Electrochemistry Part 2

Electrochemistry Part 2 for FAD1018 Basic Chemistry II. Source file: L3 Stdn Copy.pdf (34 pages, PowerPoint slides).

[!note] Direct Image Processing Content reconstructed from direct visual processing of all 34 slide images.

Learning Outcomes

  • Explain the driving force behind electrochemical cells
  • Relate cell potential to Gibbs free energy and equilibrium
  • Use the Nernst equation to calculate cell potential under non-standard conditions
  • Solve quantitative problems involving cell potential and pH

1. The Driving Force Behind Electrochemical Cells

Cell potential works like water pressure:

  • Electrons flow from higher "eagerness to give" (anode) to lower "eagerness to take" (cathode)
  • Just like water flows from high to low, electrons flow from higher to lower reduction potential

$$E = 0 \text{ at equilibrium}$$

At equilibrium:

  • There is no more "pressure difference"
  • Forward and reverse reactions are perfectly balanced
  • No net "push" to drive electrons through the wire
  • The voltage reads zero, not because nothing is happening, but because both directions are happening equally

The Dead Battery Analogy

A dead battery is not out of chemicals — the forward and reverse reactions have reached equilibrium, so there is no longer any net push to drive electrons.

2. Cell Potential and Spontaneity

$$E°{cell} = E°{cathode} - E°_{anode}$$

  • $E°_{cell} > 0$: spontaneous reaction (galvanic cell)
  • $E°_{cell} < 0$: non-spontaneous reaction (requires electrolytic cell)
  • $E°_{cell} = 0$: equilibrium (dead battery)

3. The Nernst Equation

Relates cell potential to concentration under non-standard conditions:

$$E_{cell} = E°_{cell} - \left(\frac{RT}{nF}\right) \ln Q$$

At $T = 25°C$:

$$E_{cell} = E°_{cell} - \frac{0.0592}{n} \log Q$$

Where:

  • $R$ = gas constant (8.314 J·mol⁻¹·K⁻¹)
  • $T$ = temperature in Kelvin
  • $n$ = number of electrons transferred
  • $F$ = Faraday constant (96,485 C·mol⁻¹)
  • $Q$ = reaction quotient

4. Worked Examples from Lecture

Example 1: Identify Cathode and Anode

Given half-equations, determine cathode/anode using standard reduction potentials: $$E°{cell} = E°{cathode} - E°_{anode}$$

Example 2: Calculate Cell Potential

Given:

  • $E°_{\text{Mg}^{2+}/\text{Mg}} = -2.37$ V
  • $E°_{\text{Ca}^{2+}/\text{Ca}} = -2.76$ V

Solution:

  1. Mg²⁺/Mg is more positive → cathode
  2. Ca²⁺/Ca is more negative → anode
  3. $E°_{cell} = (-2.37) - (-2.76) = +0.39$ V

Practice 4: Calculate [H⁺] and pH from Cell Potential

A galvanic cell consists of a Zn/Zn²⁺ half-cell and the Standard Hydrogen Electrode (SHE). Given:

  • $[\text{Zn}^{2+}] = 0.45$ M
  • $P_{\text{H}_2} = 2.0$ atm
  • $T = 25°C$
  • Voltmeter shows $E_{cell} = 0.65$ V

Strategy: Use the Nernst equation to solve for $[\text{H}^+]$, then calculate pH.

5. Gibbs Free Energy and Cell Potential

$$\Delta G = -nFE_{cell}$$

$$\Delta G° = -nFE°_{cell}$$

  • Negative $\Delta G$ → spontaneous reaction
  • Positive $\Delta G$ → non-spontaneous reaction
  • At equilibrium: $\Delta G = 0$ and $E_{cell} = 0$

Relationship to Equilibrium Constant

$$\Delta G° = -RT \ln K$$

Combining with $\Delta G° = -nFE°{cell}$: $$E°{cell} = \frac{RT}{nF} \ln K$$

At 25°C: $$E°_{cell} = \frac{0.0592}{n} \log K$$

Key Concepts

  • Electrochemistry — Concept page
  • Nernst Equation — Cell potential under non-standard conditions
  • Gibbs Free Energy — Thermodynamic spontaneity
  • Galvanic Cell — Spontaneous cells
  • Equilibrium Constant — K and cell potential

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