Notes on Spontaneous and Non-Spontaneous Electrochemical Cells: Galvanic, Electrolytic, and the Nernst Equation, and Thermodynamic Relationships

Definition of Spontaneity: In the context of a galvanic cell, a spontaneous reaction means that electricity is generated directly from the chemicals in solution without external intervention.
Basic Mechanism: Electricity is produced when a metal stripe is placed into a solution. This can occur even within a single beaker, but this setup presents physical and chemical challenges.
Terminology: A galvanic cell is also referred to as a voltaic cell.

Corrosion: If the electrodes (metallic pieces) are placed in the same beaker, corrosion of the metal occurs rapidly.
Surface Layers: When oxidation and reduction happen together in the same beaker, a "lust" or a specific layer of material builds up on the electrode. Over time, one of the electrodes will be completely lost or degraded, particularly the one undergoing oxidation.

To prevent degradation and manage the reaction, components are isolated into two separate beakers representing two half-reactions.
Anode (The Left Side): This is where oxidation always occurs. In a spontaneous (galvanic) cell, the anode is the negative electrode. It is the chemical with the more negative (or lower positive) reduction potential.
Cathode (The Right Side): This is where reduction always occurs. In a spontaneous cell, it is the positive electrode. It is the chemical with the less negative (or more positive) reduction potential.

The Wire: An external wire is used to convey electrons from the anode to the cathode.
The Salt Bridge: This is an inverted U-shared tube (often called a "salted bridge") that allows for the exchange of ions between the two beakers.
- It can be made of glass, plastic, or even a simple straw.
- Alternatives include filter paper or regular paper that has been rolled and flipped upside down.
- It is essential for maintaining electrical neutrality by allowing ions to pass between the anode and cathode sections.

The tendency of a substance to gain electrons is its reduction potential ( $E^\circ$ ).
Spontaneous Logic: The substance with the higher (more positive) potential will naturally gain electrons (reduction at the cathode). The substance with the lower (more negative) potential has the ability to give electrons away (oxidation at the anode).
Example (Zinc-Copper Cell):
- Copper ( $Cu^{2+}$ ): Potential is $0.34\,V$ . Reaction: $Cu^{2+} + 2e^- \rightarrow Cu_{(s)}$ . Note: "s" indicates the solid metal state, denoted as zero charge.
- Zinc ( $Zn$ ): Potential is $-0.76\,V$ . Because it is more negative, Zinc acts as the anode in a galvanic cell.
- Overall Cell Potential ( $E^\circ_{cell}$ ) calculation: $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$ .
- For Zinc and Copper: $0.34\,V - (-0.76\,V) = 1.1\,V$ .

Standard Conditions ( $E^\circ$ , $\Delta G^\circ$ ): The circle symbol indicates measurements taken at standard conditions: $1\,\text{atm}$ pressure, $25\,^\circ\text{C}$ , and $1\,\text{M}$ (one mole) concentration.
Gibbs Free Energy (Delta G): Related to cell potential via the equation $\Delta G^\circ = -nFE^\circ_{cell}$ , where $n$ is the number of electrons transferred and $F$ is the Faraday constant.
Relationships:
- If $E^\circ_{cell}$ is Positive: $\Delta G^\circ$ is negative, the reaction is spontaneous (Galvanic/Voltaic).
- If $E^\circ_{cell}$ is Negative: $\Delta G^\circ$ is positive, the reaction is non-spontaneous (Electrolytic).

The relationship between the standard cell potential and the equilibrium constant ( $K$ ) is defined by the following formula: $E^\circ_{cell} = \frac{0.0592\,V}{n} \log(K)$
Equilibrium Trends:
- If $K > 1$ (forward reaction favored): $E^\circ_{cell}$ is positive (spontaneous).
- If $K < 1$ : $\log(K)$ is negative, making $E^\circ_{cell}$ negative (non-spontaneous).

Feature	Galvanic (Voltaic) Cell	Electrolytic Cell
Spontaneity	Spontaneous ( $E^\circ_{cell} > 0$ )	Non-Spontaneous ( $E^\circ_{cell} < 0$ )
Energy Change	Chemical to Electrical	Electrical to Chemical
Anode	Oxidation; Negative (-)	Oxidation; Positive (+)
Cathode	Reduction; Positive (+)	Reduction; Negative (-)
Logic	Natural flow: negative to positive	Forced flow: outside source flips circuit
Examples	Batteries (e.g., Duracell)	Battery chargers / electrolysis

Vowel-Vowel: Anode is Oxidation (both start with vowels).
Consonant-Consonant (Speaker refers to as "Silent-Silent"): Cathode is Reduction.

When conditions deviate from the standard ( $1\,\text{atm}$ , $25\,^\circ\text{C}$ , or $1\,\text{M}$ concentration), the Nernst Equation must be used to calculate cell potential ( $E$ ).
The Nernst Equation: $E = E^\circ_{cell} - \frac{0.0592}{n} \log(Q)$
Components:
- $E$ : Cell potential under non-standard conditions.
- $E^\circ_{cell}$ : Standard cell potential ( $E^\circ_{cathode} - E^\circ_{anode}$ ).
- $n$ : Number of electrons transferred.
- $Q$ : Reaction quotient (concentrations of products over reactants at non-equilibrium).

Reference Electrode: The standard for comparison is the Standard Hydrogen Electrode (SHE), which has a reduction potential of exactly $0\,V$ .
Strongest Oxidizing Agents: Located at the top of the potential chart with the most positive potentials.
- Fluorine ( $F_2$ ): Has a very high positive potential, approximately $2.87\,V$ to $2.9\,V$ .
Strongest Reducing Agents: Located at the bottom of the chart with the most negative potentials.
- Lithium ( $Li$ ): Listed at the very end as the most negative. This means it has a high tendency to give electrons away (high oxidation potential).

The Driving Force of Lightning vs. Batteries:

Discussion Point: The driving force for both lightning and battery operation is identical: electrochemistry and chemical reactions.
Question: What do you expect in lightning? Do you expect electrons in the clouds?
Answer: Lightning involves the discharge of electrons (electrochemistry) caused by potential differences in the atmosphere, similar to the potentials discussed in chemical cells.