Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental relationship in chemistry that connects pressure, volume, temperature, and moles of a gas. It combines Boyle’s, Charles’s, and Avogadro’s laws into one equation, making it a powerful tool for understanding gases under ideal conditions.

Table of Contents

• Equation & Variables
• Derivation of Ideal Gas Law
• Molecular Perspective
• Real-Life Applications
• Limitations
• Example Problem
• Quick Reference Table
• Quiz
• MCQs
• FAQs

Equation & Variables

The Ideal Gas Law is expressed as:

PV = nRT

• P = Pressure (atm or Pa)
• V = Volume (L or m³)
• n = Number of moles
• R = Ideal Gas Constant (learn more)
• T = Temperature in Kelvin

Derivation of Ideal Gas Law

• Boyle’s Law: P ∝ 1/V (T constant)
• Charles’s Law: V ∝ T (P constant)
• Avogadro’s Law: V ∝ n (T,P constant)

Combining: V ∝ nT/P → PV = nRT

Molecular Perspective

• Gas molecules have negligible volume.
• No intermolecular forces.
• Collisions are perfectly elastic.

Real-Life Applications

• Airbags: Gas expansion after a chemical reaction.
• Ventilators: Modeling lung pressure and volume.
• Weather Balloons: Expansion with altitude.
• SCUBA Diving: Pressure & air consumption calculations.

Limitations

• Fails at high pressure & low temperature.
• Assumes point particles and no attractions.
• Corrections made using the Van der Waals Equation.

Example Problem

Q: Calculate moles in 10 L container at 2 atm, 300K (R = 0.0821 L·atm/mol·K).

Solution: n = (2×10) / (0.0821×300) ≈ 0.812 mol

Quick Reference Table

Constant	Symbol	Value	Units
Ideal Gas Constant	R	0.0821	L·atm/mol·K
Avogadro’s Number	NA	6.022 × 10²³	particles/mol

Quiz

1. What does R represent?
   Answer: Gas Constant
   Explanation: Proportionality constant in PV = nRT.
2. If T increases at constant V?
   Answer: Pressure increases
   Explanation: PV = nRT, so P ∝ T.
3. When does Ideal Gas Law fail?
   Answer: Low T, High P
   Explanation: Intermolecular forces become significant.

MCQs

1. Which laws combine to form Ideal Gas Law?
   a) Boyle, Charles, Avogadro ✅
2. Unit of R in SI?
   a) 8.314 J/mol·K ✅
3. Which gas behaves most ideally?
   a) He ✅

FAQs

Q1: What is Ideal Gas Law used for?
A: To relate pressure, volume, temperature, and moles of gases.

Q2: When do real gases deviate?
A: At high pressure and low temperature.

Q3: Is any gas truly ideal?
A: No, but many approximate ideal behavior at low pressure & high temperature.