Page 1. 1. KINETIC MOLECULAR THEORY. (KMT). Theory used to explain gas
laws. KMT assumptions are. • Gases consist of molecules in constant, random ...
KINETIC MOLECULAR THEORY (KMT)
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u2
root mean square speed
where u is the speed and M is the molar mass. • speed INCREASES with T • speed DECREASES with M
Kinetic Molecular Theory
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At the same T, all gases have the same average KE. As T goes up, KE also increases — and so does speed.
KE = _____________ At At the the same same T, T, ________________________ ________________________ As T goes up, KE also _____________ — and so does speed.
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Maxwell’s equation 3RT M
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Because we assume molecules are in motion, they have a kinetic energy.
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.
Kinetic Molecular Theory
Kinetic Molecular Theory
Distribution of Gas Molecule Speeds
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Velocity of Gas Molecules Molecules of a given gas have a speeds.
range of
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Velocity of Gas Molecules
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GAS DIFFUSION AND EFFUSION
Average velocity decreases with increasing mass.
• diffusion is the gradual mixing of molecules of different gases.
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
Rate Rate of of effusion effusion is is inversely inversely proportional proportional to to its its molar molar mass. mass.
Thomas Graham, 1805-1869. Professor in Glasgow and London.
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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.
• effusion is the movement of molecules through a small hole into an empty container.
Gas Diffusion
relation relation of of mass mass to to rate rate of of diffusion diffusion •• HCl HCl and and NH NH33 diffuse diffuse from from opposite opposite ends ends of tube. of tube. •• Gases Gases meet meet to to form form NH NH44Cl Cl •• HCl HCl heavier heavier than than NH NH33 •• Therefore, Therefore, NH NH44Cl Cl forms forms closer closer to to HCl HCl end end of of tube. tube.
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GAS DIFFUSION AND EFFUSION
He
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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.
Avogadro’s Hypothesis and Kinetic Molecular Theory
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Gas Pressure, Temperature, and Kinetic Molecular Theory
P proportional to n
Deviations from Ideal Gas Law • Real molecules have volume. • There are
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Deviations from Ideal Gas Law
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Account for volume of molecules and intermolecular forces with
(
– Otherwise a gas could not become a liquid.
P
+
n2 a ----2 V
Deviations from Ideal Gas Law Measured P P
+
n2 a ----V2
Measured V = V(ideal) V
-
nb
nRT
vol. correction
Measured V = V(ideal)
Measured P
intermol. forces
)
V
-
nb
nRT
vol. correction intermol. forces Fig. 12.20
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P proportional to 1/V
P proportional to T
VAN DER WAAL’S EQUATION .
intermolecular forces.
Boyle’s Law and Kinetic Molecular Theory
J. van der Waals, Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910.
Cl2 gas has a = 6.49, b = 0.0562 For 8.0 mol Cl 2 in a 4.0 L tank at 27 oC. P (ideal) = nRT/V nRT/V = 49.3 atm P (van der Waals) Waals) = 29.5 atm
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