Standard Reduction Potentials

Why This Matters

Standard reduction potentials are the foundation of electrochemistry—they're how you predict whether a reaction will happen spontaneously, calculate the voltage a cell can produce, and connect electrochemical behavior to thermodynamic quantities like Gibbs free energy. When you see an AP Chemistry question about galvanic cells, batteries, or corrosion, you're really being tested on your ability to use E° values to make predictions and perform calculations.

The key concepts here are spontaneity prediction, cell potential calculations, the Nernst equation, and thermodynamic relationships. Don't just memorize that "positive E°cell means spontaneous"—understand why the math works and how to apply it to unfamiliar scenarios. The exam loves to test whether you can identify oxidizing vs. reducing agents, calculate cell potentials from a table, and connect $\Delta G°$ to $E°_{cell}$. Master these relationships, and you'll handle any electrochemistry problem thrown your way.

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The Reference Point: Establishing the Scale

Every measurement needs a reference point, and electrochemistry is no exception. All standard reduction potentials are measured relative to a single, universally agreed-upon standard.

Standard Hydrogen Electrode (SHE)

• Assigned exactly 0.00 V by convention—this arbitrary reference point makes all other E° values meaningful and comparable
• Setup consists of a platinum electrode in contact with $H_2$ gas at 1 atm and $H^+$ ions at 1 M concentration
• Enables the electrochemical series by providing a consistent baseline for measuring the reduction tendency of all other half-reactions

Standard Reduction Potential Definition

• Measures the tendency of a species to gain electrons—expressed in volts (V) under standard conditions (1 M, 1 atm, 25°C)
• Higher E° values indicate stronger oxidizing agents—these species more readily accept electrons and undergo reduction
• Lower E° values indicate stronger reducing agents—these species more readily donate electrons and undergo oxidation

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The Electrochemical Series: Ranking Reactivity

The electrochemical series organizes half-reactions by their reduction potentials, giving you a powerful tool for predicting reaction outcomes. Species higher on the table (more positive E°) will oxidize species lower on the table.

Electrochemical Series

• Arranged from most positive to most negative E° values—creating a hierarchy of oxidizing and reducing strength
• Predicts reaction direction automatically—the half-reaction with higher E° proceeds as reduction, the lower one as oxidation
• Common exam values to know: $F_2$ (+2.87 V) is the strongest oxidizing agent; $Li^+$ (−3.04 V) makes Li the strongest reducing agent

Predicting Spontaneous Redox Reactions

• Positive $E°_{cell}$ indicates spontaneity—the reaction proceeds without external energy input
• Calculate using $E°_{cell} = E°_{cathode} - E°_{anode}$—always subtract the oxidation half-reaction's reduction potential
• Identify cathode and anode from E° values—the half-reaction with higher E° occurs at the cathode (reduction site)

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Calculating Cell Potential: The Math

Cell potential calculations appear constantly on the AP exam. The key is remembering that you always use reduction potentials in the formula, even for the half-reaction that runs in reverse.

Calculating Cell Potential (EMF)

• Use $E°_{cell} = E°_{cathode} - E°_{anode}$—never add the potentials; always subtract
• Represents maximum voltage the cell can produce—actual voltage is always slightly lower due to internal resistance
• Sign determines spontaneity—positive means spontaneous (galvanic cell), negative means non-spontaneous (electrolytic cell)

Nernst Equation

• Adjusts cell potential for non-standard conditions: $E = E° - \frac{RT}{nF}\ln(Q)$ or at 25°C: $E = E° - \frac{0.0592}{n}\log(Q)$
• Q is the reaction quotient—ratio of product concentrations to reactant concentrations, each raised to stoichiometric coefficients
• Explains why cell voltage decreases as reaction proceeds—as products accumulate, Q increases and E decreases toward zero

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Thermodynamic Connections: Energy and Spontaneity

Electrochemistry bridges the gap between electrical measurements and thermodynamic quantities. The relationships between E°, $\Delta G°$, and K are among the most frequently tested connections on the AP exam.

Relationship Between Gibbs Free Energy and Cell Potential

• Connected by $\Delta G° = -nFE°_{cell}$—where n is moles of electrons transferred and F is Faraday's constant (96,485 C/mol)
• Signs are opposite—positive $E°_{cell}$ gives negative $\Delta G°$, both indicating spontaneity
• Allows conversion between electrical and thermodynamic data—if you know one, you can calculate the other

Concentration Cells

• Both electrodes are identical material in different concentrations—the only driving force is the concentration difference
• Electrons flow from dilute to concentrated side—the system spontaneously moves toward equilibrium (equal concentrations)
• $E°_{cell} = 0$ but E ≠ 0—standard potential is zero because electrodes are identical, but Nernst equation gives non-zero actual potential

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Real-World Applications: Batteries and Corrosion

Understanding standard reduction potentials explains how batteries work and why metals corrode. These applications connect abstract E° values to observable phenomena.

Electrochemical Cells and Batteries

• Convert chemical energy to electrical energy—spontaneous redox reactions drive electron flow through an external circuit
• Primary cells are single-use; secondary cells are rechargeable—recharging reverses the redox reaction using external current
• Cell voltage depends on electrode materials—choosing half-reactions with large E° differences maximizes voltage output

Corrosion and Its Prevention

• Corrosion is spontaneous oxidation of metals—iron rusting ($Fe \rightarrow Fe^{2+} + 2e^-$) is accelerated by moisture and electrolytes
• Sacrificial anodes protect valuable metals—zinc or magnesium (lower E°) oxidizes preferentially, sparing the protected metal
• Galvanization and coatings create physical barriers—preventing contact with water and oxygen stops the electrochemical process

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Quick Reference Table

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Self-Check Questions

1. Given that $E°(Cu^{2+}/Cu) = +0.34$ V and $E°(Zn^{2+}/Zn) = -0.76$ V, which metal is oxidized in a galvanic cell, and what is the cell potential?

2. How does increasing the concentration of products in a galvanic cell affect the cell potential, according to the Nernst equation?

3. Compare and contrast a galvanic cell and a concentration cell—what drives electron flow in each case?

4. If $E°_{cell} = +1.10$ V and 2 moles of electrons are transferred, calculate $\Delta G°$ and explain what the sign tells you about spontaneity.

5. Why does zinc make an effective sacrificial anode for protecting iron, based on their standard reduction potentials?