7.2 General Chemistry & Materials Science

7.2 General Chemistry & Materials Science

Chemical concepts and materials science are essential components of the ESAS syllabus for the REE licensure exam. Electrical engineers must analyze electrochemical energy storage (batteries), electrodeposition, corrosion prevention in grounding grids, and material dielectric/conducting properties.

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1. Atomic Structure & Chemical Stoichiometry

The Mole Concept & Stoichiometric Relations

• Mole ($n$): Quantity containing Avogadro's number of entities ($N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}$): $n = \frac{m}{M}$ where $m$ is sample mass in grams and $M$ is molar mass in $\text{g/mol}$.

Ideal Gas Law

For ideal gases under pressure $P$, volume $V$, absolute temperature $T$, and amount $n$:

$P V = n R T$

• Universal Gas Constant ($R$):
  • $R = 8.314\ \text{J}/(\text{mol}\cdot\text{K})$
  • $R = 0.08206\ \text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})$
• Standard Temperature & Pressure (STP): $T = 0^\circ\text{C} = 273.15\ \text{K}$, $P = 1\ \text{atm}$. At STP, 1 mole of an ideal gas occupies $22.414\ \text{L}$.

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2. Electrochemistry & Faraday's Laws of Electrolysis

Electrochemistry governs chemical energy conversion in batteries, fuel cells, electroplating, and corrosion processes.

Faraday's First & Second Laws of Electrolysis

The mass $m$ of a substance liberated or deposited at an electrode during electrolysis is directly proportional to total electric charge $Q = I t$ passing through the electrolyte:

$m = \frac{Q M}{z F} = \frac{I t M}{z F}$

where:

• $I$ = constant electric current in amperes (A)
• $t$ = time duration in seconds (s)
• $M$ = molar mass of the deposited element (g/mol)
• $z$ = valence number of ions (electrons transferred per ion)
• $F$ = Faraday's Constant = $96,485\ \text{C/mol}$ (charge per mole of electrons)

Electrochemical Cell Potential & The Nernst Equation

For a general redox reaction $aA + bB \rightleftharpoons cC + dD$, the cell electromotive force $E$ under non-standard concentration conditions at $T = 298.15\ \text{K}$ ($25^\circ\text{C}$) is given by the Nernst Equation:

$E = E^0 - \frac{R T}{n F} \ln Q = E^0 - \frac{0.0592}{n} \log_{10} \left( \frac{[C]^c [D]^d}{[A]^a [B]^b} \right)$

where $E^0$ is standard cell potential, $n$ is number of moles of electrons transferred, and $Q$ is the reaction quotient.

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3. Corrosion Engineering & Prevention

Corrosion is the electrochemical deterioration of a metal resulting from reaction with its environment.

Galvanic Corrosion Mechanisms

When two dissimilar metals with different standard electrode potentials are electrically coupled in an electrolyte, the more active metal acts as the anode and undergoes accelerated oxidation (corrosion), while the noble metal acts as the cathode.

$\text{Anodic Oxidation (Loss of } e^-): \text{M} \rightarrow \text{M}^{z+} + z e^-$

$\text{Cathodic Reduction (Gain of } e^-): 2\text{H}^+ + 2e^- \rightarrow \text{H}_2 \quad \text{or} \quad \text{O}_2 + 2\text{H}_2\text{O} + 4e^- \rightarrow 4\text{OH}^-$

Corrosion Mitigation Techniques

1. Sacrificial Anode Cathodic Protection (SACP): Connecting structural steel pipes or grounding grids to a more anode-active metal (such as Zinc or Magnesium). The sacrificial anode corrodes preferentially, protecting the primary steel structure.
2. Impressed Current Cathodic Protection (ICCP): Applying an external DC power source that drives protective electrons into the structure, forcing it to remain cathodic.
3. Galvanizing: Coating steel surfaces with a protective layer of zinc.

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4. Engineering Materials & Properties

Electrical materials are categorized based on electrical resistivity $\rho$, magnetic permeability $\mu$, thermal conductivity, and mechanical strength.

Electrical & Mechanical Property Definitions

• Electrical Resistivity ($\rho$): Resistance of a unit cube: $R = \rho \frac{L}{A}$ (unit: $\Omega\cdot\text{m}$ or $\Omega\cdot\text{cmil/ft}$).
• Temperature Coefficient of Resistance ($\alpha$): Change in resistance with temperature: $R_T = R_0 [1 + \alpha_0 (T - T_0)]$
• Hooke's Law & Young's Modulus ($E$): Ratio of tensile stress $\sigma = F/A$ to axial strain $\epsilon = \Delta L / L_0$ within elastic limit: $E = \frac{\sigma}{\epsilon}$

Comparison of Common Conductor Materials

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Solved Practice Examples

Example 1: Faraday's Law Mass Deposition

Problem: A constant direct current of $15.0\ \text{Amperes}$ is passed through a copper sulfate ($\text{CuSO}_4$) electroplating bath for $2.0\ \text{hours}$. Calculate the mass of pure copper deposited at the cathode. (Molar mass of $\text{Cu} = 63.55\ \text{g/mol}$, valence $z = 2$).

Solution:

1. Calculate total time in seconds: $t = 2.0 \times 3,600 = 7,200\ \text{s}$
2. Calculate total charge passed $Q = I t$: $Q = 15.0 \times 7,200 = 108,000\ \text{Coulombs}$
3. Apply Faraday's Law formula $m = \frac{I t M}{z F}$: $m = \frac{108,000 \times 63.55}{2 \times 96,485} = \frac{6,863,400}{192,970} \approx 35.57\ \text{grams}$

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Example 2: Nernst Cell Potential

Problem: Calculate the cell potential at $25^\circ\text{C}$ for a Daniel cell $\text{Zn}(s) | \text{Zn}^{2+}(0.01\text{ M}) || \text{Cu}^{2+}(1.0\text{ M}) | \text{Cu}(s)$ given standard cell potential $E^0 = +1.10\ \text{V}$ and $n = 2$.

Solution:

1. Reaction quotient $Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.01}{1.0} = 10^{-2}$.
2. Apply the Nernst Equation at $25^\circ\text{C}$: $E = E^0 - \frac{0.0592}{n} \log_{10} Q = 1.10 - \frac{0.0592}{2} \log_{10}(10^{-2})$
3. Evaluate log and calculate potential: $\log_{10}(10^{-2}) = -2 \implies E = 1.10 - (0.0296)(-2) = 1.10 + 0.0592 = 1.1592\ \text{V}$ The cell potential increases to $1.16\ \text{V}$ due to low zinc ion concentration.