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A Gas Uniformly fills any container. Mixes completely with any other gas Exerts pressure on its surroundings. 1 Pressure is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr 2 Gases: Macroscopic Behavior Boyle’s Law: P 1/V or PV = constant (at constant T, amount of gas) Charles’ Law: V T (at constant P, amount of gas) Gay-Lussac’s Law: P T (at constant V, amount of gas) Avogadro’s Law: V n (at constant P, T; n = moles of gas) 3 11_06 Boyle’s Law P = 1.0 atm P = 2.0 atm P = 4.0 atm V = 4.0L P x V = 4.0 atm • L V = 2.0L P x V = 4.0 atm • L V = 1.0L P x V = 4.0 atm • L P1V1 = P2V2 4 Plots of P vs. V assuming Boyle’s Law holds 05_06 5_6 3.0 1.5 Volume (L) 2.0 1.40 L 1.0 0.70 L 1.0 1/V(L–1) 0.25 0.50 Pressure (atm) A 0.75 1.00 0.5 0 0 0.25 0.50 Pressure (atm) B 0.75 1.00 5 11_11 Charles's Law 0.8 1.0 g O2 Extrapolation 0.4 t = –273ºc 0.2 1.0 g CO2 0.8 0.6 0.6 1.0 g O2 1.0 g CO2 Volume (L) Volume (L) 0.4 Extrapolation 0.2 0 -250 -200 -150 -100 -50 0 Temperature (ºC) 50 0 50 100 150 200 250 300 350 Temperature (K) A B V1 V2 T1 T2 6 Additional Charles’ Law Plots 5_8 0.8 0.6 g 1.0 O2 O2 Volume (L) gC 1.0 0.4 Extrapolation g 0.5 O2 CO 2 0.5 g 0.2 t = -273C 0 - 250 -200 - 150 - 100 - 50 0 50 Temperature (°C) 7 Avogadro’s Law Balloons Holding 0.041 mol of gas at 25º C and 1 atm pressure will all have a volume = 1.0 L) V = an 8 The Ideal (or Combined) Gas Law PV = nRT the “Equation of State” for ideal gases R = proportionality constant = 0.08206 L atm mol P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins 9 Gases – Example (1) A gaseous compound has the empirical formula CHCl. A 256 mL flask, at 373 K and 750 torr pressure contains 0.800 g of the compound. Determine its molar mass and molecular formula. 10 Gases – Example (2) Molar mass = g of sample / moles in sample Moles in sample n = PV/RT n = PV/RT 1atm 1L 750.torr 256ml 760torr 1000mL 0.08205L atm/mol K 373K = 8.254 x 10-3 mol 11 Gases – Example (3) Molar mass = 0.800 g / 8.254 x 10-3 mol = 96.9 g/mol CHCl = 12.01 + 1.01 + 35.45 g/mol = 48.47 g/mol So the molecular formula is C2H2Cl2 12 Dalton’s Law of Partial Pressures For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . . 13 Kinetic Molecular Theory Gas particles are extremely tiny and distances between them are great – particles have negligible volume Gas particles move continuously, rapidly and randomly in straight lines in all directions – the collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas For gases, both gravitational forces and forces of attraction between particles are negligible – the particles exert no forces on each other 14 Kinetic Molecular Theory The average kinetic energy is the same for all gases at the same temperature; it varies proportionally with the temperature in Kelvin. When gas particles collide with one another, or with the walls of the container, no energy is lost; all collisions are perfectly elastic. 15 11_08 Explanation for Boyle’s Law Larger volume Fewer collisions per unit area Lower pressure Smaller volume More collisions per unit area Higher pressure 16 Explanation of Charles’s Law: V T 17 5-15 Explanation for Gay-Lussac’s Law: P T Temperature is increased P1 P2 T1 T2 18 Meaning of Temperature • Molecules and atoms are in constant motion. • They always have a range of velocities: 0 Maxwell-Boltzmann distribution • Temperature measures how “spread out” that distribution is. • Higher temperatures mean more fast moving molecules. 19 Maxwell-Boltzmann Distribution The Meaning of Temperature (KE)avg 3 RT 2 Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.) 20 Molar Volume “STP” P = 1 atmosphere T = 273.2 K The molar volume will be 22.42 liters 21 Real Gases Z is called the compressibility PV Z 1 nRT Kinetic Molecular Theory predicts: PV nRT or This is true only at high temperatures or low pressures! At lower temperatures and higher pressures, the ideal gas equation does not hold: PV nRT or Z PV 1 nRT The gas then has more complicated behavior. At high enough pressure or low enough temperatures, a gas will sometimes even turn to liquid or solid. 22 Van der Waals Equation In 1873, Johannes van der Waals figured out why gases show deviations from the ideal gas law He realized that the individual gas molecules: Repelled one another at short distances (higher pressures) – ideal volume is less than the measured volume by a constant related to the molecular volume Attracted one another at longer distances (lower pressures) – pressure is reduced by attractions among the molecules Van de Waals derived the following equation: 2 nRT an P 2 V nb V repulsions attractions a & b are constants that depend on the particular gas an2 P V nb nRT V2 Alternate form 23 Real Gases: Volume of gas molecules Gas molecules can’t invade each other’s “space”; available volume is reduced – measured volume exceeds ideal volume 24 Real gases: Impact of attractive forces on pressure 5_28 25 Plots of Z vs. P for Real Gases 5-24 2.0 Positive Deviations from Ideal Gas Law N2 CH4 H2 PV nRT CO2 1.0 Negative Deviations from Ideal Gas Law Ideal gas 0 • Different gases • Same temperature • T = 200 K 0 200 400 600 800 1000 P(atm) 26 Plots of Z vs. P for Nitrogen 5-25 203 K 1.8 Less ideal 293 K PV nRT 1.4 673 K 1.0 More ideal Ideal gas 0.6 Same Gas (N2) Different temperatures 0 200 400 P(atm) 600 800 27 28

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posted: | 6/26/2009 |

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Lawrence Technological University - Chemistry 1 CHM1221 Fall 06

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