The half-equations for hydrogen fuel cells can be expressed as follows:

• Anode Half-Equation:

• Cathode Half-Equation:

In a hydrogen fuel cell, hydrogen gas ($\text{H}_2$) is supplied to the anode, where it undergoes oxidation. This process involves the loss of electrons, resulting in the formation of positively charged hydrogen ions ($\text{H}^+$). The half-equation representing this oxidation reaction is:

In this equation, the term $e^-$ denotes the electrons that are released during the oxidation of hydrogen.

On the opposite side of the fuel cell is the cathode, where oxygen gas ($\text{O}_2$) is reduced, meaning it gains electrons. At the cathode, oxygen reacts with the hydrogen ions that have migrated from the anode, along with the electrons that have traveled through an external circuit. This reaction produces water ($\text{H}_2\text{O}$), which is the sole by-product of a hydrogen fuel cell. The corresponding half-equation for this reaction is:

The overall reaction occurring in a hydrogen fuel cell, which results from summing the anode and cathode half-equations, can be written as:

This equation illustrates that hydrogen and oxygen combine to produce water.

It is important to note that in these half-equations, the arrow ($\rightarrow$) can be interpreted as either “becomes” or “reacts to form.” Therefore, the anode half-equation ($\text{H}_2 \rightarrow 2\text{H}^+ + 2e^-$) can be read as “hydrogen becomes two hydrogen ions and two electrons.” Similarly, the cathode half-equation ($\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$) translates to “oxygen plus four hydrogen ions plus four electrons reacts to form two water molecules.”