3.3 Oxidation-Reduction, Electrochemistry, and Corrosion Basics

3.3 Oxidation-Reduction, Electrochemistry, and Corrosion Basics

Electrochemistry governs critical engineering phenomena including battery operations, electroplating, sensor technology, fuel cells, and structural corrosion control. The FE Other Disciplines exam evaluates redox balancing, cell EMF, non-standard Nernst potentials, Faraday's electrolysis law, and corrosion mitigation techniques.

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1. Oxidation States and Redox Reaction Fundamentals

An oxidation-reduction (redox) reaction involves the transfer of electrons between chemical species.

Definitions

• Oxidation: Loss of electrons $\rightarrow$ Oxidation state increases (becomes more positive).
• Reduction: Gain of electrons $\rightarrow$ Oxidation state decreases (becomes more negative).
• Reducing Agent: The species that loses electrons (is oxidized) and reduces another species.
• Oxidizing Agent: The species that gains electrons (is reduced) and oxidizes another species.

Mnemonic: OIL RIG — Oxidation Is Loss, Reduction Is Gain of electrons.

Rules for Assigning Oxidation Numbers

1. Free elements in uncombined states have an oxidation number of $0$ (e.g., $\text{Fe}(s), \text{O}_2(g), \text{H}_2(g)$).
2. Monatomic ions have an oxidation number equal to their ionic charge (e.g., $\text{Fe}^{3+} = +3$, $\text{Cl}^- = -1$).
3. Fluorine is always $-1$. Alkali metals (Group 1) are $+1$; Alkaline earth metals (Group 2) are $+2$.
4. Hydrogen is $+1$ when bonded to nonmetals and $-1$ when bonded to metals (hydrides).
5. Oxygen is usually $-2$ (except in peroxides like $\text{H}_2\text{O}_2$ where it is $-1$, or bound to fluorine).
6. The sum of oxidation numbers equals $0$ for neutral molecules, or the net charge for polyatomic ions.

Balancing Redox Reactions (Half-Reaction Method)

To balance complex redox reactions in acidic solution:

1. Separate the overall reaction into oxidation and reduction half-reactions.
2. Balance all elements except $\text{H}$ and $\text{O}$.
3. Balance $\text{O}$ by adding $\text{H}_2\text{O}$.
4. Balance $\text{H}$ by adding $\text{H}^+$.
5. Balance charge by adding electrons ($e^-$).
6. Multiply half-reactions by integers so electrons lost equal electrons gained, then sum and simplify.
7. (For basic solutions: add $\text{OH}^-$ to both sides equal to $\text{H}^+$ to form water and simplify).

2. Electrochemical Cells, Standard Potentials, and Nernst Equation

Electrochemical cells convert chemical energy into electrical energy (Galvanic/Voltaic cell) or use electrical energy to drive non-spontaneous reactions (Electrolytic cell).

Cell Components and Terminology

• Anode: Electrode where oxidation occurs (AN OX). Electrons leave the cell from the anode.
• Cathode: Electrode where reduction occurs (RED CAT). Electrons enter the cathode.
• Salt Bridge: Maintains electrical neutrality by allowing ion migration between half-cells.

Standard Cell Potential ($E^\circ_{\text{cell}}$)

Standard reduction potentials ($E^\circ$) are tabulated at $25^\circ\text{C}$, $1\text{ atm}$, and $1.0\text{ M}$ concentration relative to the Standard Hydrogen Electrode (SHE, $E^\circ = 0.00\text{ V}$).

NCEES Formula: Standard Cell EMF

$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

Relationship to Free Energy and Equilibrium

NCEES Formula: Gibbs Free Energy & Cell EMF

$\Delta G^\circ = -n F E^\circ_{\text{cell}}$ $\Delta G^\circ = -R T \ln K$

where:

• $n$ = number of moles of electrons transferred in balanced reaction
• $F$ = Faraday's constant ($96,485 \text{ C/mol e}^- \approx 96,500 \text{ J/(V}\cdot\text{mol e}^-)$)
• Spontaneous Galvanic Cell: $E^\circ_{\text{cell}} > 0 \implies \Delta G^\circ < 0$ and $K > 1$.
• Non-spontaneous Electrolytic Cell: $E^\circ_{\text{cell}} < 0 \implies \Delta G^\circ > 0$.

Nernst Equation for Non-Standard Concentrations

When species concentrations deviate from $1.0\text{ M}$, cell potential is adjusted using the reaction quotient $Q$:

NCEES Formula: Nernst Equation

$E = E^\circ_{\text{cell}} - \frac{R T}{n F} \ln Q$ At $T = 298.15\text{ K}$ ($25^\circ\text{C}$), substituting constants yields: $E = E^\circ_{\text{cell}} - \frac{0.0592}{n} \log_{10} Q$

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Worked Engineering Example: Galvanic Cell and Nernst Potential

Problem: A galvanic cell operates at $25^\circ\text{C}$ with a zinc anode immersed in $0.010\text{ M}$ $\text{Zn}^{2+}$ solution and a copper cathode immersed in $0.500\text{ M}$ $\text{Cu}^{2+}$ solution. Standard reduction potentials are:

• $\text{Cu}^{2+}(aq) + 2 e^- \rightarrow \text{Cu}(s), \quad E^\circ = +0.337\text{ V}$
• $\text{Zn}^{2+}(aq) + 2 e^- \rightarrow \text{Zn}(s), \quad E^\circ = -0.763\text{ V}$

1. Calculate the standard cell potential ($E^\circ_{\text{cell}}$).
2. Determine the non-standard cell potential ($E$) using the Nernst equation.

Solution:

Step 1: Calculate $E^\circ_{\text{cell}}$: Copper has a higher reduction potential, so it undergoes reduction at the cathode. Zinc undergoes oxidation at the anode. $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = +0.337\text{ V} - (-0.763\text{ V}) = +1.100\text{ V}$

Step 2: Formulate overall reaction and evaluate $Q$: Overall cell reaction: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightleftharpoons \text{Zn}^{2+}(aq) + \text{Cu}(s)$ ($n = 2\text{ mol e}^-$) $Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.010\text{ M}}{0.500\text{ M}} = 0.020$

Step 3: Apply Nernst Equation: $E = E^\circ_{\text{cell}} - \frac{0.0592}{n} \log_{10} Q$ $E = 1.100 - \frac{0.0592}{2} \log_{10}(0.020)$ $\log_{10}(0.020) = -1.6990$ $E = 1.100 - (0.0296) \times (-1.6990) = 1.100 + 0.0503 = 1.1503\text{ V} \approx 1.15\text{ V}$ Conclusion: Lowering anode concentration $[\text{Zn}^{2+}]$ relative to cathode concentration $[\text{Cu}^{2+}]$ increases cell voltage from $1.10\text{ V}$ to $1.15\text{ V}$ by shifting thermodynamic equilibrium forward.

3. Faraday's Law of Electrolysis and Corrosion Protection

Electrochemistry enables quantitative plating analysis and dictates structural degradation mechanisms.

Faraday's Law of Electrolysis

Faraday's Law dictates that the mass of substance deposited or liberated at an electrode during electrolysis is directly proportional to the total electric charge passed through the cell.

NCEES Formula: Electrodeposited Mass

$m = \frac{I \cdot t \cdot M}{n \cdot F} \quad \text{or} \quad Q_{\text{charge}} = I \cdot t$

where:

• $m$ = mass of electrodeposited substance (grams, $\text{g}$)
• $I$ = electric current (amperes, $\text{A} = \text{C/s}$)
• $t$ = time elapsed (seconds, $\text{s}$)
• $M$ = molar mass of species ($\text{g/mol}$)
• $n$ = moles of electrons transferred per mole of ion ($e^-/\text{ion}$)
• $F$ = Faraday's constant ($96,485 \text{ C/mol e}^-$)

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Worked Engineering Example: Industrial Electroplating Mass Calculation

Problem: An industrial electroplating bath plates nickel metal onto structural steel components using a current of $25.0\text{ A}$ passed for $3.00\text{ hours}$. The nickel electrolyte contains $\text{Ni}^{2+}$ ions ($M = 58.69\text{ g/mol}$). Calculate the total mass of nickel deposited.

Solution:

Step 1: Convert time to seconds: $t = 3.00\text{ hours} \times 3600\text{ s/hour} = 10,800\text{ s}$

Step 2: Compute total electrical charge ($Q$): $Q_{\text{charge}} = I \cdot t = 25.0\text{ A} \times 10,800\text{ s} = 270,000\text{ C}$

Step 3: Apply Faraday's Law ($n = 2$ for $\text{Ni}^{2+}$): $m = \frac{Q_{\text{charge}} \cdot M}{n \cdot F} = \frac{(270,000\text{ C}) \cdot (58.69\text{ g/mol})}{(2\text{ e}^-/\text{ion}) \cdot (96,485\text{ C/mol e}^-)}$ $m = \frac{15,846,300}{192,970} = 82.118\text{ g} \approx 82.1\text{ g}$ Conclusion: Operating at $25.0\text{ A}$ for $3\text{ hours}$ deposits $82.1\text{ g}$ of nickel coating onto the steel components.

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Corrosion Principles and Mitigation

Corrosion is the unintentional electrochemical destruction of metals by environmental reaction. A complete corrosion cell requires four elements: Anode, Cathode, Electrolyte, and Metallic Conductive Path.

Fundamental Corrosion Reactions (Steel in Water)

• Anodic Reaction (Oxidation): Metal dissolves, liberating electrons. $\text{Fe}(s) \rightarrow \text{Fe}^{2+}(aq) + 2 e^-$
• Cathodic Reaction (Reduction): Oxygen or hydrogen ions consume electrons.
  • Neutral/Basic Aerated Water: $\text{O}_2 + 2 \text{H}_2\text{O} + 4 e^- \rightarrow 4 \text{OH}^-$
  • Acidic Environment: $2 \text{H}^+ + 2 e^- \rightarrow \text{H}_2(g)$

Galvanic Series and Galvanic Corrosion

When two dissimilar metals are electrically coupled in an electrolyte, the metal higher (more active/anodic) in the Galvanic Series corrodes preferentially, protecting the less active (cathodic/noble) metal.

Engineering Corrosion Protection Techniques

1. Sacrificial Anode Cathodic Protection (SACP): Connecting structural steel (e.g., pipelines, ship hulls) to a more active, sacrificial metal anode (Magnesium, Zinc, or Aluminum). The active anode corrodes while steel acts as the cathode.
2. Impressed Current Cathodic Protection (ICCP): Applying an external DC power supply to drive electrons into the protected structure using inert non-consumable anodes.
3. Galvanization: Coating steel with a protective layer of Zinc. Zinc provides both a barrier and sacrificial anodic protection if scratched.
4. Inhibitors & Coatings: Epoxy paint barriers, anodic passivating inhibitors (chromates/nitrites), or cathodic inhibitors.

4. Summary Table of Electrochemical Cell Types & Corrosion Control