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Gases and the Kinetic Molecular Theory

Gases and the Kinetic Molecular Theory. Speeds of gas molecules. For a single molecule. Kinetic energy is: KE = ½ mv 2 m = mass; v = velocity For a collection of gas molecules, the average kinetic energy is:. R = ideal gas constant = 8.314 J/K  mol T = temperature in Kelvin.

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Gases and the Kinetic Molecular Theory

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  1. Gases and the Kinetic Molecular Theory

  2. Speeds of gas molecules. For a single molecule. Kinetic energy is: KE = ½ mv2 m = mass; v = velocity For a collection of gas molecules, the average kinetic energy is: R = ideal gas constant = 8.314 J/Kmol T = temperature in Kelvin

  3. How fast do gas molecules move? Called the root mean square speed of the gas. in kg/mol Equation gives speed in meters/second. What is the rms speed of O2 molecules at room temperature?

  4. Boltzmann Distributions

  5. Boltzmann Distributions and Molar Mass

  6. Boltzmann Distributions and Temperature

  7. Gas Diffusion

  8. Gas Effusion

  9. Graham’s Law of Gas Effusion: used for determining molar mass of a gas

  10. Example: A sample of ethane, C2H6, effuses through a small hole at a rate of 3.6 x 10-6 mol/hr. An unknown gas, under the same conditions, effuses at a rate of 1.3 x 10-6 mol/hr. Calculate the molar mass of the unknown gas.

  11. Gas Laws: The Ideal Gas Law PV = nRT P = pressure in atmospheres V = volume in liters N = moles of gas T = temperature in K R = gas constant = 0.08257 Latm/Kmol Two Uses: 1. You know three of the four variables and solve for the fourth. 2. You know the change in one variable and determine the change in another.

  12. The Ideal Gas Law: 1a: Determining one property, given the others A sample of N2 gas has a volume of 250. mL, a pressure of 720 mm Hg, and is at 25 oC. What is the mass of the gas?

  13. The Ideal Gas Law: 1b: Determining one property, given the others A sample of 2.60 g Ar gas has a pressure of 720 mm Hg, and is at 25 oC. What is the volume of the gas?

  14. The Ideal Gas Law: 1c: Determining one property, given the others What is the density of O2 gas at 20 oC, in grams per liter?

  15. The General Gas Law: Determining changes in a property when a different property changes. General idea: cancel properties that don’t change.

  16. The General Gas Law: P and V A gas sample at 0.95 atm has a volume of 250 mL. What will the pressure be if the volume is compressed to 100 mL? n and T are constant. General Law:

  17. The General Gas Law: n and V A 0.35 mol gas sample has a volume of 250 mL. What will the volume be if 0.20 mol more gas are added? P and T are constant. General Law:

  18. The General Gas Law: T and V A gas sample has a volume of 250 mL at 100 oC. What will the volume be if it is cooled to 10 oC? P and n are constant. General Law:

  19. The General Gas Law: T and V A car tire has a pressure of 32 psi in winter, when T = -10 oC. What will the pressure be in summer if T increases to 33 oC, but 5% of the air in the tire has leaked out? Assume V is constant.

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