V. Two More Laws (p. 322-325, 351-355) Read these pages first! Ch. 10 & 11 - Gases V. Two More Laws (p. 322-325, 351-355) Read these pages first!

The Behavior of Real Gases The molar volume is not constant as is expected for ideal gases. These deviations due to an attraction between some molecules. Finite molar molecular volume. For compounds that deviate from ideality the van der Waals equation is used: where a and b are constants that are characteristic of the gas. Applicable at high pressures and low temperatures. John A. Schreifels Chemistry 211

The Kinetic Theory – Molecular Theory of Gases Microscopic view of gases is called the kinetic theory of gases and assumes that Gas is collection of molecules (atoms) in continuous random motion. The molecules are infinitely small point-like particles that move in straight lines until they collide with something. Gas molecules do not influence each other except during collision. All collisions are elastic; the total kinetic energy is constant at constant T. Average kinetic energy is proportional to T. John A. Schreifels Chemistry 211

Gases and Gas Pressure They form homogeneous solutions. All gases dissolve in each other. Gases are compressible. Large molar volume. Barometer usually mercury column in tube; mm Hg is a measure of pressure. Manometer tube of liquid connected to enclosed container makes it possible to measure pressure inside the container. Pressure One of the most important of the measured quantities for gases defined as the force/area P = f/area. Pressure has traditionally been measured in units relating to the height of the Hg and is thus expressed as mm Hg = 1 Torr. John A. Schreifels Chemistry 211

P = dHgghHg = doilghoil or dHghHg = doilhoil. Gas Pressure Pressure is directly proportional to the height of the column in a barometer or manometer. Mercury often used but other low density liquids are used for low pressure changes: P = dHgghHg = doilghoil or dHghHg = doilhoil. E.g. Water is sometimes used to determine pressure; determine the height of water if the barometer pressure was 750 mmHg. The density of Hg = 13.596 g/cm3 and 1.00 g/cm3 respectively. Solution: John A. Schreifels Chemistry 211

Ptotal = P1 + P2 + ... B. Dalton’s Law The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. Ptotal = P1 + P2 + ... When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor.

B. Dalton’s Law Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor. GIVEN: PH2 = ? Ptotal = 94.4 kPa PH2O = 2.72 kPa WORK: Ptotal = PH2 + PH2O 94.4 kPa = PH2 + 2.72 kPa PH2 = 91.7 kPa Look up water-vapor pressure on p.899 for 22.5°C. Sig Figs: Round to least number of decimal places.

B. Dalton’s Law GIVEN: Pgas = ? Ptotal = 742.0 torr PH2O = 42.2 torr A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor. GIVEN: Pgas = ? Ptotal = 742.0 torr PH2O = 42.2 torr WORK: Ptotal = Pgas + PH2O 742.0 torr = PH2 + 42.2 torr Pgas = 699.8 torr Look up water-vapor pressure on p.899 for 35.0°C. Sig Figs: Round to least number of decimal places.

C. Graham’s Law Diffusion Spreading of gas molecules throughout a container until evenly distributed. Effusion Passing of gas molecules through a tiny opening in a container

KE = ½mv2 C. Graham’s Law Speed of diffusion/effusion Kinetic energy is determined by the temperature of the gas. At the same temp & KE, heavier molecules move more slowly. Larger m  smaller v KE = ½mv2

C. Graham’s Law Graham’s Law Rate of diffusion of a gas is inversely related to the square root of its molar mass. The equation shows the ratio of Gas A’s speed to Gas B’s speed.

C. Graham’s Law Determine the relative rate of diffusion for krypton and bromine. The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “vA/vB”. Kr diffuses 1.381 times faster than Br2.

Put the gas with the unknown speed as “Gas A”. C. Graham’s Law A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? Put the gas with the unknown speed as “Gas A”.

C. Graham’s Law An unknown gas diffuses 4.0 times faster than O2. Find its molar mass. The first gas is “Gas A” and the second gas is “Gas B”. The ratio “vA/vB” is 4.0. Square both sides to get rid of the square root sign.

TEAM PRACTICE! Work the following problems in your book. Check your work using the answers provided in the margin. p. 324 SAMPLE PROBLEM 10-6 PRACTICE 1 & 2 p. 355 SAMPLE PROBLEM 11-10 PRACTICE 1, 2, & 3