Unit 4 - Notes

CHE124 8 min read

Unit 4: Electrochemistry

1. Introduction to Electrolytes and Conductance

1.1 Electrolytes

Substances that conduct electricity in their molten state or aqueous solution due to the movement of ions are called electrolytes.

Strong Electrolytes: Completely dissociate into ions (e.g., HCl, NaOH, NaCl). High conductivity.
Weak Electrolytes: Partially dissociate (e.g., CH₃COOH, NH₄OH). Low conductivity.

1.2 Concepts of Conductance

In metallic conductors, current is carried by electrons. In electrolytic conductors, current is carried by ions.

A. Resistance ( $R$ )

Obstruction to the flow of current.
Unit: Ohm ( $\Omega$ )
Formula:
- $l$ = distance between electrodes (cm)
- $A$ = cross-sectional area of electrodes (cm²)
- $\rho$ = Specific resistance (Resistivity)

B. Conductance ( $G$ )

Reciprocal of resistance.
Unit: Siemens ( $S$ ) or Ohm⁻¹ ( $\Omega^{-1}$ ) or mho.
Formula: $G = \frac{1}{R}$

C. Specific Conductance ( $\kappa$ - Kappa)

Conductance of a solution enclosed between two electrodes of 1 cm² area separated by 1 cm distance (i.e., conductance of 1 cm³ of solution).
Formula: $\kappa = \frac{1}{\rho} = \frac{1}{R} \cdot \frac{l}{A} = G \cdot \text{Cell Constant}$
Unit: $S \cdot \text{cm}^{-1}$ or $\Omega^{-1} \cdot \text{cm}^{-1}$

D. Molar Conductance ( $\Lambda_m$ )

Conductance of all ions produced by dissolving 1 mole of electrolyte in $V$ cm³ of solution.
Formula:
- $M$ = Molarity (mol/L)
Unit: $S \cdot \text{cm}^2 \cdot \text{mol}^{-1}$

2. Cell Constant and Its Determination

Definition

The ratio of the distance between the electrodes ( $l$ ) to the area of cross-section ( $A$ ) of the electrodes is a constant for a specific conductivity cell.
$\text{Cell Constant} (K) = \frac{l}{A}$

Unit: $\text{cm}^{-1}$ or $\text{m}^{-1}$

Determination (Experimental)

Since measuring $l$ and $A$ physically is difficult due to irregular electrode surfaces, the cell constant is determined indirectly:

A standard solution of KCl (whose specific conductance $\kappa$ is known accurately at various temperatures) is used.
The resistance ( $R$ ) of this KCl solution is measured using a Wheatstone bridge circuit.
Calculation:
$\text{Cell Constant} = \text{Specific Conductance of KCl} \times \text{Measured Resistance}$
$\frac{l}{A} = \kappa \cdot R$

Numerical Example 1 (Conductance)

Problem: A conductivity cell filled with 0.1 M KCl solution has a resistance of 100 $\Omega$ . If the specific conductance of 0.1 M KCl is 1.29 $\text{S m}^{-1}$ , calculate the cell constant. If the same cell is filled with 0.02 M electrolyte solution offering a resistance of 520 $\Omega$ , calculate the Molar Conductance of the 0.02 M solution.

Solution:

Calculate Cell Constant ( $K$ ):
$K = \kappa_{KCl} \times R_{KCl}$
$K = 1.29 \, \text{S m}^{-1} \times 100 \, \Omega = 129 \, \text{m}^{-1} = 1.29 \, \text{cm}^{-1}$
Calculate $\kappa$ of 0.02 M solution:
$\kappa_{sol} = \frac{K}{R_{sol}} = \frac{129 \, \text{m}^{-1}}{520 \, \Omega} = 0.248 \, \text{S m}^{-1}$
Convert to $\text{S cm}^{-1}$ : $0.248 / 100 = 0.00248 \, \text{S cm}^{-1}$
Calculate Molar Conductance ( $\Lambda_m$ ):
$\Lambda_m = \frac{\kappa \, (\text{in S cm}^{-1}) \times 1000}{\text{Molarity}}$
$\Lambda_m = \frac{0.00248 \times 1000}{0.02}$
$\Lambda_m = 124 \, \text{S cm}^2 \text{mol}^{-1}$

3. Electrochemical Cells

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions.

3.1 Types of Cells

Feature	Electrolytic Cell	Galvanic (Voltaic) Cell
Energy Conversion	Electrical Energy $\to$ Chemical Energy	Chemical Energy $\to$ Electrical Energy
Spontaneity	Non-spontaneous ( $\Delta G > 0$ )	Spontaneous ( $\Delta G < 0$ )
Anode Charge	Positive (+)	Negative (-)
Cathode Charge	Negative (-)	Positive (+)
Electron Flow	Into cell at cathode, out at anode	Out of anode, into cathode

3.2 Galvanic Cell Structure (Daniel Cell)

A classic example consisting of Zinc and Copper half-cells.

Anode (Oxidation): Zinc rod in ZnSO₄ solution.
$\text{Zn}(s) \to \text{Zn}^{2+}(aq) + 2e^-$
Cathode (Reduction): Copper rod in CuSO₄ solution.
$\text{Cu}^{2+}(aq) + 2e^- \to \text{Cu}(s)$
Salt Bridge: A U-tube containing inert electrolyte (KCl/KNO₃) in agar-agar jelly. It maintains electrical neutrality and completes the circuit.

Detailed schematic diagram of a Daniel Cell (Galvanic Cell). Left beaker contains Zinc rod dipped in... — AI-generated image — may contain inaccuracies

4. Electrode Potentials

4.1 Origin of Single Electrode Potential

When a metal ( $M$ ) is placed in a solution of its own ions ( $M^{n+}$ ), two opposing tendencies operate:

Solution Pressure ( $P_s$ ): Tendency of metal atoms to lose electrons and pass into solution as cations (Oxidation).
Osmotic Pressure ( $P_o$ ): Tendency of metal ions from solution to gain electrons and deposit on the metal (Reduction).

If $P_s > P_o$ : Oxidation occurs (Anode). The rod becomes negatively charged.
If $P_o > P_s$ : Reduction occurs (Cathode). The rod becomes positively charged.

4.2 Helmholtz Double Layer (HDL)

The separation of charges at the interface between the electrode and the electrolyte creates a potential difference.

Fixed Layer: A layer of ions adheres directly to the electrode surface (e.g., if the rod is negative, positive ions adsorb).
Diffuse Layer: A layer of ions of opposite charge distributed in the solution near the fixed layer.
This arrangement acts like a parallel plate capacitor, generating the electrode potential.

A conceptual diagram of the Helmholtz Double Layer (HDL) at a metal-solution interface. The left sid... — AI-generated image — may contain inaccuracies

4.3 Electrochemical Series

Arrangement of elements in increasing order of their Standard Reduction Potentials ( $E^\circ$ ).

Top (Negative $E^\circ$ ): Strong reducing agents (Li, K, Na, Zn). Active metals.
Hydrogen: $E^\circ = 0.00$ V (Reference).
Bottom (Positive $E^\circ$ ): Strong oxidizing agents (Cu, Ag, Au, F₂). Noble metals.

5. Cell EMF and Nernst Equation

5.1 Cell EMF

The Electromotive Force (EMF) is the potential difference between the two electrodes when no current flows.
$E_{cell} = E_{\text{cathode}} - E_{\text{anode}} \quad (\text{Using Reduction Potentials})$
$E_{cell} = E_{\text{right}} - E_{\text{left}}$

5.2 Nernst Equation

Dependence of electrode potential on concentration and temperature.

For a half-cell reaction: $M^{n+} + ne^- \to M$
$E = E^\circ - \frac{RT}{nF} \ln \frac{[\text{Product}]}{[\text{Reactant}]}$
$E = E^\circ - \frac{RT}{nF} \ln \frac{[M]}{[M^{n+}]}$

Since $[M]$ (solid) = 1, and converting $\ln$ to $\log_{10}$ at 298 K ( $25^\circ\text{C}$ ):
$E = E^\circ - \frac{0.0591}{n} \log \frac{1}{[M^{n+}]}$
$E = E^\circ + \frac{0.0591}{n} \log [M^{n+}]$

For a full cell: $aA + bB \to cC + dD$
$E_{cell} = E_{cell}^\circ - \frac{0.0591}{n} \log \frac{[C]^c [D]^d}{[A]^a [B]^b}$

Numerical Example 2 (Nernst Equation)

Problem: Calculate the EMF of the cell at $25^\circ\text{C}$ :
$\text{Zn} \,|\, \text{Zn}^{2+} (0.01 \text{M}) \,||\, \text{Cu}^{2+} (0.1 \text{M}) \,|\, \text{Cu}$
Given: $E^\circ_{\text{Zn}^{2+}/\text{Zn}} = -0.76 \, \text{V}$ , $E^\circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34 \, \text{V}$ .