Key Concepts of Electrochemical Cells

Why This Matters

Electrochemistry sits at the intersection of thermodynamics and electricity—two pillars of the AP Chemistry curriculum. When you understand electrochemical cells, you're not just memorizing battery types; you're mastering spontaneity, Gibbs free energy, redox reactions, and the Nernst equation all at once. The AP exam loves to test whether you can predict if a reaction will occur on its own or needs an external push, and electrochemical cells are the perfect vehicle for those questions.

Here's what you need to internalize: every electrochemical cell demonstrates a fundamental principle about energy conversion and electron flow. The exam will ask you to compare cell types, calculate potentials, and explain why certain reactions require energy input while others release it. Don't just memorize which electrode is which—know what concept each cell illustrates and you'll be ready for any FRQ they throw at you.

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Spontaneous vs. Non-Spontaneous Systems

The most fundamental distinction in electrochemistry is whether a reaction happens on its own. Spontaneous reactions have negative Gibbs free energy ($\Delta G < 0$) and positive cell potential ($E°_{cell} > 0$), while non-spontaneous reactions require energy input.

Galvanic (Voltaic) Cells

• Convert chemical energy to electrical energy—these cells harness spontaneous redox reactions to produce usable electricity
• Positive cell potential ($E°_{cell} > 0$) indicates the reaction is thermodynamically favorable and will proceed without external intervention
• Anode is negative, cathode is positive—electrons flow spontaneously from the oxidation site to the reduction site through an external circuit

Electrolytic Cells

• Use electrical energy to force non-spontaneous reactions—the external power source provides the energy needed to overcome an unfavorable $\Delta G$
• Negative cell potential ($E°_{cell} < 0$) means the reaction would never occur on its own; you're essentially reversing thermodynamic preference
• Anode is positive, cathode is negative—the polarity is reversed compared to galvanic cells because an external source drives electron flow

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Reference Standards and Measurement

To compare electrode potentials, chemists need a universal baseline. The standard hydrogen electrode establishes the zero point against which all other half-reactions are measured.

Standard Hydrogen Electrode (SHE)

• Defined potential of exactly 0.00 V—this arbitrary but essential reference allows all other electrode potentials to be compared on the same scale
• Platinum electrode with $H_2$ gas at 1 atm in contact with 1 M $H^+$ solution; platinum is inert and simply facilitates electron transfer
• Half-reaction: $2H^+(aq) + 2e^- \rightarrow H_2(g)$—memorize this as your reference point for calculating standard cell potentials

Daniell Cell

• Classic galvanic cell using zinc and copper—serves as the textbook example for teaching electrode potential calculations
• $Zn$ anode ($E° = -0.76$ V) oxidizes while $Cu^{2+}$ reduces at the cathode ($E° = +0.34$ V), giving $E°_{cell} = 1.10$ V
• Salt bridge maintains electrical neutrality—allows ion flow between half-cells without mixing the solutions directly

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Concentration Effects

Not all cells rely on different chemical species. Concentration cells demonstrate that voltage can arise purely from concentration gradients, following the Nernst equation.

Concentration Cells

• Same electrode material in both half-cells—the only driving force is the difference in ion concentration between the two compartments
• Voltage calculated using the Nernst equation: $E = E° - \frac{RT}{nF}\ln Q$, where $E° = 0$ because the electrodes are identical
• Ions migrate from high to low concentration—this spontaneous movement toward equilibrium generates a small but measurable potential

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Rechargeable Battery Systems

Rechargeable batteries function as galvanic cells during discharge and electrolytic cells during charging. The reversibility of the redox reactions determines whether a battery can be recharged.

Lead-Acid Battery

• Rechargeable workhorse using $PbO_2$ and $Pb$ electrodes—the same chemistry powers car batteries and backup systems worldwide
• Sulfuric acid ($H_2SO_4$) electrolyte participates directly in the reaction, forming $PbSO_4$ on both electrodes during discharge
• High current output but heavy—the lead electrodes make these batteries impractical for portable devices despite their reliability

Lithium-Ion Battery

• Highest energy density of common rechargeable batteries—lithium's small size and low reduction potential maximize energy storage per unit mass
• Lithium ions intercalate (insert between layers) in graphite anode and metal oxide cathode during charge/discharge cycles
• No memory effect and low self-discharge—these advantages make Li-ion the standard for smartphones, laptops, and electric vehicles

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Primary (Non-Rechargeable) Cells

Primary batteries undergo irreversible reactions—once the reactants are consumed, the battery is dead. These cells prioritize shelf life, stable voltage, or low cost over rechargeability.

Leclanché Cell (Dry Cell)

• Paste electrolyte makes it portable—the "dry" design prevents leakage, unlike early wet cells with liquid electrolytes
• Zinc anode and $MnO_2$/carbon cathode—manganese dioxide acts as a depolarizer, preventing hydrogen gas buildup that would stop the reaction
• Voltage drops during use—as zinc is consumed and products accumulate, the cell potential gradually decreases (unlike mercury cells)

Mercury Cell

• Extremely stable voltage output—the flat discharge curve made these ideal for precision devices like watches and medical equipment
• $HgO$ cathode and $Zn$ anode in alkaline electrolyte; the mercury(II) oxide reduction maintains consistent potential until exhaustion
• Environmental toxicity limits modern use—mercury disposal concerns have largely replaced these with silver oxide or lithium alternatives

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Continuous Energy Conversion

Unlike batteries that store fixed amounts of chemical energy, fuel cells convert fuel continuously. As long as reactants are supplied, the cell keeps producing electricity.

Fuel Cells

• Direct conversion of fuel to electricity—typically $H_2 + \frac{1}{2}O_2 \rightarrow H_2O$, bypassing the inefficiencies of combustion
• Higher theoretical efficiency than heat engines—not limited by Carnot efficiency because they don't rely on thermal gradients
• Only byproduct is water (for hydrogen fuel cells)—this makes them attractive for zero-emission vehicles and power generation

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Quick Reference Table

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Self-Check Questions

1. Which two cell types both involve spontaneous reactions but differ in whether they store energy or convert fuel continuously? What thermodynamic quantity is negative for both?

2. A student connects two copper electrodes to solutions of $CuSO_4$ at different concentrations. What type of cell is this, and why is $E° = 0$ for this setup?

3. Compare and contrast lead-acid and lithium-ion batteries in terms of their advantages, disadvantages, and typical applications. Why can both be recharged?

4. An FRQ shows a cell with $E°_{cell} = -1.5$ V and asks whether it will function spontaneously. What type of cell must this be, and what would you need to add to make the reaction proceed?

5. Why does a mercury cell maintain constant voltage during discharge while a dry cell's voltage drops? Which property of the mercury cell made it valuable for precision instruments?