The formula for calculating the cell potential (E cell) of an electrochemical cell is E cell = E cathode - E anode.
Understanding E Cell
What is E Cell?
E cell, also known as cell potential or electromotive force (EMF), represents the potential difference between the cathode and the anode in an electrochemical cell. This difference in potential drives the movement of electrons and therefore the electrochemical reaction. A positive E cell value indicates a spontaneous reaction.
Formula Breakdown:
| Component | Description |
|---|---|
| E cell | The overall cell potential, measured in volts. This is the voltage generated by the electrochemical cell. |
| E cathode | The reduction potential of the cathode (where reduction occurs) |
| E anode | The reduction potential of the anode (where oxidation occurs) |
How to Calculate E Cell
- Identify the Cathode and Anode: Determine which electrode is undergoing reduction (cathode) and which is undergoing oxidation (anode).
- Find the Standard Reduction Potentials: Look up the standard reduction potentials (E°) for both the cathode and anode half-reactions, usually in a table of standard reduction potentials.
- Apply the Formula: Use the formula E cell = E cathode - E anode to calculate the cell potential. Remember, the E values from the table are reduction potentials, and the anode's reduction potential is used in the formula even though it is undergoing oxidation.
Spontaneity and E Cell
- A positive E cell value signifies a spontaneous reaction; this means that the reaction will proceed on its own without any external energy input.
- A negative E cell value indicates a non-spontaneous reaction, where an external energy source is required to drive the reaction.
- An E cell value of zero signifies that the reaction is at equilibrium.
Example
Let's say we have a cell with the following reactions:
- Cathode: Cu2+(aq) + 2e- → Cu(s), E° = +0.34 V
- Anode: Zn(s) → Zn2+(aq) + 2e- , E° = -0.76 V
To find the cell potential:
E cell = E cathode - E anode
E cell = (+0.34 V) - (-0.76 V)
E cell = +1.10 V
This is a spontaneous reaction with a positive E cell value.
Electrochemical Energy
The relationship between cell potential and electrochemical energy (Gibbs free energy) is given by:
ΔG = -n*F*E
where:
- ΔG is the change in Gibbs free energy
- n is the number of moles of electrons transferred in the reaction
- F is the Faraday constant (approximately 96,485 C/mol)
- E is the cell potential
This formula demonstrates how a positive cell potential corresponds to a negative Gibbs free energy, signifying a spontaneous reaction.
