Topic 8.1.27 min read
Ideal Gas Equation and Boltzmann Constant
The ideal-gas equation relates pressure, volume, amount and absolute temperature. Using molecule number instead of moles gives PV = NkT, where k = RNₐ is Boltzmann’s constant.
Choose Your Level
Beginner Level
Pressure, volume, gas amount and temperature are connected. If one changes, the ideal-gas equation predicts how the others must respond.
Recommended for Class 11
Ideal Gas Equation and Boltzmann Constant
Overview
The ideal-gas equation relates pressure, volume, amount and absolute temperature. Using molecule number instead of moles gives PV = NkT, where k = RNₐ is Boltzmann’s constant.
Learning Outcomes
- PV = nRT uses amount in moles.
- n = N/Nₐ converts molecules to moles.
- PV = NkT uses the number of molecules.
- R = 8.314 J mol⁻¹ K⁻¹.
- k = 1.3806452 × 10⁻²³ J K⁻¹.
- Ideal gases have negligible particle volume, no intermolecular force and elastic collisions.
Intermediate Level
Molar Form
| Symbol | Meaning | SI unit |
|---|---|---|
| P | pressure | Pa |
| V | volume | m³ |
| n | amount | mol |
| R | gas constant | 8.314 J mol⁻¹ K⁻¹ |
| T | absolute temperature | K |
Molecular Form
Boltzmann Constant
Ideal-Gas Conditions
- Particle volume is negligible compared with container volume.
- Particles are identical in the model.
- No intermolecular attraction or repulsion acts except during collisions.
- Collisions are perfectly elastic.
Solved Examples
Pressure of an Ideal Gas
Find the pressure of 0.50 mol gas at 300 K in 0.012 m³.
- n = 0.50 mol
- T = 300 K
- V = 0.012 m³
P = nRT/V
P = (0.50)(8.314)3000.012
Final answer: P = 1.04 × 10⁵ Pa
Number of Molecules
A gas has P = 1.0 × 10⁵ Pa, V = 0.020 m³ and T = 300 K. Find N.
N = PV/(kT)
N = (1.0 × 10⁵)0.020(1.38 × 10⁻²³)(300)
Final answer: N ≈ 4.83 × 10²³ molecules
Common Mistakes
- Use kelvin in gas and molecular-energy equations.
- Distinguish heat, temperature and internal energy.
- Convert all quantities to SI units before calculation.
Short-Question Preparation
Q. State the ideal-gas equation.
A. PV = nRT.
Q. Derive its molecular form.
A. Use n = N/Nₐ and k = RNₐ to obtain PV = NkT.
Q. Define Boltzmann’s constant.
A. k = RNₐ = 1.3806452 × 10⁻²³ J K⁻¹.
Q. State ideal-gas assumptions.
A. Negligible particle volume, no intermolecular forces and perfectly elastic collisions.
Sticky Notes
- PV = nRT uses amount in moles.
- n = N/Nₐ converts molecules to moles.
- PV = NkT uses the number of molecules.
- R = 8.314 J mol⁻¹ K⁻¹.
- k = 1.3806452 × 10⁻²³ J K⁻¹.
- Ideal gases have negligible particle volume, no intermolecular force and elastic collisions.
60-Second Revision
The ideal-gas equation relates pressure, volume, amount and absolute temperature. Using molecule number instead of moles gives PV = NkT, where k = RNₐ is Boltzmann’s constant.
Summary
The ideal-gas equation relates pressure, volume, amount and absolute temperature. Using molecule number instead of moles gives PV = NkT, where k = RNₐ is Boltzmann’s constant.
Ask-the-Tutor Modes
- Explain it simply.
- Compare the key terms.
- Solve a numerical.
- Prepare a board-style answer.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- PV = nRT uses amount in moles.
- n = N/Nₐ converts molecules to moles.
- PV = NkT uses the number of molecules.
- R = 8.314 J mol⁻¹ K⁻¹.
- k = 1.3806452 × 10⁻²³ J K⁻¹.
- Ideal gases have negligible particle volume, no intermolecular force and elastic collisions.
Common exam traps
- Wrong temperature scale
Long question structure
Definition → explanation → equations → examples.
Common Mistakes
Common Mistakes
- Mistake
Keep heat, temperature and internal energy distinct.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
PV = nRT uses amount in moles.
n = N/Nₐ converts molecules to moles.
PV = NkT uses the number of molecules.
R = 8.314 J mol⁻¹ K⁻¹.
The ideal-gas equation relates pressure, volume, amount and absolute temperature. Using molecule number instead of moles gives PV = NkT, where k = RNₐ is Boltzmann’s constant.
- Definition
- The ideal-gas equation relates pressure, volume, amount and absolute temperature. Using molecule number instead of moles gives PV = NkT, where k = RNₐ is Boltzmann’s constant.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Ready to test yourself?
You've completed the learning section.
Exam Practice
Important Question
Q1. State the ideal-gas equation.
Important Question
Q2. Derive its molecular form.
Important Question
Q3. Define Boltzmann’s constant.
Important Question
Q4. State ideal-gas assumptions.