Van der Waals Equation
Solve the Van der Waals equation for pressure of real gases given moles, volume, temperature, and gas constants.
Real Gas Behavior
The ideal gas law works well at low pressure and high temperature, but real gases deviate because molecules occupy volume and attract each other. The Van der Waals equation adds corrections for both effects.
Van der Waals Equation
$$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$ $$P = \frac{nRT}{V - nb} - \frac{an^2}{V^2}$$Constants \(a\) and \(b\) depend on the gas. Parameter \(a\) accounts for intermolecular attraction; \(b\) accounts for molecular volume. This calculator solves for pressure \(P\) in atmospheres using volume in liters, amount in moles, and temperature in kelvin with \(R = 0.082057\) L·atm/(mol·K).
Gas Presets
Preset constants are provided for carbon dioxide, nitrogen, and water vapor. Compare the Van der Waals pressure to the ideal gas result to see how strongly a gas deviates under your conditions.
Related tools: Gas Density Calculator and Equilibrium Constant Calculator.
Frequently Asked Questions
When does the Van der Waals equation matter?
Deviations are largest at high pressure, low temperature, or near the critical point. Near ambient conditions many gases are close to ideal, but CO₂ and water vapor show noticeable corrections.
What do a and b represent physically?
Constant \(a\) measures attraction between molecules. Constant \(b\) is the excluded volume per mole, related to the finite size of molecules.
Why must V be greater than nb?
The term \(V - nb\) is the free volume available for molecular motion. When \(V \leq nb\), molecules are packed beyond the model's physical limit and pressure is undefined.
How does this compare to the ideal gas law?
The ideal gas law is \(PV = nRT\). Van der Waals reduces to this form when \(a\) and \(b\) are negligible, which happens at low density.
Can this equation solve for volume or temperature?
Yes, but solving for \(V\) or \(T\) requires solving a nonlinear equation. This tool focuses on computing pressure from the other state variables.
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