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Unformatted text preview: KINETIC MOLECULAR THEORY (KMT) Theory used to explain gas laws. KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible. 1 Kinetic Molecular Theory
Because we assume molecules are in motion, they have a kinetic energy. 2 Kinetic Molecular Theory
At the same T, all gases have the same average KE. As T goes up, KE also increases — and so does speed. 3 KE = _____________ At the same T, At the same T, ________________________ ________________________
As T goes up, KE also _____________ — and so does speed. Kinetic Molecular Theory
Maxwell’s equation
u2 3RT M 4 5 Velocity of Gas Molecules
Molecules of a given gas have a speeds. 6 range of range of root mean square speed where u is the speed and M is the molar mass. • speed INCREASES with T • speed DECREASES with M Distribution of Gas Molecule Speeds Page 1 Velocity of Gas Molecules
Average velocity decreases with increasing mass. 7 8 GAS DIFFUSION AND EFFUSION
• diffusion is the gradual mixing of molecules of different gases. • effusion is the movement of molecules through a small hole into an empty container. GAS DIFFUSION AND EFFUSION
Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is • proportional to T • inversely proportional to M. Therefore, He effuses more rapidly than O 2 at same T. at 9 He GAS DIFFUSION AND EFFUSION
Graham’s law governs effusion and diffusion of gas molecules.
Rate for A Rate for B M of B M of A 10 relation of mass to rate of diffusion relation of mass to rate of diffusion •• HCl and NH33 diffuse HCl and NH diffuse from opposite ends from opposite ends of tube. of tube. •• Gases meet to form Gases meet to form NH44Cl NH Cl •• HCl heavier than NH 33 HCl heavier than NH •• Therefore, NH 44Cl Therefore, NH Cl forms closer to HCl forms closer to HCl end of tube. end of tube. Gas Diffusion 11 12 Using KMT to Understand Gas Laws
Recall that KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible. Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass. to its molar mass. Thomas Graham, 18051869. Professor in Glasgow and London. Page 2 Avogadro’s Hypothesis and Kinetic Molecular Theory 13 14 Gas Pressure, Temperature, and Kinetic Molecular Theory Boyle’s Law and Kinetic Molecular Theory 15 P proportional to n P proportional to T P proportional to 1/V Deviations from Ideal Gas Law
• Real molecules have volume. • There are 16 Deviations from Ideal Gas Law
Account for volume of molecules and intermolecular forces with 17 Deviations from Ideal Gas Law
Measured P P + n2 a V2 Measured V = V(ideal) V nb nRT 18 VAN DER WAAL’S EQUATION .
Measured P Measured V = V(ideal) intermolecular forces.
– Otherwise a gas could not become a liquid. vol. correction intermol. forces (
Fig. 12.20 P + n2 a 2 V ) V  nb nRT vol. correction intermol. forces J. van der Waals, Waals, 18371923, Professor of Physics, Amsterdam. Nobel Prize 1910. Cl2 gas has a = 6.49, b = 0.0562 gas For 8.0 mol Cl 2 in a 4.0 L tank at 27 oC. in P (ideal) = nRT/V = 49.3 atm nRT/V P (van der Waals) = 29.5 atm Waals) Page 3 ...
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 Fall '08
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