Zinc-air batteries are actively being researched because one reactant (oxygen) is provided in infinite supply for free. The standard cell potential for this battery is 1.65 V. Calculate the cell potential when the partial pressure of oxygen in the cell is 0.190 atm and the temperature is 25.0 $\circ$ C. The reaction in the cell converts Zn(s) and O₂(g) into ZnO(s).

Question

Quizplus · Accepted Answer

The cell potential can be calculated using the Nernst equation:
Ecell = E°cell - (RT/nF) ln(Q), where:
- E°cell = standard cell potential = 1.65 V
- R = gas constant = 8.31 J/(mol*K)
- T = temperature = 298 K
- n = number of moles of electrons transferred in the balanced equation = 2
- F = Faraday constant = 96,485 C/mol
- Q = reaction quotient = [ZnO]/([Zn][O2]^0.5), assuming the partial pressure of oxygen is proportional to its concentration in the gas phase
- [ZnO] = activity of ZnO(s) = 1 (as it is a pure solid)
- [Zn] = activity of Zn(s) = 1 (as it is a pure solid)
- [O2] = partial pressure of oxygen = 0.190 atm

Plugging in the values:
Ecell = 1.65 V - (8.31 J/(mol*K) * 298 K / (2 * 96,485 C/mol) * ln(1/0.190^0.5))
Ecell = 1.64 V
Therefore, the best choice is C (1.64 V).

Zinc-Air Batteries Are Actively Being Researched Because One Reactant (Oxygen) ∘\circ∘

Zinc-Air Batteries Are Actively Being Researched Because One Reactant (Oxygen) $\circ$