Electrochemical Cells

• Cell Potential ($E_{cell}$): Also known as electromotive force (EMF), this is the measure of the driving force behind the electron flow, representing the potential difference between two electrodes.

• Standard Hydrogen Electrode (SHE): This is the universal reference point with a defined potential of $0.00\text{ V}$ under standard conditions ($1.0\text{ M}$, $298\text{ K}$, $100\text{ kPa}$).

• Thermodynamic Favorability: The relationship between cell potential and Gibbs Free Energy is defined by the equation $\Delta G^\circ = -nFE_{cell}^\circ$. A positive $E_{cell}^\circ$ indicates a spontaneous reaction.

• Faraday's Constant ($F$): This represents the magnitude of electric charge per mole of electrons, approximately $96,485\text{ C/mol } e^-$.

Standard Potential Calculation

$E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ$

• Note: Both values used in this formula must be standard reduction potentials.

• Cell Notation: A shorthand way to represent a cell: $\text{Anode} | \text{Anode Ion} || \text{Cathode Ion} | \text{Cathode}$. The single line $|$ represents a phase boundary, and the double line $||$ represents the salt bridge.

• Calculating Non-Standard Potentials: When concentrations or pressures deviate from $1.0\text{ M}$ or $1\text{ atm}$, the Nernst Equation is applied: $E = E^\circ - \frac{RT}{nF} \ln Q$.

• Simplified Nernst Equation: At $298\text{ K}$, the formula simplifies to $E = E^\circ - \frac{0.0592}{n} \log Q$, where $Q$ is the reaction quotient.

• Electrolysis Calculations: To find the mass of a substance plated during electrolysis, use the relationship $Q = I \cdot t$ (Charge = Current $\times$ Time) and convert charge to moles of electrons using Faraday's constant.

• Anode vs. Cathode: Regardless of the cell type, oxidation always occurs at the anode and reduction always occurs at the cathode. The polarity flip in electrolytic cells is due to the external power source forcing electrons onto the cathode.

• Check the $n$ value: Always identify the total number of electrons transferred in the balanced redox equation before using the Nernst or Gibbs equations.

• Standard Reduction Potentials: Remember that tables provide reduction potentials. If you need an oxidation potential, you must reverse the sign, but the $E_{cathode} - E_{anode}$ formula already accounts for this.

• Units in Faraday's Law: Ensure time is always in seconds when using $Q = It$. Common mistakes involve using minutes or hours directly.

• Predicting Spontaneity: If a calculated $E_{cell}$ is negative, the reaction is non-spontaneous in the forward direction but spontaneous in the reverse direction.

• Stoichiometry and $E^\circ$: Do NOT multiply the standard electrode potential by stoichiometric coefficients. $E^\circ$ is an intensive property and does not change with the amount of substance.

• Salt Bridge Function: Students often think the salt bridge allows electrons to flow through it. In reality, electrons only flow through the wire; the salt bridge allows ions to flow to balance charge.

• Equilibrium vs. Dead Cell: A cell at equilibrium has $Q = K$ and $E_{cell} = 0$. This is often referred to as a 'dead battery' because there is no longer a potential difference to drive current.