Advanced Topic 248 of 1102 States of Matter & Solutions
Van der Waals Equation
Corrects the ideal gas law with constants a for attractions and b for molecular volume.
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In-depth explanation of Van der Waals Equation
The van der Waals equation corrects the ideal gas law for the finite size of molecules and for their mutual attractions. It is written (P + a n^2/V^2)(V - nb) = nRT, where the term a n^2/V^2 corrects the pressure for attractions and the constant b represents the excluded volume of the molecules. Larger values of a indicate stronger attractions, meaning the gas is easier to liquefy, while larger b indicates larger molecules. The constants are determined experimentally for each gas. The equation also predicts a liquid-gas critical point and describes real gases better at high pressure.
Going deeper: Van der Waals Equation
Key ideas: Rearranged: P = nRT/(V - nb) - a n^2/V^2. The b term shrinks free volume and raises pressure, while a lowers pressure. Typical constants: He a = 0.034, b = 0.0237; NH3 a = 4.17, b = 0.0371 in L2 atm per mol2 and L per mol. The b value is about four times the actual volume of the molecules in a mole.
Common mistakes and connections: Students swap the roles of a and b, or forget that n is squared in the pressure correction. Another error is using it as an exact law; it is an approximation that fails near the critical region. Cubic in V, so it has up to three roots. Links to compressibility factor, critical constants (Tc = 8a/27Rb) and liquefaction.
Visualization of Van der Waals Equation
The van der Waals equation (P + a n2/V2)(V - nb) = nRT adds attraction (a) and excluded volume (b); below Tc the isotherm shows a loop. The interactive lesson shows this as a live animation or chart.
Worked example and use case
For carbon dioxide a is 3.59 L² atm/mol² and b is 0.0427 L/mol, and these values are used to correct the ideal pressure.
Frequently asked questions about Van der Waals Equation
What is Van der Waals Equation?
Corrects the ideal gas law with constants a for attractions and b for molecular volume.
Is Van der Waals Equation a beginner, intermediate or advanced topic?
Van der Waals Equation is a advanced topic in States of Matter & Solutions. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Van der Waals Equation?
Study these earlier topics in States of Matter & Solutions first: Gas Density, Gas Stoichiometry, Real Gases.
What comes after Van der Waals Equation?
The next topics in States of Matter & Solutions are Compressibility Factor and Critical Temperature.
Can I practise Van der Waals Equation with quizzes?
Yes. The interactive lesson includes a self-check question on Van der Waals Equation, and the States of Matter & Solutions quiz draws on every topic in this area.
Where Van der Waals Equation fits in States of Matter & Solutions
Van der Waals Equation is topic 29 of 109 in States of Matter & Solutions.