3_Kinetic_Model_of_Gases_final

3_Kinetic_Model_of_Gases_final - The Kinetic Model of Gases...

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Fall 2011 The Kinetic Model of Gases CHEM 300
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Kinetics allow us to understand the molecular behavior of gases Gas laws give us no real understanding of the molecular behavior of gases How is the pressure of a gas related to the motion of individual molecules? Why do gases expand when heated at constant pressure?
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Assumptions needed to develop a kinetic theory of gases A gas is made up of a great number of atoms or molecules, separated by distances that are large compared to their size. The molecules have mass but negligible volume, compared to the average distance traveled Molecules are in random motion. There is no interaction between molecules or atoms (attractive or repulsive), except collisions Collisions are elastic, i.e. Kinetic Energy is conserved.
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Intermolecular forces Ionic (Coulomb) ion-ion (attractive or repulsive) Dipolar (Van der Waal) ion-dipole, dipole-dipole, dipole-induced dipole Hydrogen bonding A type of dipolar interaction (-C=O H-N-) Dispersion forces (London) induced dipole-induced dipole
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v 2 = v x 2 + v y 2 + v z 2 Velocity is a vector quantity Velocity is a vector quantity It has both magnitude and direction Can be resolved into three mutually components v x , v y , v z
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Development of an equation for pressure based on simple physical principles M = mN A Collision of the molecule with the wall is elastic (velocity is – v x after collision) Pressure = Force/Area Force = momentum/time Area = ! 2 Force = mv x 2 / ! for one molecule (exerted on the wall as a result of collision) Force = N mv x 2 / ! for N molecules Pressure = (N mv x 2 / ! )/ ! 2 p= N mv x 2 / ! 3 p = Nmv x 2 V = nMv x 2 V N = nN A
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v 2 = v 1 2 + v 2 2 + v N 2 N v x 2 = v y 2 = v z 2 = v 2 3 p = Nm v 2 3 V By expressing the velocity in three dimensions, we can convert to volume When N is large: Use mean-square velocity ( v 2 ) or < v 2 > Assume molecular motions along x, y, and z are equally probable when N large p = Nmv x 2 V
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p = Nm v 2 3 V p = 2 N 3 V E k We can relate pressure to kinetic energy Pressure is directly proportional to the average kinetic energy and the mean-square velocity The larger the velocity the more frequent the collisions and the greater the change in momentum.
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k B = 1.381 x 10 -23 J K -1 p = 2 N 3 V E k 2 N 3 V E k = N
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3_Kinetic_Model_of_Gases_final - The Kinetic Model of Gases...

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