Van der Waals pressure = 40.009 bar
- Ideal gas law
- 49.912 bar
- Difference
- -19.84 %
- Z = PV/nRT
- 0.8016
P = nRT ÷ (V − nb) − a n² ÷ V², with R = 0.083145 L bar mol⁻¹ K⁻¹. Z below 1 means attractions dominate (the gas is easier to compress than an ideal gas); Z above 1 means molecular volume dominates.
How it works
The van der Waals equation is (P + an²/V²)(V − nb) = nRT, rearranged here to P = nRT ÷ (V − nb) − an² ÷ V². The a term lowers the pressure because molecules attract each other; the b term raises it because the molecules themselves take up part of the volume. Constants are in L² bar mol⁻² and L mol⁻¹.
The compressibility factor Z = PV ÷ nRT is 1 for an ideal gas. Values below 1 mean attractions dominate; above 1, molecular size dominates. The equation is a big improvement on the ideal gas law but is itself approximate near condensation and at very high pressures.
Frequently asked questions
- What do a and b mean?
- a measures how strongly the molecules attract each other (large for polar or large molecules such as water and ammonia); b is roughly the volume of one mole of the molecules themselves.
- When does the ideal gas law fail?
- At high pressure (molecules are crowded, so their size matters) and low temperature (they move slowly, so attractions matter). At room temperature and 1 atm, most gases are within about 1 % of ideal.
- Why is the van der Waals pressure of CO₂ lower than the ideal value?
- CO₂ molecules attract each other fairly strongly (a = 3.64 L² bar mol⁻²), which reduces how hard they hit the walls.
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