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Chpt 5 - Gases Gas Law Development Daltons Partial pressure law Grahams effusion Kinetic Theory –Root-mean-square velocity van der Waals equation of state HW: Chpt 5 - pg , #s 5, 22, 23, 25, 31, 32, 35, 39, 41, 46, 55, 64, 66, 71, 75, 77, 81, 91, 95, 97, 101, 124 Due Mon 10/4

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Torricelli barometer The height in mm of mercury above the surface of the resevoir of mercury determines the pressure. The units are mmHg. mmHg is also the same unit as Torr. i.e. standard pressure is 760 mmHg and 760 Torr Pressure is? Units?

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Simple Manometer Similar to the barometer, the height difference of the Hg relates the pressure difference in the unknown gas bulb side to the current atmospheric pressure. The higher Hg side has the _____ pressure. (higher/lower)

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Boyles Law Constant temperature experiments demonstrated the PV=constant graphing this yields an inverse relationship Thus if the pressure of volume changes at a constant temperature P 1 V 1 = P 2 V 2

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Plot of PV vs. P for Several Gases This graph shows Boyles linear relationship for the PxV. The constant depends on the gas

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Charless Law Constant pressure experiments demonstrated that Volume is directly proportional to Temperature (Kelvin) V 1 = V 2 T 1 T 2 Several gases were used & all extrapolate to zero volume and the same temperature at negative 273 o C

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Plots of V vs. T( º C) Charless Law Experiment results Demonstrates a unique absolute zero at o C

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Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 Avogadros Law - equal volumes of gas contain equal particles of gas V = k n At constant temperature and pressure the volume is directly proportional to the number of moles of gas.

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Ideal Gas Law Putting it all together, we can calculate that constant now. The universal gas constant R. PV=R or PV=nRT nTR = l *atm/mol*K =8.31 l *kpa/mol*K

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Density / Molar Mass with Ideal gas law Molar mass, MM = ? What are the units? So, moles = ? Density, d = ?Use L for density since gas So, mass = ? Combine and get expression for moles n= N= PV = dV Thus MM = dRT volume will be in Liters RT MM P

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Daltons Law of Partial Pressures The gases in a mixture act independently and thus the forces (and pressures) are additive. P total = P 1 + P 2 + P 3 + …

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Kinetic Molecular Theory Ideal Gas Behavior –Particles assumed to have zero volume –Particles in constant motion –Particles exert no forces on each other –KE ave is directly proportional to T (K) Check out Appendix 2 to see derivation of ideal gas law PV=nRT

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Kinetic Theory also KE ave = 3/2 RT Root square mean velocity u rms = sqrt(3RT/M) –Where M is mass of a mole in kg –So now we can calculate ave velocities of gases

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Effusion of Gas into Evacuated Chamber If more than one type of gas or more than one isotope, which gas effuses faster? Lighter gas moves Faster!! KE = 1/2 mv 2

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Relative Molecular Speed Distribution of H 2 and UF 6

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Diffusion Rates of NH 3 and HCl Molecules Through Air Relative diffusion/effusion rate pg. 213 textbook rate 1 = Sqrt(M 2 ) rate 2 Sqrt(M 1 ) lighter gas is faster

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Ideal vs. Real Gases All of the gases are real!!! They just behave ideally at certain temperatures and pressures. Think of the KMT assumptions, what conditions would gases fail to act ideally. Low temperatures (gases condense) & High pressures (force the gases together so they have to interact)

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Plots of PV/nRT vs. P for Several Gases

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Plot of PV/nRT vs. P for N 2 Gas This graph shows that at higher temperatures gases behave closer to ideal even at high pressures. Recall that gases behave ideally at low pressures and high temperatures.

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van der Waals Equation van der Waals equation is entire gas law relationship with corrections for real volume and molecular attractions. pg.216 textbook with Table 5.3 for some common gases (P obs + correction) x ( V - nb) = nRT This formula is also given on AP exam sheet.

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Values of the van der Waals Constants for Common Gases a is a measure of intermolecular attractions (it is the correction to the pressure to account for attractions for each other) b is a measure of size of the molecule (it is the volume correction)

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