Final answer:
To find the electrochemical cell potential and spontaneity, we calculate the standard cell potential and adjust for concentrations using the Nernst equation. The standard cell potential is 0.617 V, indicating spontaneous reaction under standard conditions. A positive cell potential after Nernst equation adjustment signifies spontaneity under the provided conditions.
Step-by-step explanation:
To calculate the potential of the electrochemical cell and determine if it is spontaneous, we need to know the standard electrode potentials for each half-cell and the reaction quotient Q for the Nernst equation. Given that °Sn4+/Sn2+=0.154 V and °Fe3+/Fe2+=0.771 V, we can determine the cell potential (°Ecell).
The half-cell with the higher reduction potential typically undergoes reduction in the cell, whereas the half-cell with the lower reduction potential undergoes oxidation. In this case, the iron (Fe) couple has the higher reduction potential, so it will undergo reduction, and the tin (Sn) couple will undergo oxidation.
The standard cell potential (°Ecell) is calculated by subtracting the standard potential of the oxidation half-cell from the reduction half-cell. Thus, °Ecell = °Fe3+/Fe2+ - °Sn4+/Sn2+ = 0.771 V - 0.154 V = 0.617 V.
Next, we calculate Ecell using the Nernst equation:
Ecell = °Ecell - (0.0591/n) × log(Q)
Where n is the number of electrons transferred and Q is the reaction quotient, given by Q = ([Sn2+]2)/([Sn4+][Fe3+]2/2[Fe2+]).
Substituting the values:
Q = (0.00322)/(0.1 · (0.12/0.0053))
Ecell = 0.617 V - (0.0591/2) × log(Q), as 2 electrons are transferred.