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I. Physical Properties Ch. 12 - Gases

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A. Kinetic Molecular Theory b Particles in an ideal gas… have no volume. have elastic collisions. are in constant, random, straight- line motion. dont attract or repel each other. have an avg. KE directly related to Kelvin temperature.

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B. Real Gases b Particles in a REAL gas… have their own volume attract each other b Gas behavior is most ideal… at low pressures at high temperatures in nonpolar atoms/molecules

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

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

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D. Temperature ºF ºC K -45932212 -2730100 0273373 K = ºC + 273 b Always use absolute temperature (Kelvin) when working with gases.

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E. Pressure Which shoes create the most pressure?

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E. Pressure b Barometer measures atmospheric pressure Mercury Barometer Aneroid Barometer

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E. Pressure b Manometer measures contained gas pressure U-tube ManometerBourdon-tube gauge

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E. Pressure b KEY UNITS AT SEA LEVEL 101.325 kPa (kilopascal) 1 atm 760 mm Hg 760 torr 14.7 psi

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F. STP Standard Temperature & Pressure 0°C 273 K 1 atm101.325 kPa -OR- STP

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II. The Gas Laws BOYLES CHARLES GAY- LUSSAC Ch. 12 - Gases

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A. Boyles Law P V PV = k

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A. Boyles Law b The pressure and volume of a gas are inversely related at constant mass & temp P V PV = k

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A. Boyles Law

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V T B. Charles Law

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

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B. Charles Law

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P T C. Gay-Lussacs Law

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

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= kPV PTPT VTVT T D. Combined Gas Law P1V1T1P1V1T1 = P2V2T2P2V2T2 P 1 V 1 T 2 = P 2 V 2 T 1

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GIVEN: V 1 = 473 cm 3 T 1 = 36°C = 309K V 2 = ? T 2 = 94°C = 367K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 E. Gas Law Problems b A gas occupies 473 cm 3 at 36°C. Find its volume at 94°C. CHARLES LAW T V (473 cm 3 )(367 K)=V 2 (309 K) V 2 = 562 cm 3

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GIVEN: V 1 = 100. mL P 1 = 150. kPa V 2 = ? P 2 = 200. kPa WORK: P 1 V 1 T 2 = P 2 V 2 T 1 E. Gas Law Problems b A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. BOYLES LAW P V (150.kPa)(100.mL)=(200.kPa)V 2 V 2 = 75.0 mL

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GIVEN: V 1 = 7.84 cm 3 P 1 = 71.8 kPa T 1 = 25°C = 298 K V2 = ?V2 = ? P 2 = 101.325 kPa T 2 = 273 K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (71.8 kPa)(7.84 cm 3 )(273 K) =(101.325 kPa) V 2 (298 K) V 2 = 5.09 cm 3 E. Gas Law Problems b A gas occupies 7.84 cm 3 at 71.8 kPa & 25°C. Find its volume at STP. P T V COMBINED GAS LAW

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GIVEN: P 1 = 765 torr T 1 = 23°C = 296K P 2 = 560. torr T 2 = ? WORK: P 1 V 1 T 2 = P 2 V 2 T 1 E. Gas Law Problems b A gas pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GAY-LUSSACS LAW P T (765 torr)T 2 = (560. torr)(309K) T 2 = 226 K = -47°C

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III. Ideal Gas Law (p. 334-335, 340-346) Ch. 10 & 11 - Gases

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V n A. Avogadros Principle

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V n b Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas

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PV T VnVn PV nT B. Ideal Gas Law = k UNIVERSAL GAS CONSTANT R=0.0821 L atm/mol K R=8.315 dm 3 kPa/mol K = R

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B. Ideal Gas Law UNIVERSAL GAS CONSTANT R=0.0821 L atm/mol K R=8.315 dm 3 kPa/mol K PV=nRT

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GIVEN: P = ? atm n = 0.412 mol T = 16°C = 289 K V = 3.25 L R = 0.0821 L atm/mol K WORK: PV = nRT P(3.25)=(0.412)(0.0821)(289) L mol L atm/mol K K P = 3.01 atm B. Ideal Gas Law b Calculate the pressure in atmospheres of 0.412 mol of He at 16°C & occupying 3.25 L. IDEAL GAS LAW

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GIVEN: V = ?V = ? n = 85 g T = 25°C = 298 K P = 104.5 kPa R = 8.315 dm 3 kPa/mol K B. Ideal Gas Law b Find the volume of 85 g of O 2 at 25°C and 104.5 kPa. = 2.7 mol WORK: 85 g 1 mol = 2.7 mol 32.00 g PV = nRT (104.5)V=(2.7) (8.315) (298) kPa mol dm 3 kPa/mol K K V = 64 dm 3 IDEAL GAS LAW

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Ch. 10 & 11 - Gases IV. Gas Stoichiometry at Non-STP Conditions (p. 347-350)

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A. Gas Stoichiometry b Moles Liters of a Gas STP - use 22.4 L/mol Non-STP - use ideal gas law b Non- STP Problems Given liters of gas? start with ideal gas law Looking for liters of gas? start with stoichiometry conv.

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1 mol CaCO 3 100.09g CaCO 3 B. Gas Stoichiometry Problem b What volume of CO 2 forms from 5.25 g of CaCO 3 at 103 kPa & 25ºC? 5.25 g CaCO 3 = 1.26 mol CO 2 CaCO 3 CaO + CO 2 1 mol CO 2 1 mol CaCO 3 5.25 g? L non-STP Looking for liters: Start with stoich and calculate moles of CO 2. Plug this into the Ideal Gas Law to find liters.

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WORK: PV = nRT (103 kPa)V =(1mol)(8.315 dm 3 kPa/mol K )(298K) V = 1.26 dm 3 CO 2 B. Gas Stoichiometry Problem b What volume of CO 2 forms from 5.25 g of CaCO 3 at 103 kPa & 25ºC? GIVEN: P = 103 kPa V = ? n = 1.26 mol T = 25°C = 298 K R = 8.315 dm 3 kPa/mol K

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WORK: PV = nRT (97.3 kPa) (15.0 L) = n (8.315 dm 3 kPa/mol K ) (294K) n = 0.597 mol O 2 B. Gas Stoichiometry Problem b How many grams of Al 2 O 3 are formed from 15.0 L of O 2 at 97.3 kPa & 21°C? GIVEN: P = 97.3 kPa V = 15.0 L n = ?n = ? T = 21°C = 294 K R = 8.315 dm 3 kPa/mol K 4 Al + 3 O 2 2 Al 2 O 3 15.0 L non-STP ? g Given liters: Start with Ideal Gas Law and calculate moles of O 2. NEXT

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2 mol Al 2 O 3 3 mol O 2 B. Gas Stoichiometry Problem b How many grams of Al 2 O 3 are formed from 15.0 L of O 2 at 97.3 kPa & 21°C? 0.597 mol O 2 = 40.6 g Al 2 O 3 4 Al + 3 O 2 2 Al 2 O 3 101.96 g Al 2 O 3 1 mol Al 2 O 3 15.0L non-STP ? g Use stoich to convert moles of O 2 to grams Al 2 O 3.

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Ch. 10 & 11 - Gases V. Two More Laws (p. 322-325, 351-355)

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A. Daltons Law b The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P 2 +... P atm = P H2 + P H2O

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GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H2 + 2.72 kPa P H2 = 91.7 kPa A. Daltons Law b 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. Look up water-vapor pressure on p.899 for 22.5°C. Sig Figs: Round to least number of decimal places. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.

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GIVEN: P gas = ? P total = 742.0 torr P H2O = 42.2 torr WORK: P total = P gas + P H2O 742.0 torr = P H2 + 42.2 torr P gas = 699.8 torr b 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? DALTONS LAW Look up water-vapor pressure on p.899 for 35.0°C. Sig Figs: Round to least number of decimal places. A. Daltons Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the gas and water vapor.

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B. Grahams Law b Diffusion Spreading of gas molecules throughout a container until evenly distributed. b Effusion Passing of gas molecules through a tiny opening in a container

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B. Grahams Law KE = ½mv 2 b 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 because…

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B. Grahams Law b Grahams Law Rate of diffusion of a gas is inversely related to the square root of its molar mass. Ratio of gas As speed to gas Bs speed

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b Determine the relative rate of diffusion for krypton and bromine. Kr diffuses 1.381 times faster than Br 2. B. Grahams Law The first gas is Gas A and the second gas is Gas B. Relative rate mean find the ratio v A /v B.

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b 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? B. Grahams Law Put the gas with the unknown speed as Gas A.

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b An unknown gas diffuses 4.0 times faster than O 2. Find its molar mass. B. Grahams Law The first gas is Gas A and the second gas is Gas B. The ratio v A /v B is 4.0. Square both sides to get rid of the square root sign.

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TEAM PRACTICE! b 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

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