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
Key equation
PV=nRT
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
Key equation
n=NNA
Key equation
PV=NNART=N(RNA)T
Key equation
PV=NkT
Boltzmann Constant
Key equation
k=RNA=1.3806452×10-23\ J K-1
Key equation
[k]=[ML2T-2K-1]
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.
1
Given
n = 0.50 mol
T = 300 K
V = 0.012 m³
2
Working
P = nRT/V
3
Step 2
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.
1
Working
N = PV/(kT)
2
Step 2
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.
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Exam preparation
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 mistakes
Keep heat, temperature and internal energy distinct.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
