A fuel cell that can provide power for buses is the phosphoric acid fuel cell, PAFC - VCE - SSCE Chemistry - Question 8 - 2008 - Paper 1

The half-reaction at the cathode can be written as:

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

On the diagram, an arrow should be drawn from the right side of the cell towards the left, indicating the movement of H₂PO₄⁻ ions from the anode to the cathode as the cell delivers an electrical current.

To calculate the energy delivered per mole of hydrogen, we use the formula:

$E = Q \cdot V$

where:

• $n = 2$ moles (for the 2 electrons transferred),
• $Q = nF$ (where $F = 96500 \: C/mol$, Faraday's constant),
• $V = 0.92 \: V$.

Thus, the calculations are:

$Q = nF = 2 \times 96500 \, C/mol = 193000 \, C$ $E = Q \cdot V = 193000 \, C \times 0.92 \, V = 177560 \, J = 177.56 \: kJ$

The energy efficiency can be calculated by comparing the energy delivered by the fuel cell to the heat of combustion of hydrogen, which is 241.8 kJ/mol.

Using the formula for efficiency:

$\text{Efficiency} = \left( \frac{E_{delivered}}{E_{combustion}} \right) \times 100$

Substituting the values:

$\text{Efficiency} = \left( \frac{177.56 \: kJ}{241.8 \: kJ} \right) \times 100 \approx 73.5\%$