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THE GASEOUS STATE Gas Laws (6) Stoichiometry Gas Mixtures Kinetic Molecular Theory of Gases Effusion and Diffusion Real Gases

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GAS State of Matter Compressible since molecules are far apart. Takes the shape and volume of container. Forms homogeneous mixtures with other gases. Pressure is a gas property which tells us about the amount of gas present.

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PRESSURE Pressure = Force/Area Devices to measure pressure: manometer and barometer Pressure Units –pascal = N/m 2 = kg/(m s 2 ) SI derived unit –1 mm Hg = 1 torr –1 std atm = 760 torr = 1.01325E+05 Pa = @100kPa

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GAS LAWS (empirical laws) Boyle’s Law relates V vs P: V α 1/P or PV = k at constant n and T (Fig 9.6) Charles’ Law relates V vs T (K): V α T or V/T = k at constant n and P (Fig 9.8) Avogadro’s Law relates V vs n: V α n or V/n = k at constant P and T

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GAS LAWS (empirical laws) IDEAL GAS LAWPV = nRT –Equation of state for ideal gas –Note universality of equation; I.e. identity of the gas is unknown –Limiting law (limit of high T and low P) R = Gas Constant = 0.0821 (L-atm)/(mol-K) = 8.3145 J/(mol-K)

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OTHER Note that T must be in units of Kelvin (K = o C + 273) STP means 1 atm AND 273.15 K Molar volume of a gas = Volume of one mole of gas at STP = 22.414 L

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STOICHIOMETRY of GAS PHASE REACTIONS Use gas laws in stoichiometric problems Law of Combining Volumes (Gay-Lussac) Use the gas laws to find molar mass: –Use V, P, T and Ideal Gas Law to find n. –Use n and the mass, m, to find molar mass, M = m/n –Use P, T and density of gas, d, to find M because M = dRT/P

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GAS MIXTURES DALTON’S LAW –Law of Partial Pressures –P TOTAL = P = ∑ P i at constant T and V –P i = n i RT/V = partial pressure of a gas –x i = mole fraction = n i /n TOTAL = P i /P TOTAL COLLECTING GASES OVER WATER –P TOTAL = P = P g + P w

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KINETIC MOLECULAR THEORY OF GASES (1) GAS MOLECULES ARE FAR APART FROM EACH OTHER THEIR VOLUME IS NEGLIGIBLE THEY MOVE RAPIDLY AND RAMDONLY IN ALL DIRECTIONS AND AT VARIOUS SPEEDS INTERMOLECULAR FORCES ARE NEGLIGIBLE EXCEPT FOR COLLISIONS

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KINETIC MOLECULAR THEORY (2) COLLISIONS ARE ELASTIC THE AVERAGE KINETIC ENERGY OF A MOLECULE IS PROPORTIONAL TO T. EXPLAINS MACROSCOPIC PROPERTIES LIKE P, T, V, v AND EMPIRICAL GAS LAWS

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KINETIC MOLECULAR THEORY (QUANT.) Average kinetic energy = [(3/2) RT] α T Root mean square velocity –u rms = √(3RT/M) where R = 8.314 J/(K-mol) Diffusion: Mixing of gases –Diffusion distance traveled α (1/ √ M) Effusion –Passage of gas through orifice into a vacuum –Graham’s Law: Effusion rate α (1/ √ M)

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REAL GASES IDEAL: PV= nRT VDW: P eff V eff = nRT –(P + n 2 a/V 2 ) (V -nb) = nRT –First term accounts for non-zero attractive intermolecular forces –Second term accounts for non-zero molecular size

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