04 // Interactive Formula Compendium // CHEMISTRY-THERMOP · V = n · R · T
Ideal Gas Law Equation of State
The ideal gas law PV = nRT connects absolute pressure P (Pa), volume V (m³), amount of substance n (mol), and absolute temperature T (K) through R = 8.3144626 J/(mol·K).
Formula Reference
Main Formula
P · V = n · R · T
Rearranged Forms
P = ρ · R_specific · T
P₁V₁ / T₁ = P₂V₂ / T₂
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| P | Absolute Gas Pressure | Pa |
| n | Amount of Gas | mol |
| T | Absolute Temperature | K |
| V | Container Volume | m³ |
Inputs & Parameters
[mol]
[K]
[m³]
Calculated Result (Absolute Gas Pressure)
P =99,158.28Pa
Formula Notes & Background
- Unifies Boyle's Law (V ∝ 1/P), Charles's Law (V ∝ T), and Avogadro's Law (V ∝ n); microscopically PV = (2/3)N⟨K_trans⟩ from kinetic theory.
- At IUPAC STP (T = 273.15 K, P = 100 kPa), molar volume V/n = 22.711 L/mol (22.414 L/mol at 1 atm = 101.325 kPa).
Step-by-Step Examples
#1: 2.00 mol of nitrogen gas held in a 50 L (0.050 m³) cylinder at 25 °C (298.15 K).
n = 2.00 molT = 298.15 KV = 0.050 m³
P = (2.00 × 8.31446 × 298.15) / 0.050 = 4,957.91 / 0.050
→ P = 99,158 Pa (99.16 kPa ≈ 0.979 atm)
#2: Molar volume of an ideal gas at 273.15 K and 101,325 Pa (1 atm).
n = 1 molT = 273.15 KP = 101,325 Pa
V = (1 × 8.31446 × 273.15) / 101,325
→ V = 0.022414 m³ (22.414 L)
Was this tool helpful?
Frequently Asked Questions
Why must temperature always be in Kelvin?+
Gas pressure and kinetic energy vanish at absolute zero (0 K = −273.15 °C); using Celsius introduces arbitrary zero-offset errors and negative pressures.
When should I switch to the Van der Waals equation?+
At high pressures (>10–20 bar) or near condensation temperatures where finite molecular volume b and intermolecular attraction a become significant.
What value of R is used with Liters and atmospheres?+
Use R = 0.082057 L·atm/(mol·K) when P is in atm and V is in liters, or R = 8.31446 J/(mol·K) in pure SI (Pa and m³).