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The Gas Laws

The Gas Laws. I. Kinetic Theory. -_________ ________ provides a ______ that explains the properties of ________, _________, and ______ in terms of __________ that are always in ________ and the ________ that exist between them. kinetic. theory. model. solids. liquids. gases.

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The Gas Laws

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  1. The Gas Laws I. Kinetic Theory -_________ ________ provides a ______ that explains the properties of ________, _________, and ______ in terms of __________ that are always in ________ and the ________ that exist between them kinetic theory model solids liquids gases particles motion forces -actual gases don’t always obey, but ___________ the ____________made by the _________ ________ approximate assumptions kinetic theory A. Gas particles do not attract or repel eachother B. Gas particles are much smaller than the distances between them C. Gas particles are in constant, random motion D. No energy is lost in the collisions of gas particles E. All gases have same average kinetic energy at same temperature

  2. The Gas Laws II. Boyle’s Law -the _______ of a gas _________ _________ with the _________, providing the ___________ is held ________ volume varies inversely pressure temperature constant P1 V2 ___ ___ P1V1 = P2V2 or = P2 V1 If a sample of Argon gas occupies a volume of 10.0 liters at a pressure of 200 kilopascals, at what pressure would the same sample of gas occupy 5.0 liters, if the temperature remains constant? Robert Boyle (1627-1691) P1 V2 ___ ___ = P2 V1 200 kPa 5.0 L ______ ____ = P2 10.0 L P2 = 400 kPa

  3. The Gas Laws II. Boyle’s Law If a sample of Carbon dioxide gas occupies a volume of 35.0 liters at a pressure of 1.10 atmospheres, what volume would the same sample of gas occupy at 1.25 atmospheres, if the temperature remains constant? Boyle’s Vacuum Chamber, Designed by Robert Hooke P1 V2 ___ ___ = P2 V1 1.10 atm V2 _____ _______ = 1.25 atm 35.0 L V2 = 30.8 L

  4. The Gas Laws III. Charles’s Law -the _______ of a gas _________ _________ with the ___________, providing the _________ is held ________ volume varies directly temperature pressure constant V1 T1 ___ ___ V1T2 = V2T1 or = V2 T2 If a sample of Chlorine gas occupies a volume of 250 milliliters at a temperature of 22°C, what volume would the same sample of gas occupy at -22°C, if the pressure remains constant? We need a temperature scale with no zero, and no negative values! Jacques Charles (1746-1823) V1 T1 ___ ___ = V2 T2 °C K = + 273 250 mL 250 mL 295 K 22°C ______ _____ ______ ____ = = V2 V2 251 K -22°C V2 V2 = 213 mL = -250 mL? A negative volume?

  5. The Gas Laws III. Charles’s Law -_________ _____ is the _______ possible theoretical temperature, equal to _________, and is the ___________ at which the ________ of a sample of gas is _____, and all ________, __________ movement of particles ________ absolute zero lowest -273.15°C temperature volume zero random Brownian ceases -the coldest _______ temperature is _______, or _________, the temperature of ______ _______ actual 4.22 K William Thomson (Lord Kelvin) (1824-1907) -268.78°C liquid Helium

  6. The Gas Laws III. Charles’s Law If a sample of methane gas occupies a volume of 14.75 liters at a temperature of 68°F, at what temperature, in °F, would the same sample of gas occupy 16.00 liters, if the pressure remains constant? Charles’s Hydrogen-filled balloon over Paris, 1783 V1 °F T1 = 9/5 °C + 32 ___ ___ = V2 T2 °C K = + 273 14.75 L 293 K ______ _____ = 16.00 L T2 T2 = 318 K T2 = 113°F

  7. The Gas Laws IV. Gay-Lussac’s Law -the _______ of a gas _________ _________ with the ___________, providing the _________ is held ________ pressure varies directly temperature volume constant P1 T1 ___ ___ P1T2 = P2T1 or = P2 T2 If the pressure in a propane tank is 965 mm Hg at a temperature of 25°C, what would the pressure in the tank be at 50°C, if the volume remains constant? Joseph Gay-Lussac (1778-1850) P1 T1 ___ ___ = P2 T2 °C K = + 273 965 mm Hg 298 K _________ _____ = P2 323 K P2 = 1040 mm Hg

  8. The Gas Laws IV. Gay-Lussac’s Law If the air pressure in an autoclave is 833 torr at a temperature of 212°F, at what temperature, in °F, would the air pressure be 900 torr, if the volume remains constant? Gay-Lussac and Jean-Baptiste Biot in Hydrogen balloon, 1804 P1 °F T1 = 9/5 °C + 32 ___ ___ = P2 T2 K = °C + 273 373 K 833 torr ______ _____ = 900 torr T2 T2 = 403 K T2 = 266°F

  9. The Gas Laws V. Combined Gas Law -the _______ of a gas is _________ proportional to ________ and directly proportional to ___________, and ________ is __________ proportional to ____________ pressure inversely volume P1V1 P2V2 temperature _____ _____ = T1 T2 volume directly temperature If the volume of a sample of Hydrogen sulfide gas is 2.00 liters at a pressure of 110 kilopascals and a temperature of 30.0°C, what is the volume of the same sample of Hydrogen sulfide, in liters, at a temperature of 80.0°C and a pressure of 440 kilopascals? P1V1 P2V2 (110 kPa) (440 kPa) V2 (2.00 L) _____ _____ _____________ __________ = = 303.0 K T1 T2 353.0 K V2 = 0.582 L °C K = + 273

  10. The Gas Laws V. Combined Gas Law If a Helium-filled balloon at sea level has a volume of 2.1 liters at a pressure of 0.998 atmospheres and a temperature of 36°C, and it is released and rises to an elevation at which the temperature is 28°C and the pressure is 0.900 atmospheres, what will be the new volume of the balloon? P1V1 P2V2 (0.900 atm) V2 (2.1 L) (0.998 atm) _____ _____ _____________ __________ = = T1 T2 309 K 301 K V2 = 2.3 L °C K = + 273

  11. The Gas Laws VI. Avogadro’s Principle -______ ________ of gases at the same ____________ and _________ contain ______ numbers of ________ equal volumes temperature pressure Amadeo Avogadro (1776-1856) equal particles -one ______ of gas contains __________ particles and occupies _______ at _________ temperature and pressure, which is ______ and ________ mole 6.02 x 1023 22.4 L standard 0.00°C 1.00 atm How many molecules in 3.73 liters of ozone at STP? 1 mole O3 6.02 x 1023 molecules O3 3.73 L O3 x ___________ x _________________ = 1.00 x 1023 molecules O3 22.4 L O3 1 mole O3 conversion factor

  12. The Gas Laws VI. Avogadro’s Principle What is the volume, in liters, of 0.881 moles of Fluorine gas at STP? 22.4 L F2 0.881 mole F2 x ________ = 19.7 L F2 1 mole F2 How many moles of Nitrogen gas are in 2.00 liters at STP? 1 mole N2 2.00 L N2 x ________ = 0.0893 moles N2 22.4 L N2 What is the volume, in liters, of 5.0 kilograms of methane at STP? 1000 grams CH4 1 mole CH4 22.4 L CH4 5.0 kg CH4 x ____________ x ______________ x _________ = 7.0 x 103 L CH4 1 kg CH4 16.043 grams CH4 1 mole CH4 conversion factor What mass, in grams, of Nitrogen dioxide occupies 15.50 liters at STP? 1 mole NO2 46.005 grams NO2 15.50 L NO2 x __________ x ______________ = 31.8 g NO2 22.4 L NO2 1 mole NO2

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