Gas Laws and Ideal Gas Equation

• Understand Boyle's, Charles', and Gay-Lussac's laws and their mathematical forms
• Derive the combined gas law and ideal gas equation PV = nRT
• Apply Dalton's law of partial pressures and mole fraction
• Distinguish STP and SATP conditions and use them in calculations
• Solve multi-step problems involving gas mixtures
• Recognise the assumptions behind ideal behaviour and where they break down

Level 1 — Foundations

Boyle's Law (temperature constant): PV = constant → P₁V₁ = P₂V₂

Charles' Law (pressure constant): V/T = constant → V₁/T₁ = V₂/T₂ (T in Kelvin!)

Gay-Lussac's Law (volume constant): P/T = constant → P₁/T₁ = P₂/T₂

Avogadro's Law (T and P constant): V ∝ n → equal volumes of all gases at same T and P contain equal number of molecules

Key relationships at a glance:

Level 2 — JEE depth

Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂ (n constant)

Ideal Gas Equation: PV = nRT

Values of R:

• R = 8.314 J mol⁻¹ K⁻¹ (SI; use when P in Pa, V in m³)
• R = 0.0821 L atm mol⁻¹ K⁻¹ (use when P in atm, V in litres)
• R = 8.314 Pa m³ mol⁻¹ K⁻¹

Molar mass from ideal gas: M = mRT/PV (m = mass in grams)

Standard conditions:

• STP (IUPAC 1982 onwards): 0°C (273.15 K), 1 bar; molar volume ≈ 22.7 L/mol
• STP (older, still used in NCERT/JEE): 0°C, 1 atm; molar volume = 22.4 L/mol
• SATP: 25°C (298 K), 1 bar; molar volume ≈ 24.8 L/mol

Dalton's Law of Partial Pressures: P_total = P₁ + P₂ + P₃ + ... = ΣPᵢ

Each gas behaves independently; Pᵢ is the pressure gas i would exert alone in the same volume.

Mole fraction and partial pressure: xᵢ = nᵢ/n_total = Pᵢ/P_total → Pᵢ = xᵢ × P_total

Aqueous tension: when a gas is collected over water, P_dry gas = P_total − P_water vapour

JEE trap: Always convert °C to K. Forgetting this is the single most common error. T(K) = T(°C) + 273.

JEE trap: In Dalton's law, the volume must be the same for all gases. If given separate volumes, find moles first, then use n_total and new volume.

Gas at STP occupies 5.6 L — find moles and mass (M = 32 g/mol)

At STP (0°C, 1 atm), molar volume = 22.4 L/mol

n = V / V_molar = 5.6 L / 22.4 L mol⁻¹ = 0.25 mol

mass = n × M = 0.25 mol × 32 g/mol = 8 g

Answer: 0.25 mol, 8 g

3 mol of gas at 2 atm and 27°C — find volume

PV = nRT
T = 27 + 273 = 300 K
R = 0.0821 L atm mol⁻¹ K⁻¹

V = nRT/P = (3 × 0.0821 × 300) / 2
  = 73.89 / 2
  = 36.95 L ≈ 36.9 L

Answer: ≈ 36.9 L

• Q1: A gas occupies 4 L at 300 K and 1 atm. What volume does it occupy at 600 K and 2 atm?
• Q2: Calculate the number of moles in 11.2 L of CO₂ at STP (0°C, 1 atm).
• Q3: A mixture contains 2 mol N₂ and 3 mol O₂ at total pressure 5 atm. Find the partial pressure of each gas.
• Q4: Find the molar mass of a gas if 2 g occupies 1.12 L at STP.
• Stretch: Q5: A cylinder contains N₂ and H₂O vapour at 30°C. Total pressure is 800 mmHg. Aqueous tension at 30°C = 31.8 mmHg. Find mass of N₂ if volume = 5 L (R = 62.4 mmHg·L/mol·K).

NCERT Chapter 5 link: Chapter 5 (Class 11) — "States of Matter" covers all four gas laws, derivation of PV = nRT, Dalton's law, and numerical applications. Pay attention to solved examples 5.1 to 5.6 which directly map to JEE question types.

Exam connections: JEE Mains regularly tests (a) combined gas law single-step numericals, (b) Dalton's law with mole fraction, (c) molar mass from PV=nRT, and (d) volume at different STP/SATP conditions. JEE Advanced may ask multi-step problems involving gas mixtures reacting partially.

Study strategy: Master unit consistency first — write R with units every time. Then practise converting all conditions to a standard form (n, P, V, T) before applying PV = nRT. Do 10 numericals varying the unknown each time (sometimes solve for P, sometimes V, sometimes n).

• Use the platform-native live simulation or PhET-style tool for this topic.
• Mirror / body / home activity: Use a balloon, syringe, or bicycle pump — compress it (Boyle's) or warm it up (Charles') and describe what you observe for your portfolio.
• Voice or text reflection with AI Mentor: explain the concept to a younger student or family member.

• "Explain this concept to a Class 6 student using one real example from an Indian home, school, market, or festival."
• "What is one common mistake students make here, and how would you catch yourself making it?"
• Stretch: "How does this connect to coding, robotics, money, health, environment, or a future career?"

• Complete the core practice + one extension activity (photo, table, short reflection, or mini-project) for base XP + topic badge.
• 5-7 day streak or family discussion note = multiplier + visible artifact in parent/principal dashboard.
• Best real-world application stories (anonymised) featured on class or national leaderboard.

• One hands-on project or measurement using the Drishti kit or household items that makes the concept physical.
• Direct link to at least one Future Skill track (Money Management, Green Tech, Cyber Defenders, Micro-Entrepreneurship, AI Mastery, Sustainable Living, Personality Development).
• Coding extension where relevant (simple script, simulation, or data logging).

This material emphasises experiential "learning by doing", competency (apply/create/analyse), vocational exposure, critical thinking, and multidisciplinary connections. Designed to feed live worlds, AI Mentor (with memory), gamification, robotics, parent analytics, and future skills — not just exam prep.

Portfolio Evidence Idea: Your photo/table/reflection/project + one sentence on "How this helps me in real life or a possible future path."

Open the Practice tab for aligned questions (easy/medium/hard + case-based) with full AI scaffolding.

See curriculum for cross-links and the full future-skills/robotics chapters.