Van der Waals Calculator

Calculate real gas pressure, volume, or temperature using the van der Waals equation: (P + a/V^2)(V - b) = RT. Accounts for molecular volume and intermolecular forces.

🔬 Real Gas📐 (P + a/V²)(V - b) = RT🧪 Chemistry

Pressure P (atm)

Volume V (L/mol)

Temperature T (K)

van der Waals constants a,b from gas type (CO₂: a=3.59, b=0.0427)

Constant a (L²·atm/mol²)

Constant b (L/mol)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Van der Waals Calculator	See formula	(P + a/V²)(V - b) = RT	atm

Step-by-Step Examples

Example 1

CO₂ at High Pressure

CO₂ (a=3.59, b=0.0427): V=1.0 L/mol, T=300 K. Find P.

P = RT/(V-b) - a/V²
P = (0.08206×300)/(1.0-0.0427) - 3.59/1.0²
P = 25.70 - 3.59 = 22.11 atm
Ideal gas: P = 24.62 atm

✓ 22.11 atm (vdW) vs 24.62 atm (ideal) — 10% difference

Example 2

Ideal Gas Comparison

He (a=0.034, b=0.0238): V=2.0 L/mol, T=300 K.

P_vdW = 0.08206×300/(2.0-0.0238) - 0.034/4.0
P_vdW = 12.48 - 0.0085 = 12.47 atm
Ideal: 12.31 atm

✓ 12.47 atm (helium nearly ideal, small correction)

Example 3

H₂O Vapor

H₂O (a=5.536, b=0.0305): V=3.0 L/mol, T=500 K.

P = 0.08206×500/(3.0-0.0305) - 5.536/9.0
P = 13.81 - 0.615 = 13.19 atm
Ideal: 13.68 atm

✓ 13.19 atm — water vapor deviates from ideal

Real-World Applications

💨

High-Pressure Chemistry

At pressures above 10 atm, ideal gas law errors exceed 5%. Van der Waals needed.

🧪

Physical Chemistry

Real gas behavior is a core topic in physical chemistry courses.

🏭

Industrial Processes

High-pressure reactors must account for non-ideal gas behavior.

☔

Atmospheric Science

Water vapor behavior in atmosphere uses real gas corrections.

Common Mistakes to Avoid

⚠️

Forgetting to subtract b

(V - b) not V in the denominator. b accounts for volume of the gas molecules themselves.

⚠️

Wrong constants for your gas

Each gas has unique a and b values. CO₂ a=3.59, N₂ a=1.39, H₂O a=5.536. Always look up the correct values.

⚠️

Applicable to moderately non-ideal gases

Van der Waals is better than ideal gas law but still an approximation. Fails near critical point.

Frequently Asked Questions

What do a and b represent? ▾

a corrects for intermolecular attractions (reduces effective pressure). b corrects for molecular volume (reduces available volume). Larger molecules have larger a and b.

When does van der Waals give different results? ▾

At high pressures (dense gas, molecules crowd) and low temperatures (attractive forces important). Near critical point, deviations are largest.

What is critical temperature? ▾

Temperature above which a gas cannot be liquefied regardless of pressure. Tc = 8a/(27Rb). CO₂ Tc = 304.2 K, water Tc = 647 K.

Which gas is most ideal? ▾

Noble gases at low pressure, especially He and Ne with tiny a values. He: a=0.034, nearly perfect ideal gas behavior.

What other real gas equations exist? ▾

Redlich-Kwong, Peng-Robinson, Soave-Redlich-Kwong. These are more accurate for engineering but more complex than van der Waals.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

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