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Kinetic Molecular Theory

This unit delves into the Kinetic Molecular Theory, which describes the behavior of gas particles. We explore the historical context of Brownian Motion identified by Robert Brown in 1827, leading to Einstein's 1905 explanation of atomic existence. Key properties of gases such as pressure, temperature, and volume are linked to particle motion. We discuss the implications of molecular collisions on pressure and how temperature relates to kinetic energy. Additionally, concepts like diffusion and effusion are examined, alongside Graham’s Law on gas effusion rates.

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Kinetic Molecular Theory

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  1. Kinetic Molecular Theory Unit 11 Chapter 13

  2. Making Brownies • In 1827, Robert Brown noticed that pollen grains jiggle about for no apparent reason when viewed under a microscope. • He could not explain why the pollen grains moved. • All small particles will do this. • This apparently random motion is known as Brownian Motion.

  3. Random Motion…in Motion Location of particles every 30 s Reproduction from Les Atomes by Jean Baptiste Perrin (1914)

  4. E = I know Everything! • In 1905, Einstein effectively proves the existence of atoms by explaining Brownian Motion as the result of random collisions between the particles and gas molecules.

  5. Kinetic-Molecular Theory • Theory used to explain macroscopic properties of gases such as: • Pressure • Temperature • Volume • Due to the motion of tiny particles (atoms / molecules)

  6. Randomness Isn’t So Random When molecules strike the sides, pressure is produced! More Collisions per unit of time creates greater pressure! This has been slowed down… a lot!

  7. Billions of Tiny Little Punches • Collisions between molecules and the walls of the container produce the pressure (lots of little collisions). • The pressure pushes on the sides of a container. • Molecules that are spread out (i.e. with large volumes) collide less • (and therefore produce less pressure).

  8. Come on Baby Light My Fire! • Temperature (average Kinetic Energy) is directly proportional to the speed of the molecule! • Higher speeds = higher force • Root Mean Square Speed (vrms) is the average speed of the molecules R = 8.3145 J/mol·K Mm = molar mass in kg/mol

  9. Speed… • At 0°C, average velocity of nitrogen molecules: • vrms = 493 m/s • (1,100 mph)

  10. Speed and Mass Diffusion • Since the speed of a molecule is related to the molar mass, • Heavier molecules move more slowly than lighter ones!

  11. Diff…Eff…Conf… • Diffusion: The general movement of particles from an area of higher concentration to an area of lower concentration. • Effusion: The movement of individual molecules through a hole in a solid.

  12. Visual Effusion

  13. Eschew Obfuscatory Verbiage • In 1846, Thomas Graham determined that the rate of effusion of a gas is inversely proportional to the square root of its mass • Under similar conditions, Graham’s Law: M = molar mass

  14. The Reason Your Balloons All Die! • Given that Argon effuses through an opening at 2.00 mmol/min, how quickly will Helium effuse through the same opening? • RateAr(MAr)0.5 = RateHe(MHe)0.5 • RateAr = 2.00 mmol/min MAr = 39.95 g/mol • RateHe = ? MHe = 4.00 g/mol • (2.00 mmol/min)(39.95 g/mol)0.5 = RateHe(4.00)0.5 • RateHe = 6.320601237 • RateHe = 6.32 mmol/min

  15. Look Ma, no Scale! • Nitrogen effuses through an opening 2.283 times faster than an unknown gas. What is the molar mass of the unknown gas? • RateN2(MN2)0.5 = RateUnk(MUnk)0.5 • RateN2 = RateUnk * 2.283 • RateUnk * 2.283* (28.02)0.5 = RateUnk(MUnk)0.5 • 12.0848 = (MUnk)0.5 • MUnk = 146.0 g/mol SF6

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