fuel cell, a fuel (e.g. H2) is oxidised continuously at one electrode and an oxidant (usually O2) is reduced at the other, with the reactants fed in continuously from outside (unlike a normal galvanic cell where reactants are built into the electrodes). This lets the chemical energy of combustion be converted directly and efficiently into electrical energy, without the losses of first burning the fuel and then running a heat engine.

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The Apollo Space Programme used Hydrogen-Oxygen Fuel Cells — specifically, the Alkaline Fuel Cell (AFC) — to generate electricity and drinking water for the astronauts.

The H₂–O₂ fuel cell is drawn as two porous carbon (Pt/Pd-catalysed) electrodes standing in an aqueous KOH electrolyte, with H₂ gas fed continuously to the anode and O₂ gas fed continuously to the cathode; the external wire connecting the electrodes carries the current produced.

Description of the labelled diagram (since a diagram itself can't be rendered here, every element you need to draw and label is described):

1. A rectangular cell (container) filled with concentrated aqueous KOH electrolyte.
2. Two porous carbon electrodes, coated/impregnated with a catalyst (finely divided Pt or Pd), dipping into the electrolyte from either side — label the left one Anode (−) and the right one Cathode (+).
3. H₂ gas is bubbled in continuously at the anode side (label the inlet arrow "H₂ in").
4. O₂ gas is bubbled in continuously at the cathode side (label the inlet arrow "O₂ in").
5. An external circuit (a wire with a load/bulb or ammeter) connects the two electrodes above the cell, with the electron flow arrow shown going from anode → external circuit → cathode.
6. Water outlet shown near the electrolyte, since $H_2O$ is the only product formed and is continuously removed to keep the KOH concentration constant.

Electrode reactions (label these next to the diagram):

Anode (oxidation): $2H_2(g) + 4OH^-(aq) \rightarrow 4H_2O(l) + 4e^-$

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