How is the volume solved?

We use a robust bisection method to obtain the real gas root with V > nb.

Van der Waals Equation Calculator

Q: What units should I use for a and b?

Use a in L²·atm·mol⁻² and b in L·mol⁻¹ with R = 0.082057 L·atm·mol⁻¹·K⁻¹.

Q: Can I enter temperature in °C?

Yes. We convert to Kelvin internally: T_K = T_°C + 273.15.

Calculate real-gas pressure or volume using the Van der Waals equation. Compare with the ideal gas result, see all intermediate steps, and use presets for common gases (CO₂, N₂, O₂, CH₄, NH₃, He, H₂) or enter your own a and b constants.

Background

Real gases deviate from the ideal gas law due to finite molecular size and intermolecular attractions. The Van der Waals model corrects the pressure by adding a(n/V)² and the volume by subtracting nb, giving accurate results for many conditions away from extreme high-pressure/low-temperature limits.

Choose what to solve and enter values:

Solve for:

Pressure (P)

Volume (V)

Gas preset (fills a, b):

Units for constants: a in L²·atm·mol⁻², b in L·mol⁻¹.

a (L²·atm·mol⁻²):

b (L·mol⁻¹):

Amount (n, mol):

Temperature:

Units: °C K

Volume (V, L):

Pressure (P):

Units: atm bar kPa

Quick picks:

Result:

No results yet. Choose what to solve for and enter values.

How to use this calculator

Solve P: Enter gas (or a, b), n, V, and T (°C or K). We compute P and show the ideal-gas comparison.
Solve V: Enter gas (or a, b), n, P (atm/bar/kPa), and T. We solve for V numerically (real-gas root) and show the ideal-gas estimate.
Units used: a (L²·atm·mol⁻²), b (L·mol⁻¹), R = 0.082057 L·atm·mol⁻¹·K⁻¹.

Valid for many real-gas conditions; accuracy decreases near condensation (very high P or low T).

Formula & Equation Used

Van der Waals equation for real gases:

(P + a \frac{n^{2}}{V^{2}}) (V - n b) = n R T

Ideal-gas comparison:

P {ideal}_{} = \frac{n}{V} R T

Example Problems & Step-by-Step Solutions

Example 1 (Solve P, CO₂)

CO₂ at 25 °C, n=1.00 mol, V=24.0 L, a=3.592, b=0.04267.
P_ideal = nRT/V ≈ 1.02 atm. Van der Waals: P = nRT/(V − nb) − a(n/V)² ≈ 0.95 atm.

Example 2 (Solve V, CO₂)

P=1.00 atm, T=25 °C, n=1.00 mol → V_ideal ≈ 24.47 L. Solve (P + a n²/V²)(V − nb) = nRT numerically → V ≈ 24.9 L.

Frequently Asked Questions

Q: What units should I use for a and b?

a in L²·atm·mol⁻², b in L·mol⁻¹ (consistent with R = 0.082057 L·atm·mol⁻¹·K⁻¹).

Q: Can I enter temperature in °C?

Yes; we convert to Kelvin internally: T_K = T_°C + 273.15.

Q: How is volume solved?

We use a robust bisection method to find the real, physically meaningful root V > nb.

The Ideal Gas Law