# Van der Waals Calculator

Easily calculate the pressure, volume, temperature or quantity in moles of a gas using this Van der Waals equation calculator. Supports a variety of input metrics such as Celsius, Fahrenheit, Kelvin, Pascals, bars, atmospheres, and volume in both metric and imperial units cubed.

## About the Van der Waals gas calculator

This is a gas law calculator which incorporates the van der Waals equation into one easy to use tool you can use as a:

- gas pressure calculator
- gas volume calculator
- gas quantity calculator
- gas temperature calculator

The van der Waals equation is a better approximation to a real gas than the ideal gas law (see "Applicability" below). To use the calculator, enter the three known measures and the two substance-specific constants to calculate the fourth measure. The calculator uses the combined gas law formula discussed below to perform the computations. It supports both imperial and metric units for volume and pressure and 5 different temperature scales: Kelvin, Celsius, Fahrenheit, Rankine and Reamur, both as input and as output.

The units supported for volume are: mm^{3}, cm^{3}, m^{3}, ml, L (litre), gallons, fluid ounces, cubic inches, cubic feet and cubic yards. Units supported for pressure are Pascals, kiloPascals, MegaPascals, GigaPascals, milibars, bars, atmospheres, millimeters of Hg liquid, millimeters of H_{2}O liquid, and pound-force per squared inches (psi).

## Van der Waals equation of state

The Van der Waals equation is an expansion of the ideal gas law formula used for ideal gas law calculation which accounts for the volume of real gas molecules and for the molecular attraction forces which make real gases more compressible than an ideal gas. This first is achieved by replacing V with **(V _{m} - b)** in the ideal gas formula where b is the volume occupied by one mole of the particular molecule (a.k.a. repulsion parameter) and V

_{m}is the molar volume. The second is achieved by adding to the observed pressure a

**a / V**term in which a is a constant which depends on the particular gas and is sometimes referred to as an "attraction parameter".

_{m}^{2}The above substitutions in the PV = nRT formula lead to the formula **(P + a / V _{m}^{2})(V_{m} - b) = RT** which through simple transformation can be expressed in the more familiar form of the Van der Waals equation:

where **P** is the pressure in Pascals, **V** is the volume in m^{3}, **n** is the quantity in moles, **T** is the absolute temperature in Kelvins and finally **R** is the universal gas constant, **a** is the aforementioned substance-specific constant. R is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole (the pressure–volume product). In SI based units it is 8.3144598(48) kg⋅m^{2}⋅mol^{−1}⋅K^{−1}⋅s^{−2}. A mole is the amount of substance which contains as many elementary entities as there are atoms in 12 g of carbon-12.

## Applicability of the Van der Waals formula

The van der Waals equation is quite reasonable for liquid and low-pressure gaseous states below the critical temperature of the gas or liquid in question. It is an even more significant improvement over the ideal gas law for temperatures above the critical (The critical temperature of a substance is such that at and above it vapor of the substance cannot be liquefied, regardless of the amount of pressure being applied).

The equation diverges from experimental behavior when the liquid phase and a gas phase would be in equilibrium (vapor–liquid equilibrium). Such "metastable" states are qualitatively (though likely not quantitatively) predicted by the van der Waals equation of state. Empirically-based corrections can be used such as the Maxwell's correction, at the cost of simplicity. The van der Waals equation is still used in textbooks as a pedagogic tool for understanding vapor–liquid behavior and equations of state. Some other, more accurate equations of state such as the Redlich–Kwong and Peng–Robinson equation of state are simply modifications of the van der Waals equation.

#### References

[1] NIST Special Publication 330 (2008) - "The International System of Units (SI)", edited by Barry N.Taylor and Ambler Thompson, p. 52

[2] "The International System of Units" (SI) (2006, 8th ed.). *Bureau international des poids et mesures* pp. 142–143. ISBN 92-822-2213-6

#### Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:

Georgiev G.Z., *"Van der Waals Calculator"*, [online] Available at: https://www.gigacalculator.com/calculators/van-der-waals-equation-calculator.php URL [Accessed Date: 14 Dec, 2019].