Quick Summary
Gaseous state is a numerical-heavy chapter with high NEET weightage (2–3 questions). Master gas law formulae, unit conversions, and the concept of real vs ideal gases. Board exams test derivations of gas laws and van der Waals equation significance.
Key Concepts and Definitions
- Ideal gas: Gas that obeys PV = nRT exactly at all conditions
- Real gas: Gas that deviates from ideal behaviour at high P and low T
- STP (Standard Temperature and Pressure): 0°C (273 K) and 1 bar
- Root mean square speed (u_rms): √(3RT/M)
- Average speed (u_avg): √(8RT/πM)
- Most probable speed (u_mp): √(2RT/M)
- Diffusion: Spreading of gas molecules from high to low concentration
- Effusion: Escape of gas through a pinhole
Formulae
| Law / Concept | Formula |
|---|---|
| Boyle's Law | P₁V₁ = P₂V₂ (constant T, n) |
| Charles' Law | V₁/T₁ = V₂/T₂ (constant P, n) |
| Gay-Lussac's Law | P₁/T₁ = P₂/T₂ (constant V, n) |
| Avogadro's Law | V ∝ n (constant T, P) |
| Ideal Gas Equation | PV = nRT |
| Combined Gas Law | P₁V₁/T₁ = P₂V₂/T₂ |
| Graham's Law | Rate ∝ 1/√M |
| van der Waals | (P + an²/V²)(V − nb) = nRT |
| u_rms | √(3RT/M) |
| Compressibility factor Z | Z = PV/nRT |
Gas Laws — Graphical Summary
- Boyle's Law: P vs 1/V is a straight line; P vs V is a hyperbola
- Charles' Law: V vs T (K) is a straight line through origin
- Gay-Lussac's: P vs T (K) is a straight line through origin
Real Gases and Deviation from Ideal Behaviour
| Condition | Behaviour |
|---|---|
| Low pressure, high T | Approaches ideal |
| High pressure | Z > 1 (volume effect dominates) |
| Low temperature | Z < 1 (attractive forces dominate) |
van der Waals constants:
- 'a': measure of intermolecular attraction (higher for polar/large molecules)
- 'b': measure of molecular volume (excluded volume)
Kinetic Molecular Theory
1. Molecules have negligible volume compared to container 2. No intermolecular forces in ideal gas 3. Molecules move in straight lines with random directions 4. All collisions are perfectly elastic 5. Average kinetic energy = (3/2)kT where k = Boltzmann constant
From KMT: KE = ½mu² = (3/2)kT → u_rms = √(3kT/m) = √(3RT/M)
Important Questions
One Mark (5)
- State Boyle's law.
- What is the value of R in J mol⁻¹ K⁻¹?
- Write Graham's law of diffusion.
- Define compressibility factor Z.
- At what conditions does a real gas behave ideally?
Short Answer 3-mark (3)
- Derive the combined gas law from Boyle's and Charles' laws.
- A gas at 27°C and 1 atm occupies 2 L. What volume will it occupy at 127°C and 2 atm?
- Explain why real gases deviate from ideal behaviour at high pressure.
Long Answer 5-mark (2)
- State and explain the postulates of kinetic molecular theory. Derive the expression for root mean square speed.
- Write the van der Waals equation for real gases. Explain the significance of constants a and b.
Common Mistakes
- Using Celsius instead of Kelvin in gas law calculations — always convert T to Kelvin.
- Forgetting to use consistent units (P in atm/bar, V in L, R = 0.0821 L·atm/mol·K or 8.314 J/mol·K).
- Confusing u_rms, u_avg, and u_mp — they have different formulae.
- Applying van der Waals to ideal gas problems.
Board Exam Tips
- At least one gas law numerical appears every year — know all formula variants.
- Graham's law problems (comparing rates of diffusion) are frequent 3-mark questions.
- Kinetic molecular theory postulates are a guaranteed 5-mark question.
- NEET: Z vs P graphs and conditions for ideal behaviour are common MCQs.
Revision Checklist
- [ ] All five gas laws written with conditions
- [ ] PV = nRT numerical solved with correct R value
- [ ] u_rms, u_avg, u_mp formulae noted and compared
- [ ] van der Waals constants a and b explained
- [ ] Z > 1 and Z < 1 conditions understood
Frequently Asked Questions
At constant temperature and fixed amount of gas, the pressure is inversely proportional to volume: PV = constant (P₁V₁ = P₂V₂).