Chapter Summary/Important Topics

• Real vs. Ideal Gases

All Real Gases DO NOT Behave Ideally When…

• Under high pressures ( P > 5 atm )

• At low temperatures

• Under such conditions, PV = nRT does not make accurate predictions.

Volume Adjustment for Gases Under High Pressure

• The Ideal Gas Equation assumes that molecules do not have their own volumes.

• The V in PV = nRT is the volume of empty space in the container.

• The volumes of gas particles are negligible, when compared to the overall volume of the container, at relatively low pressures (~1 atm). This is due to the fact that they are very small and very far apart.

• At high pressures, molecules are compressed into a much smaller volume of space, and the volume occupied by the molecules becomes significant.

• Volume occupied by particles is negligible.

• Volume occupied by particles is significant.

V ideal = V measured - nb

• V measured = the volume of empty space plus the volume of the gas particles. This is the volume that would be measured in the lab.

• V ideal = The corrected volume, which can be used in the ideal gas equation. it is the volume of actual empty space in the container.

• n = moles of gas

• b = a constant for the type of gas

Forces of Attraction in Real Gases

• Ideal gas law assumes there are no forces of attraction between gaseous particles, but… FORCE IS PROPORTIONAL TO 1/d^6.

Pressure Adjustment for Gases Under High Pressures (Low Volume)

• When gas particles are very close together, the pressure they exert may be less than what the ideal gas equation would predict.

• Neighboring molecules exert forces of attraction on one another when they are very close together.

• Such forces pull a gas molecule in the direction opposite to its motion.

• This reduces the pressure resulting from impacts within the walls of the container.

• Low Pressures Systems: No forces of attraction reducing impact velocity.

• High Pressure Systems: Forces of attraction reduce impact velocity.

P ideal = P measured + (n²a/v²)

• P measured = The pressure measured in the lab

• P ideal = the pressure that would be expected when using the ideal gas equation.

• n = the number of moles of gas

• a = a constant for the specific gas in the system

• V = the volume of the system ( V measured)

Van Der Waals Equation

{P + (n²a/V²)}(V - nb) = nRT

• P = actual or measured pressure (atm)

• n = moles of gas

• a and b = constants for the specific gas in question

• V = actual or measured volume (L)

• T = temperature (K)

• R = 0.0821

Gases do not behave ideally at low temperatures

• The ideal has law assumes that gases experience no intermolecular forces of attraction.

• At high temperatures, the kinetic energy of gas particles overcomes any intermolecular forces of attraction.

• At low temperatures, gas particles move slower and are closer together. Attractions between molecules exist under these conditions.

Non-Ideal Behaviour and Condensation

• Intermolecular forces of attraction increase as the distance between particles decreases

• This can lead to condensation at sufficiently low temperatures and/or exceptionally high pressures.

• This applies to all gases, even those with relatively weak intermolecular forces.

• Condensation can occur rapidly when the temperature of a system drops.

  • KE of gas particles is reduced and they move closer together.

  • Under these conditions, intermolecular forces can cause particles to stick together when they collide.

• Condensation can also occur at high pressures.

  • Gas Particles are closer together and experience a higher rate of collisions.

  • Intermolecular forces between particles can cause them to condense.

• When a gaseous system is approaching the point where condensation will occur, the forces of attraction between gas particles are at a maximum.

• This results in the largest possible decrease in measured pressure, and thus, a large deviation from ideal behaviour.