GASES manometers pressure Kinetic theory of gases Units of pressure Behavior of gases Partial pressure of a gas Pressure vs. volume Pressure vs. temperature Temperature vs. volume Diffusion/effusion Combined gas law 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: P1V1 = P2V2
Charles’ Law • Volume-temperature relationships • For a sample of a gas at constant pressure, volume and temperature are directly related. • Equation form:
Guy-Lussac’s Law • Pressure temperature relationships • For a sample of a confined gas at constant volume, temperature and pressure are directly related.
Combined Gas Law • Sometimes, all three variables change simultaneously • This single equation takes care of the other three gas laws!
Dalton’s Law of Partial Pressures • For a mixture of (nonreacting) gases, the total 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 bubbling the gas through water
If a question asks about something relating to a “dry gas”, Dalton’s Law must be used to correct for the vapor pressure of water! Table: Vapor Pressure of Water
Ideal Gas Law • The number of moles of gas affects pressure and volume, also! • n, number of moles • n V • n P • P 1/V • P T • V T Where R is the universal gas constant R = 0.0821 L●atm/mol●K
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:
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: • Substitute and evaluate:
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, • Rearrange:
Solution, cont. • Substitute and evaluate: