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# 10 - Chemistry 2000 Lecture 10 The kinetic molecular theory...

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Chemistry 2000 Lecture 10: The kinetic molecular theory of matter Marc R. Roussel

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The kinetic molecular theory of gases I Matter is in constant movement and, as we have seen, subject to a variety of intramolecular (bonding) and intermolecular forces. I Can we use basic ideas from physics to connect the microscopic picture developed previously to our everyday macroscopic world? I Yes, if we take a statistical approach. I This is made possible because of the very large size of Avogadro’s number and with the help of the law of large numbers . I In this context, the law of large numbers says that the behavior of a system containing many molecules is unlikely to deviate significantly from the statistical average of the properties of the individual molecules.
Assumptions of the kinetic molecular theory for ideal gases I The particles (molecules or atoms) of the gas are small compared to the average distance between them. Corollary: The particles occupy a negligible fraction of the volume. I These particles are in constant motion. I There are no intermolecular forces acting between them, except during collisions. I a good approximation for real gases provided the gas is at a sufficiently low pressure so that the distance between the molecules is very large. I At constant temperature, the energy of the gas is constant.

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Pressure of an ideal gas Basic bits of physics we need: Pressure: p = F / A Newton’s second law: F = ma = m Δ v Δ t Newton’s third law: For every action there is an equal and opposite reaction. I The pressure on the wall of a container will be the force exerted on it due to collisions of molecules with the wall divided by the area of the wall. I This force will be the negative of the sum of the average forces experienced by all the molecules.
I For simplicity, imagine a rectangular container containing an ideal gas. I Consider a single particle impacting the wall: x y z -v x v x I We choose the coordinate system so that the x axis is perpendicular to the wall. I The y and z components of the velocity won’t affect the pressure on this wall. I If the total energy is conserved, then on average , the x component of the velocity after collision is just the negative of this component before collision.

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I Δ v x = v x , after - v x , before = - v x - v x = - 2 v x I How often do collisions with this wall occur?
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10 - Chemistry 2000 Lecture 10 The kinetic molecular theory...

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