CH 11 – Physical Characteristics of Gases: Objectives Describe how the kinetic-molecular theory of matter explains ideal gases Differentiate between ideal and real gases Describe temperature & pressure and convert units. State the conditions of STP Explain and calculate the relationship between volume, temperature and pressure of gases Perform the calculations with the combined gas law Calculate partial pressures from Dalton’s law. Use the Ideal Gas Law to solve molar gas problems. Use Graham’s Law to solve gas effusion problems.

A. Kinetic-Molecular Theory of Ideal Gases Particles in an ideal gas… –are far apart relative to their size. –have elastic collisions (no loss of kinetic energy). –are in constant, random, rapid motion. –don’t attract or repel each other. –have an avg. KE directly related to temperature.

A. Kinetic-Molecular Theory of Ideal Gases

B. Real Gases Particles in a REAL gas… –have their own volume –attract each other Gas behavior is most ideal… –at low pressures –at high temperatures –in nonpolar atoms/molecules (He, Ne, H 2, N 2, I 2 etc.)

C. Characteristics of gases Gases expand to fill any container. –random motion, no attraction Gases are fluids (like liquids). –no attraction Gases have very low densities. –no volume = lots of empty space

C. Characteristics of gases Gases can be compressed. –no volume = lots of empty space Gases undergo diffusion & effusion. –random motion

D. Temperature ºF ºC K K = ºC Always use absolute temperature (Kelvin) when working with gases.

E. Pressure Which shoes create the most pressure?

E. Pressure Barometer –measures atmospheric pressure Mercury Barometer Aneroid Barometer Invented by Evangelista Torricelli

E. Pressure KEY UNITS AT SEA LEVEL – kPa (kilopascal) –1 atm –760 mm Hg –760 torr –14.7 psi (pounds per square inch) These are all equalities for conversion

F. STP Standard Temperature & Pressure 0°C 273 K 1 atm kPa -OR- STP

G. Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P When a H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor.

L. Sample Problems - Dalton GIVEN: P gas = ? P total = torr P H2O = 42.2 torr WORK: P total = P gas + P H2O torr = P gas torr P gas = torr A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? Look up water-vapor pressure on p.859 for 35.0°C. The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor. Go to 2 nd to last page of note packet!

L. Sample Problems - Dalton 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 H 2 and water vapor. GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H kPa P H2 = 91.7 kPa Look up water-vapor pressure on p.859 for 22.5°C.

H. Boyle’s Law V P PV = k

H. Boyle’s Law The pressure and volume of a gas are inversely related –at constant mass & temp P 1 V 1 = P 2 V 2

I. Charles’ Law V T

The volume and absolute temperature (K) of a gas are directly related –at constant mass & pressure ALL TEMPS IN KELVIN

J. Gay-Lussac’s Law P T

The pressure and absolute temperature (K) of a gas are directly related –at constant mass & volume

Concept Check – assuming other things constant P decreasesVolume T increasesPressure V increasesTemperature P decreasesTemperature T decreasesvolume V increasespressure IF… THEN… Increases Decreases Increases Decreases

K. Combined Gas Law = k PV PTPT VTVT T P1V1T1P1V1T1 = P2V2T2P2V2T2

Sample Problems A gas occupies 473 cm 3 at 36°C. Find its volume at 94°C. GIVEN: V 1 = 473 cm 3 T 1 = 36°C = 309K T 2 = 94°C = 367K V 2 = ? WORK: TT VV CHARLES’ Law?:

Sample Problems GIVEN: V 1 = 100. mL P 1 = 150. kPa V 2 = ? P 2 = 200. kPa WORK: P 1 V 1 = P 2 V 2 A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. BOYLE’S PPVV Law?:

Sample Problems GIVEN: V 1 = 7.84 cm 3 P 1 = 71.8 kPa T 1 = 25°C = 298 K P 2 = kPa T 2 = 273 K V 2 = ? WORK: A gas occupies 7.84 cm 3 at 71.8 kPa & 25°C. Find its volume at STP. P  T  VV COMBINED GAS LAW Law?:

L. Avogadro’s Law Equal volumes of gases contain ___________________. equal numbers of moles constant temperature and pressure V n

M. The Ideal Gas Law PV=nRT R=UNIVERSAL GAS CONSTANT R= Latm/molK R=8.315 LkPa/molK n = number of moles

Sample Problem 1 Calculate the pressure in atmospheres of mol of He at 16°C & occupying 3.25L GIVEN:WORK: P = ? atm n = mol T = 16°C = 289 K V = 3.25 L R = PV = nRT P(3.25)=(0.412)(0.0821)(289) L mol L  atm/mol  K K P = 3.01 atm L*atm/mol*K

Sample Problem 2 Find the volume of 85 g of O 2 at 25°C and kPa. GIVEN:WORK: V = ? n = 85 g T = 25°C = 298 K P = kPa R = L*kPa/mol*K PV = nRT ( ) = 2.7 mol 85 g O 2 32 g O 2 1 mol O 2 (104.5)V=(2.7)*(8.315)*(298) V = 64L n