The Kinetic Molecular Theory

1. The Kinetic Molecular Theory • A model to explain the behavior of ideal gases • The particles are small compared to the distances between the particles • Assume that the volume of the individual particles is negligible

2. The Kinetic Molecular Theory • The particles are always moving. • Particles colliding against the walls of the container result in the pressure exerted by the gas.

3. Kinetic Molecular Theory • The particles do not exert any force on each other; they neither attract nor repel each other. • The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas

4. The Kinetic Molecular Theory • The true test of a model • The predictions based on the model should fit the experimental observations

5. The Kinetic Molecular Theory • Boyle’s Law • Decrease the volume, the gas particles will hit the wall more often • More collisions, more pressure • I.e., as the volume decreases, the pressure increases

6. The Kinetic Molecular Theory • Gay-Lussac’s Law • Increase the temperature, and the kinetic energy of the gas molecules will increase, their speed will increase, so the molecules will hit the wall with greater force and greater frequency • I.e, as the temperature increases, the pressure increases.

7. The Kinetic Molecular Theory • Charles’ Law • Increase the temperature, and the gas molecules will have greater kinetic energy, and thus, greater speed. The particles will hit the walls more often. To keep the pressure constant, the volume would have to increase to compensate for the increased speed. • I.e., At constant pressure, as temperature increases, the volume increases.

8. The Kinetic Molecular Theory • Avogadro’s Law • Increase the number of gas particles at a given temperature would result in more collisions, and thus more pressure. To keep the pressure constant, the volume would have to increase. • I.e., At some constant temperature and pressure, as the number of particles increase, the volume increases.

9. The Kinetic Molecular Theory • Dalton’s Law of Partial Pressures • Since all gas particles are independent of each other, it doesn’t matter what the identity of the individual particles are. • The sum of the pressures of the individual gases would give the total pressure.

10. The Kinetic Molecular Theory • The Meaning of Temperature • The Kelvin temperature indicates the average kinetic energy of gas particles • Two different gases at the same temperature will have the same average kinetic energy • From physics: • (KE)ave = 3/2 RT • This equation means, higher temperature, greater motion

11. Real Gases • No such thing as an ideal gas • Real gases begin to behave like ideal gases under ideal conditions. • at low pressures • At high temperatures

12. Real Gases • Look at real gas behavior • Graph of PV/nRT vs P • For ideal gases, PV / nRT = 1 at any pressure • For real gases, PV / nRT approaches 1 at very low pressures (below 1 atm)

13. Real Gases • What is the effect of temperature when plotting PV / nRT vs. P? • PV / nRT approaches 1 at low pressure and at high temperatures

14. Real Gases • Johannes van Der Waals • Developed an equation for real gases • Received a Nobel prize for his work

15. Volumeless Do not interact with each other Finite volumes Particles do take up space Volume of the gas is actually less than the volume of the container Particles do attract each other Ideal Gases vs. Real Gases

16. van der Waals Equation • Correction factors for the ideal gas law • Correct for the volume: • The actual volume of a real gas is • V – nb • V = volume of the container • n = # moles of gas particles • b = constant, determined using experimental results

17. van der Waals Equation • Correction factors for the ideal gas law • Correct for the attractive forces between particles • Attractive forces would result in fewer, as well as slightly weaker collisions, resulting in less pressure.

18. van der Waals Equation • Pobs = observed pressure • P’ = pressure expected from the ideal gas law • Pobs = P’ – correction factor

19. van der Waals Equation • The correction factor for the attractive forces would also have to be experimentally determined. • Depends on • concentration of gas molecules (moles/liter or n/V) • more gas molecules, more interactions • Correction factor: a(n/V)2 • a = proportionality constant

20. van der Waals Equation • Pobs = nRT – a (n/V)2 V – nb Rearrange to get van der Waals equation: [Pobs + a(n/V)2] x (V – nb) = nRT ( Pcorrected. Vcorrected = nRT)

21. van der Waals Equation • A real gas becomes more like an ideal gas at low pressure… • Low pressure implies a large volume for the gas particles…the volume of the gas becomes the volume of the container as the gas particles (nb becomes very small) get farther apart • note that b is smaller when gas particles are smaller (b for He is 0.0237 L/mol while b for Xe is 0.0511 L/mol)

22. van der Waals Equation • A real gas becomes more like an ideal gas at high temperature… • High temperature means the gas particles have high kinetic energy and are moving past each other with greater speeds, giving the particles less of a chance to feel any attractive force. Pobs approaches Pideal

23. Real Gases and Ideal Gases • In summary, a real gas approaches the behavior of an ideal gas • at low pressure (large container) • at high temperature • when the gas experiences few attractive forces (the more nonpolar the particle, the weaker the attractive forces)