Chemistry Physical - How to Solve: Gaseous State (Ideal Gas Law, Dalton’s Law, Kinetic Theory, Van der Waals Equation) – NEET UG Guide

How to Solve: Gaseous State (Ideal Gas Law, Dalton’s Law, Kinetic Theory, Van der Waals Equation) – NEET UG Guide

Introduction

Mastering the Gaseous State unlocks 5-7 direct questions in NEET UG (Physics + Chemistry), worth 20+ marks—enough to boost your rank by 10,000+ places. Whether it’s calculating lung pressure in respiration or industrial gas storage, these laws explain real-world phenomena and high-scoring exam problems.

WHAT YOU NEED TO KNOW FIRST

Before diving in, ensure you understand:
1. Basic algebra (rearranging equations, unit conversions).
2. Pressure, volume, temperature (PVT) relationships (Boyle’s, Charles’s, Gay-Lussac’s laws).
3. Mole concept (Avogadro’s number, molar mass).

If any of these are shaky, stop now and review them—this guide assumes you’re solid on them.

KEY TERMS & FORMULAS

1. Ideal Gas Law

Formula: PV = nRT - P = Pressure (atm, Pa, mmHg) → MEMORISE UNITS - V = Volume (L, m³) → 1 m³ = 1000 L - n = Moles of gas (mol) - R = Universal gas constant → MEMORISE VALUES: - 0.0821 L·atm·mol⁻¹·K⁻¹ (most common for NEET) - 8.314 J·mol⁻¹·K⁻¹ (if pressure is in Pa) - T = Temperature (ALWAYS in Kelvin) → K = °C + 273

When to use: When any 3 variables (P, V, n, T) are given, and you need the 4th.

2. Dalton’s Law of Partial Pressures

Formula: P_total = P₁ + P₂ + P₃ + … - P_total = Total pressure of gas mixture - P₁, P₂, … = Partial pressures of individual gases

Partial Pressure Formula: P₁ = (n₁ / n_total) × P_total - n₁ = Moles of gas 1 - n_total = Total moles of all gases

When to use: When gases are mixed (e.g., air = N₂ + O₂ + CO₂).

3. Kinetic Theory of Gases

Key Equations:
1. Root Mean Square Speed (u_rms): u_rms = √(3RT / M) - R = 8.314 J·mol⁻¹·K⁻¹ - M = Molar mass (kg/mol) → Convert g/mol to kg/mol (÷1000) - T = Temperature (K)

1. Average Kinetic Energy (KE_avg): KE_avg = (3/2) kT
2. k = Boltzmann constant = 1.38 × 10⁻²³ J/K → MEMORISE
3. T = Temperature (K)

When to use: - u_rms → Comparing speeds of different gases. - KE_avg → Relating temperature to energy.

4. Van der Waals Equation (Real Gases)

Formula: [P + (an²/V²)] [V - nb] = nRT - a = Attraction correction (given in exam) - b = Volume correction (given in exam) - n, P, V, R, T = Same as Ideal Gas Law

When to use: When the question explicitly mentions "real gas" or gives a and b values.

STEP-BY-STEP METHOD

Step 1: Identify the Given & Required

• Read the question carefully.
• List all given values (P, V, n, T, etc.) with units.
• Circle what you need to find.

Step 2: Choose the Right Formula

• Ideal Gas Law? → PV = nRT
• Gas mixture? → Dalton’s Law
• Speed/energy? → Kinetic Theory
• Real gas? → Van der Waals

Step 3: Convert Units (CRUCIAL!)

• Pressure: atm → Pa (×101325) or mmHg → atm (÷760)
• Volume: mL → L (÷1000) or cm³ → m³ (×10⁻⁶)
• Temperature: °C → K (+273)
• Moles: Mass → Moles (÷ molar mass)

Step 4: Plug & Solve

• Substitute values into the formula.
• Solve for the unknown.
• Check units in the final answer.

Step 5: Verify Reasonableness

• Does the answer make sense?
• Example: If temperature increases, pressure should increase (if V is constant).
• Example: u_rms should be higher for lighter gases (e.g., H₂ > O₂).

WORKED EXAMPLES

Example 1 – Basic (Ideal Gas Law)

Question: A 2 L container holds 0.5 moles of O₂ at 27°C. What is the pressure inside?

Step-by-Step Solution:
1. Given: - V = 2 L - n = 0.5 mol - T = 27°C = 27 + 273 = 300 K - R = 0.0821 L·atm·mol⁻¹·K⁻¹

1. Formula: PV = nRT

2. Rearrange for P: P = (nRT) / V

3. Plug in values: P = (0.5 × 0.0821 × 300) / 2 P = (12.315) / 2 P = 6.1575 atm

4. Check:

5. Units: atm (correct)
6. Reasonable? Yes (0.5 mol in 2 L at 300 K ≈ 6 atm).

What we did and why: - Converted °C to K (mandatory for gas laws). - Used PV = nRT because only P was unknown. - Verified units and reasonableness.

Example 2 – Medium (Dalton’s Law)

Question: A mixture contains 2 g H₂ and 8 g O₂ in a 10 L container at 27°C. Find the partial pressure of H₂.

Step-by-Step Solution:
1. Given: - Mass of H₂ = 2 g → Molar mass = 2 g/mol → n_H₂ = 2/2 = 1 mol - Mass of O₂ = 8 g → Molar mass = 32 g/mol → n_O₂ = 8/32 = 0.25 mol - V = 10 L - T = 27°C = 300 K - R = 0.0821 L·atm·mol⁻¹·K⁻¹

1. Find total moles (n_total): n_total = n_H₂ + n_O₂ = 1 + 0.25 = 1.25 mol

2. Find total pressure (P_total) using Ideal Gas Law: PV = nRT → P = (nRT)/V P_total = (1.25 × 0.0821 × 300) / 10 P_total = 3.07875 atm

3. Find partial pressure of H₂ (P_H₂): P_H₂ = (n_H₂ / n_total) × P_total P_H₂ = (1 / 1.25) × 3.07875 P_H₂ = 2.463 atm

What we did and why: - Converted masses to moles (essential for gas laws). - Calculated total pressure first, then used Dalton’s Law for partial pressure. - Ensured all units were consistent (L, atm, K).

Example 3 – Exam-Style (Kinetic Theory + Real Gas)

Question: At 300 K, compare the root mean square speeds of H₂ and O₂. If the same gases are at high pressure (real gas conditions), which correction term (a or b) in the Van der Waals equation will have a greater effect on H₂?

Step-by-Step Solution:

Part 1: u_rms Comparison

1. Formula: u_rms = √(3RT / M)
2. For H₂:
3. M = 2 g/mol = 0.002 kg/mol
4. u_rms(H₂) = √(3 × 8.314 × 300 / 0.002) = 1934 m/s
5. For O₂:
6. M = 32 g/mol = 0.032 kg/mol
7. u_rms(O₂) = √(3 × 8.314 × 300 / 0.032) = 483 m/s
8. Conclusion: H₂ is faster (lighter gas).

Part 2: Van der Waals Correction

1. H₂ has weak intermolecular forces → Low ‘a’ value (attraction correction).
2. H₂ has very small size → Low ‘b’ value (volume correction).
3. At high pressure:
4. Volume correction (b) dominates because gas molecules occupy significant space.
5. H₂’s ‘b’ term will have a greater effect than ‘a’ (since ‘a’ is already small).

What we did and why: - Used u_rms formula to compare speeds (lighter gas = faster). - Analyzed Van der Waals terms based on molecular properties (size vs. attraction). - Exam trap: Many students forget that ‘b’ dominates at high pressure, not ‘a’.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before Exam)

"Listen up—this is your 60-second crash course for Gaseous State in NEET:

1. Ideal Gas Law (PV = nRT): Memorise R = 0.0821 L·atm·mol⁻¹·K⁻¹. Always convert °C to K.
2. Dalton’s Law: Total pressure = sum of partial pressures. Partial pressure = (moles of gas / total moles) × total pressure.
3. Kinetic Theory: u_rms = √(3RT/M). Lighter gas = faster speed. KE_avg = (3/2)kT.
4. Van der Waals: [P + (an²/V²)][V - nb] = nRT. ‘a’ = attraction, ‘b’ = volume.
5. Common mistakes: Wrong units, forgetting Kelvin, mixing up ‘a’ and ‘b’.
6. Exam traps: Hidden unit conversions, real gas disguised as ideal.

Now go solve 3 problems—one from each topic. You’ve got this!