The standard emf for the cell using the overall cell reaction below is +2.20 V: 2Al(s) + 3I₂(s) → 2AI³⁺(aq) + 6I^-(aq)
The emf generated by the cell when [AI³⁺] = 3.0 × 10^-3 M and [I^-] = 0.50 M is ________ V.

Question

Quizplus · Accepted Answer

The Nernst equation gives us a way to calculate the cell potential under non-standard conditions:

Ecell = E°cell - (RT/nF)lnQ

where:
- E°cell is the standard cell potential
- R is the gas constant (8.314 J/mol*K)
- T is the temperature in kelvin
- n is the number of moles of electrons transferred in the balanced cell reaction
- F is Faraday's constant (96,485 C/mol)
- Q is the reaction quotient, calculated from the concentrations of the species involved in the cell reaction

First, let's determine the balanced half-reactions and the overall cell reaction:
Al(s) → Al3+(aq) + 3e-
I2(s) + 2e- → 2I-(aq)
2Al(s) + 3I2(s) → 2Al3+(aq) + 6I-(aq)

The standard cell potential is +2.20 V, so:

E°cell = +2.20 V

The reaction quotient is calculated as follows:

Q = [AIP13+][IP1−]6/[I2]3

Substitute the given concentrations into the reaction quotient equation:

Q = [(3.0 × 10-3)(0.50)6]/(0.50)3 = 54.0

The number of moles of electrons transferred in the balanced equation is 6.

Substituting these values into the Nernst equation:

Ecell = +2.20 V - [(8.314 J/mol*K) * (298 K) / (6 * 96,485 C/mol) * ln(54.0)]

Ecell = +2.27 V

Therefore, the answer is B) 2.27.

The Standard Emf for the Cell Using the Overall Cell