van der Waals' equation

or van der Waals e·qua·tion

[ , ih-kwey-shuhnwawlz; Dutch vahn der vahls ]

Phonetic (Standard)IPA

noun

, Thermodynamics.

an equation of state relating the pressure, volume, and absolute temperature of a gas, taking into account the finite size of the molecules and the attractive force between them.

van der Waals equation

/ ˈvæn də ˌwɑːlz /

noun

an equation of state for a non-ideal gas that takes account of intermolecular forces and the volume occupied by the molecules of the gas

van der Waals equation

An equation that relates the pressure, volume, and absolute temperature of a gas taking into account the finite size of molecules, and their intermolecular attraction, having the form RT = ( P + av ^-2)( v − b ), where R is the gas constant, T is the absolute temperature, P is the pressure, v is the volume of fluid per molecule, a is a measure of the attraction of the molecules for each other (due to van der Waals forces ), and b is the volume occupied by a single molecule. The equation accurately captures phase transitions between liquid and gas phases of substances.
See also ideal gas law

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Word History and Origins

Origin of van der Waals' equation¹

Named after J. D. van der Waals (1837–1923), Dutch scientist

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More About Van Der Waals Equation

What is van der Waals equation?

Van der Waals equation is an equation that relates the temperature, pressure, and volume of a non-ideal gas and takes into account both the intermolecular forces between the gas molecules and the volume of the gas molecules themselves.

A gas is a form of matter in which the molecules are free to move around. An ideal gas is a fictional gas in which the gas molecules don’t attract each other and are so small that their size doesn’t affect their behavior. The ideal gas law is used to relate several properties of ideal gases.

However, gases in reality are not ideal and van der Waals equation adjusts the ideal gas law to account for the effects of the forces that gas molecules exert on each other (known as van der Waals’ forces) and the volume of the gas molecules themselves.

Van der Waals equation is RT = (P+av-2)(v-b), where:

R is the universal gas constant
T is the temperature of the gas
P is the pressure of the gas
v is the volume of the gas
a is a measure of the attraction of the molecules for each other (due to van der Waals forces)
b is the volume occupied by a single molecule

In van der Waals equation, the values of a and b will be unique to each gas. Because van der Waals equation accounts for the unique properties of each gas, it more accurately describes the properties of real gases.

Why is van der Waals equation important?

Van der Waals equation is named for the scientist who formulated it, Dutch physicist Johannes Diderik van der Waals. Van der Waals formulated his equation in 1873 and used it to explain his theory of why gases behave differently under high pressures.

If you take a chemistry class, your teacher will likely have you determine the properties of gases using van der Waals equation. Usually, you will know all but one of the gas’s properties and will use van der Waals equation to determine the unknown property. For example, you might not know the temperature or pressure of a gas. To find it, you would plug all the other values into van der Waals equation, which would give you the value of the unknown property.

Did you know … ?

As you might have guessed, the van der Waals force is also named after Johannes Diderik van der Waals. In 1910, van der Waals was awarded the Nobel Prize in physics for his work on the van der Waals equation.

What are real-life examples of van der Waals equation?

This video shows a chemistry teacher solving a problem using van der Waals equation.

I hate Van Der Waals equation. #APChemIsKiller

— Brookelyn Raye (@brookelynraye) October 26, 2011

Just the existence of the Van der Waals equation makes me want to change my major far far away from Chemistry as possible

— Nico loves Shawarma (@nianlu48) December 2, 2016

What other words are related to van der Waals equation?

Quiz yourself!

True or False?

Van der Waals equation accounts for the intermolecular forces between the gas molecules of real gases.

van der Waals van der Waals force

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