Electrochemistry: Cells, Batteries, Faraday’s Laws & Industrial Uses

What is Electrochemistry?

Electrochemistry is the branch of chemistry that studies the relationship between electricity and chemical reactions. It deals with two main processes:

1. Electrolysis: Using electricity to drive a non-spontaneous chemical reaction (e.g., charging a battery).
2. Galvanic (Voltaic) Cells: Using a spontaneous chemical reaction to produce electricity (e.g., a lemon battery).

Key Concepts:

• Redox Reactions: All electrochemical processes involve oxidation (loss of electrons) and reduction (gain of electrons).
• Electrodes: Two conductors (anode and cathode) where redox reactions occur.
• Electrolyte: A solution or paste that allows ions to move between electrodes.

1. Galvanic Cells (Voltaic Cells)

A galvanic cell converts chemical energy into electrical energy through a spontaneous redox reaction.

How it Works:

1. Anode (–ve electrode): Oxidation occurs here. Electrons are released into the external circuit. Example: $\text{Zn}\to {\text{Zn}}^{2+}+2e^{-}$
2. Cathode (+ve electrode): Reduction occurs here. Electrons are gained from the external circuit. Example: $2{\text{H}}^{+}+2e^{-}\to {\text{H}}_2$
3. Salt Bridge: Allows ions to move and maintain electrical neutrality.

Diagram of a Simple Galvanic Cell (Zn-Cu Cell):

![zinc copper galvanic cell diagram](/media/68f434f360509b80e93f.png "Labelled diagram of a Zn-Cu galvanic cell showing Zn anode, Cu cathode, salt bridge, and flow of electrons. (Image: Original: Ohiostandard Vector: AntiCompositeNumber, CC BY-SA 4.0, via Wikimedia Commons)")

graph LR
    A["Zn(s) --> Zn2+ + 2e-"] -->|"Electrons flow"| B["External Circuit"]
    C["Cu2+ + 2e- --> Cu(s)"] -->|"Salt Bridge"| D["ZnSO4 solution"]
    B --> C
    D -->|"SO4^2- ions"| E["CuSO4 solution"]

Example: Zn-Cu Cell

• Anode (Oxidation): $\text{Zn}\to {\text{Zn}}^{2+}+2e^{-}$
• Cathode (Reduction): ${\text{Cu}}^{2+}+2e^{-}\to \text{Cu}$
• Overall Reaction: $\text{Zn}+{\text{Cu}}^{2+}\to {\text{Zn}}^{2+}+\text{Cu}$

Standard Cell Potential ($E_{\text{cell}}^{\circ }$)

• $E_{\text{cell}}^{\circ }=E_{\text{cathode}}^{\circ }-E_{\text{anode}}^{\circ }$
• For Zn-Cu cell: $E_{\text{cell}}^{\circ }=0.34\text{V}-(-0.76\text{V})=1.10\text{V}$

2. Electrolytic Cells

Electrolytic cells use external electricity to force a non-spontaneous reaction (e.g., charging a battery, electroplating).

How it Works:

1. Anode (+ve electrode): Oxidation occurs (electrons are pulled away). Example: $2{\text{H}}_2\text{O}\to {\text{O}}_2+4{\text{H}}^{+}+4e^{-}$
2. Cathode (–ve electrode): Reduction occurs (electrons are pushed in). Example: $2{\text{H}}_2\text{O}+2e^{-}\to {\text{H}}_2+2{\text{OH}}^{-}$

Diagram of Electrolysis of Water:

![electrolysis of water apparatus](/media/19459f484d0f9d83b1bd.png "Labelled setup showing inert electrodes (Pt or C), power supply, and gas collection. (Image: Ivan Akira, CC BY-SA 3.0, via Wikimedia Commons)")

graph LR
    A["Power Supply (+ve)"] --> B["Anode: Oxidation"]
    C["Cathode: Reduction"] --> D["Power Supply (-ve)"]
    B -->|"O2 gas"| E["Gas Collection"]
    C -->|"H2 gas"| F["Gas Collection"]
    G["Water"] --> B & C

Example: Electrolysis of Molten NaCl

• Anode (Oxidation): $2{\text{Cl}}^{-}\to {\text{Cl}}_2+2e^{-}$
• Cathode (Reduction): ${\text{Na}}^{+}+e^{-}\to \text{Na}$
• Overall Reaction: $2\text{NaCl}\to 2\text{Na}+{\text{Cl}}_2$

3. Faraday’s Laws of Electrolysis

Faraday’s laws explain how much substance is deposited or liberated during electrolysis.

First Law:

The amount of substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.

Mathematically: $$m=Z\times I\times t$$ Where:

• $m$ = mass deposited (g)
• $Z$ = electrochemical equivalent (g/C)
• $I$ = current (A)
• $t$ = time (s)

Second Law:

When the same quantity of electricity is passed through different electrolytes, the amount of substance deposited is proportional to the equivalent weight of the substance.

Mathematically: $$m\propto \frac{\text{Molar Mass}}{\text{Valency}}$$

Example: Calculating Mass of Copper Deposited

Given:

• Current ($I$) = 2 A
• Time ($t$) = 10 minutes = 600 s
• Electrochemical equivalent of Cu ($Z$) = 0.000329 g/C

Solution: $$m=Z\times I\times t=0.000329\times 2\times 600=0.3948\text{g}$$

4. Nernst Equation

The Nernst equation relates the cell potential ($E$) to the standard cell potential ($E^{\circ }$) and the concentrations of reactants/products.

$$E=E^{\circ }-\frac{RT}{nF}\ln Q$$ At 298 K (25°C): $$E=E^{\circ }-\frac{0.0592}{n}\log Q$$

Where:

• $E$ = cell potential (V)
• $E^{\circ }$ = standard cell potential (V)
• $R$ = gas constant (8.314 J/mol·K)
• $T$ = temperature (K)
• $n$ = number of electrons transferred
• $F$ = Faraday’s constant (96,500 C/mol)
• $Q$ = reaction quotient ($\frac{[\text{Products}]}{[\text{Reactants}]}$)

Example: Calculating Cell Potential for a Zn-Cu Cell

Given:

• $E_{\text{cell}}^{\circ }=1.10\text{V}$
• $[{\text{Zn}}^{2+}]=0.1\text{M}$
• $[{\text{Cu}}^{2+}]=0.01\text{M}$
• $n=2$

Solution: $$Q=\frac{[{\text{Zn}}^{2+}]}{[{\text{Cu}}^{2+}]}=\frac{0.1}{0.01}=10$$ $$E=1.10-\frac{0.0592}{2}\log 10=1.10-0.0296=1.0704\text{V}$$

5. Batteries and Fuel Cells

Primary and Secondary Cells:

Example: Lead-Acid Battery

• Anode (Oxidation): $\text{Pb}+{\text{HSO}}_4^{-}\to {\text{PbSO}}_4+{\text{H}}^{+}+2e^{-}$
• Cathode (Reduction): ${\text{PbO}}_2+{\text{HSO}}_4^{-}+3{\text{H}}^{+}+2e^{-}\to {\text{PbSO}}_4+2{\text{H}}_2\text{O}$
• Overall Reaction: $\text{Pb}+{\text{PbO}}_2+2{\text{H}}_2{\text{SO}}_4\to 2{\text{PbSO}}_4+2{\text{H}}_2\text{O}$

6. Corrosion and Its Prevention

Corrosion is the oxidation of metals (e.g., rusting of iron) due to reaction with oxygen and moisture.

How Corrosion Occurs (Iron Rusting):

$$4\text{Fe}+3{\text{O}}_2+6{\text{H}}_2\text{O}\to 4{\text{Fe(OH)}}_3$$ $$2{\text{Fe(OH)}}_3\to {\text{Fe}}_2{\text{O}}_3\cdot {\text{H}}_2\text{O}+2{\text{H}}_2\text{O}$$

Prevention Methods:

1. Barrier Protection: Paint, grease, or plastic coatings.
2. Sacrificial Protection: Attach a more reactive metal (e.g., Zn) to the iron (galvanization).
3. Cathodic Protection: Use an external current to prevent oxidation.

7. Electroplating

Electroplating is used to coat a cheap metal with a thin layer of expensive metal (e.g., silver plating, chromium plating).

Example: Silver Plating a Spoon

• Electrolyte: Silver nitrate (${\text{AgNO}}_3$)
• Anode: Silver ($\text{Ag}$)
• Cathode: Spoon (to be plated)
• Reaction:
  • Anode: $\text{Ag}\to {\text{Ag}}^{+}+e^{-}$
  • Cathode: ${\text{Ag}}^{+}+e^{-}\to \text{Ag}$

Exam Tip: How to Score Full Marks

1. Diagrams: Always draw labelled diagrams for galvanic and electrolytic cells. Show the direction of electron flow and ion movement.
2. Equations: Write balanced half-reactions and overall reactions for cells.
3. Calculations:
   • For Faraday’s laws, remember $m=ZIt$.
   • For Nernst equation, substitute values carefully and show all steps.
4. Applications: Link theory to real-world examples (e.g., batteries, corrosion, electroplating).
5. Key Terms: Define terms like anode, cathode, electrolyte, salt bridge, and overpotential.

NEB Board-Style Questions (Practice)

Short Answer:

1. Define electromotive force (emf) of a cell.
2. Why is a salt bridge necessary in a galvanic cell?
3. Write the Nernst equation and explain its significance.

Long Answer:

4. Describe the construction and working of a lead-acid battery. Why is it called a secondary cell?
5. Calculate the mass of copper deposited when a current of 5 A is passed through a solution of copper sulfate for 2 hours. (Given: $Z_{\text{Cu}}=0.000329\text{g/C}$)
6. Explain the principle of electroplating. How is silver plating carried out?

Summary Table: Galvanic vs. Electrolytic Cells