Universal Gas Constant (R)
The universal gas constant R = 8.314 J/(mol·K) connects pressure, volume, temperature, and moles in ideal gas calculations.
The Formula
The universal gas constant R is the fundamental constant that appears in the ideal gas law. It links macroscopic properties of gases: pressure, volume, temperature, and amount of substance.
The value of R depends on the units you use. The most common value is R = 8.314 J/(mol·K).
Variables
| Symbol | Meaning |
|---|---|
| P | Pressure of the gas (in pascals, Pa, or atmospheres, atm) |
| V | Volume of the gas (in liters, L, or cubic meters, m³) |
| n | Number of moles of gas (mol) |
| R | Universal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K)) |
| T | Absolute temperature (in kelvin, K) |
Common Values of R
| Value | Units | Used When |
|---|---|---|
| 8.314 | J/(mol·K) | SI units (Pa and m³) |
| 0.0821 | L·atm/(mol·K) | Pressure in atm, volume in liters |
| 1.987 | cal/(mol·K) | Energy in calories |
| 62.36 | L·mmHg/(mol·K) | Pressure in mmHg |
Example 1
Calculate the volume of 2 moles of an ideal gas at 300 K and 1 atm.
Use PV = nRT with R = 0.0821 L·atm/(mol·K)
V = nRT / P = (2)(0.0821)(300) / 1
V = 49.26 / 1
V ≈ 49.3 L
Example 2
A container holds 0.5 mol of gas at 25°C in a 10 L vessel. What is the pressure in atm?
Convert temperature: T = 25 + 273.15 = 298.15 K
Rearrange: P = nRT / V
P = (0.5)(0.0821)(298.15) / 10
P = 12.24 / 10
P ≈ 1.22 atm
When to Use It
The universal gas constant R appears in many areas of physics and chemistry.
- Ideal gas law calculations (PV = nRT)
- Thermodynamic equations involving entropy and free energy
- Kinetic theory of gases (average kinetic energy = 3/2 RT per mole)
- Chemical equilibrium constants and reaction rates (Arrhenius equation)
- Statistical mechanics and Boltzmann distribution
Remember: always convert temperature to kelvin and match the value of R to your pressure and volume units.