Van der Waals Equation Calculator

The van der Waals equation corrects the ideal gas law for molecular size and attraction.

How the Math Works

The van der Waals equation corrects the ideal gas law by accounting for molecular volume and intermolecular forces. The term (V - nb) subtracts the space occupied by gas molecules themselves (b is the excluded volume per mole), while the a·n²/V² term adds back the attractive forces between molecules that reduce pressure. Here, n is moles of gas, R is the gas constant, T is temperature, V is volume, and a and b are substance-specific constants derived from experimental data. This adjustment transforms the idealized PV = nRT relationship into a more accurate model for real gases.

Practical Applications

To use this calculator, input the number of moles (n), temperature (T), volume (V), and the van der Waals constants (a and b) for your specific gas. The calculator first computes nRT divided by (V minus nb), then subtracts a·n² divided by V² to yield the corrected pressure. For example, calculating ammonia gas (a = 4.17, b = 0.0371 L/mol) at 300 K in a 5 L container with 2 moles gives a more accurate pressure than the ideal gas law would predict, especially at high pressures or low temperatures where real gas effects dominate.

Day-to-Day Use

This calculation matters whenever gases are compressed, stored, or processed under non-ideal conditions. Natural gas pipelines, refrigeration systems, and chemical manufacturing rely on accurate pressure predictions to ensure safety and efficiency. Understanding these corrections helps explain why bicycle tires feel harder in cold weather or why gas cylinders require pressure relief valves — real gases behave differently than simple theory suggests, and these calculations keep our modern infrastructure running smoothly and safely.

Worked example

CO₂ (a 0.364, b 4.27×10⁻⁵), 1 mol, 300 K, 0.022 m³ → about 112 kPa.

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