Coulomb’s law concepts

Coulomb's Law describes the electrostatic force between two charged particles. This fundamental principle is essential for understanding atomic structure, chemical bonding, and periodic trends.

Key Definition

Coulomb's Law states: The electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The Mathematical Formula

F = k(q₁q₂)/r²

Where:

• F = electrostatic force (Newtons, N)
• k = Coulomb's constant (8.99 × 10⁹ N·m²·C⁻²)
• q₁ and q₂ = charges on particles (Coulombs, C)
• r = distance between charge centres (metres, m)

Essential Terminology

Electrostatic attraction: Force between oppositely charged particles (negative force value)

Electrostatic repulsion: Force between like-charged particles (positive force value)

Nuclear charge (Z): Number of protons in the nucleus, determines positive charge

Effective nuclear charge (Z_eff): Net positive charge experienced by an electron after accounting for shielding by inner electrons

Memory Aid - QDIR: "Queen's Diamonds Increase Radiance" reminds you that force depends on Quarges (multiplied), Distance (squared), and has an Inverse Relationship with distance.

Key Relationships

• Doubling charge → force increases by factor of 2
• Doubling distance → force decreases by factor of 4 (1/2² = 1/4)
• Tripling distance → force decreases by factor of 9 (1/3² = 1/9)

Understanding Coulomb's Law in Chemistry

Coulomb's Law explains why ionic compounds have high melting points. In sodium chloride (NaCl), Na⁺ and Cl⁻ ions experience strong electrostatic attraction. The small ionic radii and full unit charges create enormous forces holding the crystal lattice together, requiring substantial energy to break these interactions.

Real-World Analogy: The Magnetic Ball Pit

Imagine two powerful magnets in a ball pit. When magnets are close together (small r), you feel intense attraction—hard to pull apart! Move them farther apart, and the force weakens dramatically. Now imagine one magnet is twice as strong (doubled q)—the pull is exactly twice as intense. This mirrors how Coulomb's Law operates with charged particles.

Periodic Trends Explained

Atomic radius trends directly relate to Coulomb's Law. Moving across Period 3 (Na → Ar), nuclear charge increases but electrons occupy the same shell. The increased q₁ (nuclear charge) with constant r means stronger electrostatic attraction, pulling electrons closer and reducing atomic radius.

Ionization energy increases across periods because greater nuclear charge requires more energy to overcome the electrostatic attraction between nucleus and outer electrons.

Everyday Applications

Electrostatic precipitators in power stations use Coulomb's Law—charged plates attract oppositely charged ash particles, removing pollution from exhaust gases. The closer the plates (r decreases), the stronger the force capturing particles.

Xerography (photocopying) relies on electrostatic forces. Toner particles are attracted to charged regions on a drum where charge magnitude and distance determine image quality.

Real Chemistry: Ion-dipole interactions in dissolving ionic compounds demonstrate Coulomb's Law—water's partial charges interact with ions, with force depending on charge and separation distance.

Example 1: Comparing Electrostatic Forces

Question: Calculate the ratio of electrostatic force between a nucleus and electron when the distance doubles.

Solution:

Step 1: Write Coulomb's Law for initial situation F₁ = k(q₁q₂)/r₁²

Step 2: Write equation for doubled distance F₂ = k(q₁q₂)/(2r₁)² = k(q₁q₂)/4r₁²

Step 3: Calculate ratio F₁/F₂ = [k(q₁q₂)/r₁²] ÷ [k(q₁q₂)/4r₁²] = 4

Answer: Force decreases by factor of 4 (becomes ¼ of original value)

Examiner Note: Always show the mathematical working. Cambridge awards method marks even with numerical errors.

Example 2: Ionic Radius and Force

Question: Explain why Mg²⁺ has higher hydration enthalpy than Na⁺ using Coulomb's Law.

Solution:

Step 1: Identify relevant charges

• Mg²⁺: q = +2
• Na⁺: q = +1

Step 2: Consider ionic radii

• Mg²⁺: smaller radius (same period, more protons)
• Therefore smaller r in Coulomb's Law

Step 3: Apply Coulomb's Law reasoning F = k(q₁q₂)/r²

Mg²⁺ has double the charge AND smaller radius. Both factors increase force substantially.

Step 4: Link to hydration enthalpy Stronger electrostatic attraction between Mg²⁺ and water dipoles → more energy released → higher (more negative) hydration enthalpy.

Answer: Mg²⁺ has greater charge (+2 vs +1) and smaller radius, both increasing electrostatic force with water molecules (Coulomb's Law), releasing more energy upon hydration.

Cambridge Tip: Link Coulomb's Law explicitly to energy changes—examiners award marks for making these connections clear.