Gas Model
a = 3.61 L²·atm/mol² · b = 0.0429 L/mol · Tc = 304.1 K
Parameters
Container volume
0.0110000
Absolute gas temperature
-273.15000
Moles of gas (or mass if molar mass is known)
0.00110000
Results
Pressure
—
atmCompressibility Factor (Z)
—
a = 3.61 L²·atm/mol² · b = 0.0429 L/mol · Tc = 304.1 K
Container volume
Absolute gas temperature
Moles of gas (or mass if molar mass is known)
—
atm—
The ideal gas law describes the behavior of a hypothetical gas where molecules do not interact and occupy no volume. The equation of state is:
where P is the pressure, V the volume, n the amount of substance in moles, R the universal gas constant (0.0820574 L·atm·mol⁻¹·K⁻¹, NIST value rounded to 7 significant figures), and T the absolute temperature in Kelvin.
In 1873, Johannes Diderik van der Waals proposed a modification that incorporates two corrections to the ideal model:
The constants a and b are specific to each gas and are experimentally determined. Gases with strong intermolecular forces (like H₂O) have high a values, while noble gases like He have values close to zero.
The compressibility factor measures the deviation from ideal behavior:
The critical temperature (Tc) is the temperature above which a gas cannot be liquefied by compression alone, regardless of the applied pressure. When T < Tc, the Van der Waals equation may predict regions where liquid and gas phases coexist (Van der Waals loop), and the equation loses quantitative validity in that region.
Pressure:
Volume (cubic):
Temperature:
| Gas | a | b | Tc (K) |
|---|---|---|---|
| He | 0.0346 | 0.0238 | 5.2 |
| N₂ | 1.370 | 0.0387 | 126.2 |
| O₂ | 1.364 | 0.0318 | 154.6 |
| CO₂ | 3.610 | 0.0429 | 304.1 |
| H₂O | 5.460 | 0.0305 | 647.1 |
Units: a in L²·atm/mol², b in L/mol.
Atkins, P. W., & de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press. Chapter 1: The properties of gases.