The van der Waals equation | Khan Academy

TL;DR

The ideal gas law can be modified to consider the volume and intermolecular forces of real gases, resulting in the Van der Waals equation.

Transcript

• [Instructor] We have so far spent many videos talking about the ideal gas law, that pressure times volume is equal to the number of moles times the ideal gas constant times temperature measured in kelvin. What we're going to do in this video is attempt to modify the ideal gas law to try to take into account when we're dealing with real gases, gas... Read More

Key Insights

• 🫢 The ideal gas law needs modification to account for real gases with volume and intermolecular forces.
• 🫢 The modified equation, known as the Van der Waals equation, includes terms for the reduction in pressure due to intermolecular forces and the actual volume of gas particles.
• 👮 The term for intermolecular forces is derived from Coulomb's law and is proportional to the squared concentration of particles.

Questions & Answers

Q: How does the ideal gas law need to be modified for real gases?

The ideal gas law needs to incorporate the actual volume of gas particles by replacing the volume term with the container volume minus the volume of the particles. Additionally, a term accounting for intermolecular forces needs to be added.

Q: Can intermolecular forces ever add to the pressure instead of reducing it?

In some scenarios where repulsive forces exist between particles, they could add to the pressure. In such cases, a negative term can be subtracted to make the contribution additive.

Q: How is the term for intermolecular forces derived?

The term is derived by considering Coulomb's law, which states that the force between two charged particles is proportional to the charge on each particle divided by the distance squared. The term is proportional to the squared concentration of particles.

Q: What is the Van der Waals equation?

The Van der Waals equation is the modified form of the ideal gas law that takes into account the volume and intermolecular forces of real gases. It includes terms for the reduction in pressure due to intermolecular forces and the actual volume of gas particles.

Summary & Key Takeaways

• The ideal gas law, which relates pressure, volume, moles, gas constant, and temperature, needs to be modified when dealing with real gases.

• To account for the actual volume of gas particles, the volume term in the ideal gas law is replaced with the container volume minus the volume of the particles.

• The intermolecular forces between particles also need to be considered, and a term is added to the equation to account for the reduction in pressure due to these forces.