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Gas Densities, Partial Pressures, and Kinetic-Molecular Theory

Gas Densities, Partial Pressures, and Kinetic-Molecular Theory. Sections 10.5-10.8. Objectives. Apply the ideal-gas equation to real gas situations. Interpret the kinetic-molecular theory of gases. Gas Densities and Molar Mass. Rearrange the ideal-gas equation : n = P V RT

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Gas Densities, Partial Pressures, and Kinetic-Molecular Theory

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  1. Gas Densities, Partial Pressures, and Kinetic-Molecular Theory Sections 10.5-10.8

  2. Objectives • Apply the ideal-gas equation to real gas situations. • Interpret the kinetic-molecular theory of gases

  3. Gas Densities and Molar Mass • Rearrange the ideal-gas equation : n = P V RT • Multiply both sides by molar mass, M nM = PM V RT • Product of n/V and M = density in g/L Moles x grams = grams Liter mole liter

  4. Gas Densities and Molar Mass • Density is expressed: D = PM RT • Density depends on pressure, molar mass, and temperature

  5. Gas Mixtures and Partial Pressure • Dalton’s Law of Partial Pressures: • Total pressure of a mixture equals sum of the pressures that each would exert if present alone. Pt = P1 + P2 + P3 + ….

  6. Gas Mixtures and Partial Pressures • Thus: P1 = n1 (RT); P2 = n2 (RT); P3 = n3 (RT);… V V V • And Pt = (n1 + n2 + n3 + ….) RT = nt (RT) V V

  7. Mole Fraction, X P1 = n1 RT/ V = n1 Pt = nt RT/ V = nt Thus… P1 = (n1/nt)Pt = X1Pt

  8. Example • Mole fraction of N2 in air is 0.78 (78%). If the total pressure is 760 torr, what is the partial pressure of N2?

  9. Homework • 59-67, odd only

  10. Kinetic-Molecular Theory • Explains why gases behave as they do • Developed over 100 year period • Published in 1857 by Rudolf Clausius

  11. Kinetic Molecular Theory * Theory of moving molecules You Must Know the 5 Postulates of the Kinetic Molecular Theory of Gases (page 421).

  12. Root-mean-square speed, u • Speed of a molecule possessing average kinetic energy Є = ½ mu2 Є is average kinetic energy m is mass of molecule • Both Є and u increase as temperature increases

  13. Application to Gas Laws • Effect of a V increase at constant T: - Average kinetic energy does not change when T is constant. Thus rms speed is unchanged. With V increase, there are fewer collisions with container walls, and pressure decreases (Boyle’s Law).

  14. Application to Gas Laws 2. Effect of a T increase at constant V: - Increase T means increase of both average kinetic energy and rms speed. No change in V means there will be more collisions with walls.

  15. Molecular Effusion & Diffusion u = 3RT M *Derived equation from the k-m theory **Less massive gas molecules have higher rms speed

  16. Effusion • Escape of gas molecules through a tiny hole into an evacuated space

  17. Diffusion • Spread of one substance throughout a space or throughout a second substance

  18. Graham’s Law of Effusion • Effusion rate of a gas is inversely proportional to the square root of its molar mass. • Rates of effusion of two gases: * At same T and P in containers with identical pinholes

  19. Graham’s Law of Effusion

  20. Diffusion and Mean Free Path • Similar to Effusion (faster for lower mass molecules) • BUT diffusion is slower than molecular speeds because of molecular collisions • Mean Free Path: average distance traveled by a molecule between collisions

  21. Homework • 69, 71, 73, 75, 76, 77, and 79

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