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Gases GASES manometers pressure Kinetic theory of gases Units of pressure Behavior of gases Partial pressure of a gas Pressure vs. Pressure vs. Temperature vs. volume temperature volume Combined gas law Diffusion/effusion Ideal gas law Properties of Gases • Very low density • Low freezing points • Low boiling points • Can diffuse (rapidly and spontaneously spread out and mix) • Flow • Expand to fill container • Compressible Kinetic Molecular Theory of Gases • Particles move non-stop, in straight lines. • Particles have negligible volume (treat as points) • Particles have no attractions to each other (no repulsions, either). • Collisions between particles are “elastic” (no gain or loss of energy) • Particles exert pressure on the container by colliding with the container walls. Kinetic Energy • Energy due to motion • KE = ½ mv2 Temperature • Temperature is a measure of average kinetic energy. – Temperature measures how quickly the particles are moving. (Heat IS NOT the same as temperature!) – If temperature increases, kinetic energy increases. • Which has greater kinetic energy: a 25 g sample of water at 25oC or a 25 g sample of water at -15oC? Why use the Kelvin scale? • In the Kelvin scale, there is an absolute correlation between temperature and kinetic energy. – As temperature in Kelvin increases, kinetic energy increases. • Absolute zero: All molecular motion ceases. There is no kinetic energy. –0 K Kelvin-Celsius Conversions • K = oC + 273.15 • oC = K – 273.15 Kelvin-Celsius conversions • The temperature of liquid nitrogen is -196oC. What is this temperature in Kelvin? • Convert 872 Kelvin to Celsius temperature. Pressure • Pressure = force/area • Atmospheric pressure – Because air molecules collide with objects • More collisions greater pressure Pressure Units • Atmosphere • Pounds per square inch (psi) • mm Hg • Torr • Pascal (Pa) or kilopascal (kPa) 1 atm = 14.7 psi = 760 mm Hg = 760 torr = 101.3 kPa Barometer • Torricelli-1643 • Air molecules collide with liquid mercury in open dish • This holds the column up! • Column height is an indirect measure of atmospheric pressure Manometer • Two types: open and closed • Use to measure the pressure exerted by a confined gas Chapter 15 Wrapup (Honors) • At the same temperature, smaller molecules (i.e., molecules with lower gfm) have faster average velocity. • Energy flows from warmer objects to cooler objects. • Plasma – High energy state consisting of cations and electrons • Found in sun, fluorescent lights Boyle’s Law • Pressure-volume relationships • For a sample of a gas at constant temperature, pressure and volume are inversely related. • Equation form: P 1 V 1 = P2 V 2 Charles’ Law • Volume-temperature V1 V2 relationships T1 T2 • For a sample of a gas at constant pressure, volume and temperature are directly related. • Equation form: V1 V2 T1 T2 Guy-Lussac’s Law • Pressure temperature relationships • For a sample of a confined gas at constant volume, temperature and pressure are directly related. P P2 1 T1 T2 Combined Gas Law • Sometimes, all three variables change simultaneously • This single equation takes care of the other three gas laws! P1V1 P2V2 T1 T2 Dalton’s Law of Partial Pressures • For a mixture of (nonreacting) gases, the total Ptot P P2 ... 1 pressure exerted by the mixture is equal to the sum of the pressures exerted by the individual gases. Collecting a sample of gas “over water” • Gas samples are sometimes collected by Ptot Pgas PH 2O bubbling the gas through water • If a question asks about something relating to a “dry Ptot Pgas PH 2O gas”, Dalton’s Law must be used to Table: Vapor Pressure of Water correct for the vapor pressure of water! Ideal Gas Law • The number of moles of gas PV nRT affects pressure and volume, also! – n, number of moles • nV • nP • P 1/V Where R is the universal gas constant • PT R = 0.0821 L●atm/mol●K • VT Ideal vs. Real Gases • Ideal gas: completely obeys all statements of kinetic molecular theory • Real gas: when one or more statements of KMT don’t apply – Real molecules do have volume, and there are attractions between molecules When to expect ideal behavior? • Gases are most likely to exhibit ideal behavior at… – High temperatures – Low pressures • Gases are most likely to exhibit real (i.e., non-ideal) behavior at… – Low temperatures – High pressures Diffusion and Effusion • Diffusion – The gradual mixing of 2 gases due to random spontaneous motion • Effusion – When molecules of a confined gas escape through a tiny opening in a container Graham’s Law • Thomas Graham (1805-1869) • Do all gases diffuse at the same rate? • Graham’s law discusses this quantitatively. • Technically, this law only applies to gases effusing into a vacuum or into each other. Graham’s Law • Conceptual: – At the same temperature, molecules with a smaller gfm travel at a faster speed than molecules with a larger gfm. • As gfm , v • Consider H2 vs. Cl2 Which would diffuse at the greater velocity? Graham’s Law • The relative rates of diffusion of two gases vary inversely with the square roots of the gram formula masses. • Mathematically: rate1 gfm2 rate2 gfm1 Graham’s Law Problem • A helium atom travels an average 1000. m/s at 250oC. How fast would an atom of radon travel at the same temperature? • Solution: – Let rate1 = x rate2 = 1000. m/s – Gfm1 = radon 222 g/mol – Gfm2 = helium = 4.00 g/mol Solution (cont.) • Rearrange: x gfm2 rate2 gfm1 gfm2 x rate2 gfm1 • Substitute and evaluate: m 4.00 g / mol x 1000. 134 m / s s 222g / mol Applications of Graham’s Law • Separation of uranium isotopes – 235U – Simple, inexpensive technique – Used in Iraq in early 1990’s as part of nuclear weapons development program • Identifying unknowns – Use relative rates to find gfm Problem 2 • An unknown gas effuses through an opening at a rate 3.16 times slower than that of helium gas. What is the gfm of this unknown gas? Solution • Let gfm2 = x rate2 = 1 gfm1 = 4.00 rate1 = 3.16 • From Graham’s Law, 2 rate1 gfm2 rate 2 gfm1 • Rearrange: (rate1 ) 2 2 gfm1 gfm2 (rate2 ) Solution, cont. • Substitute and evaluate: (3.16 ) 2 2 4 39 .9 g / mol 1