Final answer:
To calculate the theoretical potential of the cell involving SHE and ammonia/ammonium half-cell, we need the half-cell potential for the latter, which is not provided.
Step-by-step explanation:
To calculate the theoretical potential of the given cell that includes the standard hydrogen electrode (SHE), we need to know the reaction and the corresponding half-cell potential. The reaction at the anode can be represented as the oxidation of hydrogen:
2H2(g) → 4H+(aq) + 4e-
The given cell involves ammonia and ammonium ions, so the reaction at the cathode involves the reduction of ammonium ions to ammonia and hydrogen:
NH4+(aq) + e- → NH3(aq) + ½ H2(g)
The standard potential of SHE is 0 V. However, the exact potential for the ammonia/ammonium half-cell is not given here, but it would be derived from experimental data.
For the purpose of this example, assuming we have a standard potential for the ammonia/ammonium reaction, we would use the formula:
Ecell = Ecathode - Eanode
With SHE as the reference, Eanode is 0 V, so the cell potential would simply be the standard potential of the ammonia/ammonium half-cell.
Without the exact potential for the ammonia/ammonium half-cell, a theoretical potential cannot be determined.