Calculate the cell potential for the electrochemical cell consisting of Ag metal in a 0.500 M AgNO3 solution and Fe metal in a 3.0 M Fe(NO3)3 solution.
From E = Eo - (0.0592/n)*log(red/ox) for each (one as an oxidation and the other as a reduction) add the two. The total will be Ecell.
To calculate the cell potential for this electrochemical cell, we can use the Nernst Equation. The Nernst Equation relates the cell potential to the concentrations of the species involved in the cell and the standard electrode potential.
The Nernst Equation is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
- Ecell represents the cell potential.
- 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 chemical equation.
- F is Faraday's constant (96485 C/mol).
- ln(Q) is the natural logarithm of the reaction quotient.
In this case, we will use the standard electrode potentials (E°cell) for each half-reaction. The half-reactions for the given system are:
Ag+ + e- → Ag (E°red = 0.80 V)
Fe3+ + 3e- → Fe (E°red = -0.04 V)
The balanced chemical equation is:
3Ag + Fe(NO3)3 → 3AgNO3 + Fe
Now, let's calculate the cell potential step by step:
1. Calculate the reaction quotient (Q) using the concentrations of the species involved in the cell.
Q = [Ag+]^3 / [Fe3+]
= (0.500 M)^3 / (3.0 M)
= 0.042 M^2
2. Substitute the values into the Nernst equation:
Ecell = E°cell - (RT/nF) * ln(Q)
= (0.80 V) - [(8.314 J/(mol·K)) * (298 K) / (3 mol)] * ln(0.042)
= 0.80 V + 0.0592 V * ln(0.042)
Calculating this expression will give you the cell potential for the electrochemical cell consisting of Ag metal in a 0.500 M AgNO3 solution and Fe metal in a 3.0 M Fe(NO3)3 solution.