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# RelativeResourceManager1 - CH1. The properties of gases...

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CH1. The properties of gases Equations of state 1 The kinetic model of gases 1.4 The pressure of a gas according to the kinetic model 1.5 The average speed of gas molecules 1.6 The Maxwell distribution of speeds 1.7 Diffusion and effusion 1.8 Molecular collisions

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2 Kinetic Molecular Theory •Temperature and pressure are macroscopic properties of gases . These properties are related to molecular motion, which is a microscopic phenomenon . The kinetic theory of gases correlates between macroscopic properties and microscopic phenomena. Kinetics means the study of motion, and in this case motions of gas molecules . •Years ago, a mathematician named Ludwig Boltzmann figured out that the kinetic energy of a system such as this was distributed in a predictable way. Even though the individual objects continually exchanged kinetic energy with each other, there was a predictable result to how the kinetic energy was distributed .
3 Kinetic Molecular Theory Assumptions of the kinetic molecular theory 1. gases consist of particles constantly moving through space in random directions and with various speeds Gas particles are always in motion except for the very specific condition known as Absolute Zero . 2. gas particles have no volume This is based on the idea that all real gas particles are of extremely small volume. To establish uniformity among the many real gases it is assumed that they all are of the same volume. That volume is zero.

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4 Kinetic Molecular Theory 3. gas particles have no attraction between them As the gas particles collide with one another, they will not interact with each other. They will not establish any bonding or interactions of any sort. In addition, any collisions with the walls of any container will also occur free from any attractive forces. The average kinetic energy (KE) of gas particles is proportional to the temperature in kelvins
5 Pressure and speed Pressure and volume of gas are related as and molar mass is M = mN A root mean square speed is pV 3 1 nMc 2 2 / 1 2 / 1 2 3 M RT v c c is proportional to the square root of T c is proportional to square root of M

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6 Maxwell distribution of speed J.C. Maxwell derived a precise distribution of speed of molecules at temperature T, (f is a fraction of molecules with speed v) Range of speeds broaden as T increases! RT Mv v RT M v F with v v F f 2 / 2 2 / 3 2 e 2 4 ) ( ) ( We will use F(v) to calculate the fraction of molecules in a given range of speeds v, F(v). v
7 Diffusion of a gas particle through a space filled with other particles. Effusion is the escape of a gas through a small hole. KMT enables to calculate the frequency with which molecular collisions occur and the distance a molecule travel on average between collisions Mean free path: Collision frequency: z Cross section: = d 2 c z

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8 Graham’s Law of Effusion PROBLEM: Calculate the ratio of the effusion rates of helium and methane (CH
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## This note was uploaded on 02/09/2011 for the course CHEM 3050 taught by Professor Staff during the Spring '08 term at Kennesaw.

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RelativeResourceManager1 - CH1. The properties of gases...

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