Objective/Warm-Up SWBAT solve Dalton’s Law and Graham’s Law Problems. What is the ideal gas law?

A list of gear for an expedition to Mount Everest includes climbing equipment, ski goggles, a down parka with a hood, and most importantly compressed-gas cylinders of oxygen. You will find out why a supply of oxygen is essential at higher altitudes.

The contribution each gas in a mixture makes to the total pressure is called the partial pressure exerted by that gas.

Dalton’s Law of Partial Pressure The total pressure is equal to the sum of the pressure of each gas in a container. P total = P A + P B + P C + … OR P x = (Moles X/Total moles)(P total )

Three gases are combined in container T. 100 kPa + 250kPa + 200kPa = 550kPa

The partial pressure of oxygen must be kPa or higher to support respiration in humans. The climber below needs an oxygen mask and a cylinder of compressed oxygen to survive. Atmospheric pressure at the top of the world (29,000ft above sea level) = 30kPa

14.6

Diffusion

Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout.

Graham’s Law Bromine vapor is diffusing upward through the air in a graduated cylinder.

Graham’s Law After several hours, the bromine has diffused almost to the top of the cylinder.

Diffusion and effusion DiffusionDiffusion The random and spontaneous mixing of molecules. EffusionEffusion The escape of molecules through small holes in a barrier.

During effusion, a gas escapes into a vacuum through a tiny hole in its container.

Relates the rates of effusion of two gases to their molar masses. This law notes that larger molecules move more slowly. Graham’s law Rate A MM B Rate B MM A =

Helium effuses (and diffuses) nearly three times faster than nitrogen at the same temperature.

Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.

Graham’s law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. This law can also be applied to the diffusion of gases. KE = ½ mass  velocity 2 Two gases at the same temperature have equal kinetic energy, but their masses are different. HEAVIER = SLOWER

A helium filled balloon will deflate sooner than an air-filled balloon. Helium atoms are less massive than oxygen or nitrogen molecules. So the molecules in air move more slowly than helium atoms with the same kinetic energy.

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Kinetic-molecular theory This theory explains the behavior of gases. Gases consist of very small particles (molecules) which are separated by large distances. Gas molecules move at very high speeds - hydrogen molecules travel at almost 4000 mph at 25 o C. Pressure is the result of molecules hitting the container. At 25 o C and 1 atm, a molecule hits another molecule and average of times/sec.

Kinetic-molecular theory No attractive forces exist between ideal gas molecules or the container they are in. Energy of motion is called kinetic energy. Average kinetic energy = mv 2 Because gas molecules hit each other frequently, their speed and direction is constantly changing. The distribution of gas molecule speeds can be calculated for various temperatures. 1212

Kinetic-molecular theory Fraction having each speed Molecular speed (m/s) O 2 at 25 o C O 2 at 700 o C H 2 at 25 o C Average speed

We can plot the compressibility factor (PV/nRT) for gases. If the gas is ideal, it should always give a value of 1. Obviously, none of these gases are ‘ideal.’ Real gases Compressibility factor Pressure, atm H2H2 N2N2 CH 4 C2H4C2H4 NH 3

Real gases As pressure approaches zero, all gases approach ideal behavior. At high pressure, gases deviate significantly from ideal behavior.Why? Attractive forces actually do exist between molecules. Molecules are not points -- they have volume.

Van der Waals equation This equation is a modification of the ideal gas relationship. It accounts for attractive forces and molecular volume. P + an 2 V 2 (V - nb) = nRT () Correction for Molecular volume Correction for attractive forces between molecules

Van der Waals constants a b GasFormula L 2 atm mol -2 L mol -1 Ammonia NH Argon Ar Chlorine Cl Helium He Hydrogen H Nitrogen N Water H 2 O Xenon Xe