The Kinetic Molecular Theory

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The Kinetic Molecular Theory

• A model to explain the behavior of ideal gases
• The particles are small compared to the distances
  between the particles
• Assume that the volume of the individual
  particles is negligible

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The Kinetic Molecular Theory

• The particles are always moving.
• Particles colliding against the walls of
• the container result in the pressure exerted
  by the gas.

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Kinetic Molecular Theory

• The particles do not exert any force on each
  other they neither attract nor repel each other.
• The average kinetic energy of the gas particles
  is directly proportional to the Kelvin
  temperature of the gas

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The Kinetic Molecular Theory

• The true test of a model
• The predictions based on the model should fit the
  experimental observations

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The Kinetic Molecular Theory

• Boyles Law
• Decrease the volume, the gas particles will hit
  the wall more often
• More collisions, more pressure
• I.e., as the volume decreases, the pressure
  increases

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The Kinetic Molecular Theory

• Gay-Lussacs Law
• Increase the temperature, and the kinetic energy
  of the gas molecules will increase, their speed
  will increase, so the molecules will hit the wall
  with greater force and greater frequency
• I.e, as the temperature increases, the pressure
  increases.

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The Kinetic Molecular Theory

• Charles Law
• Increase the temperature, and the gas molecules
  will have greater kinetic energy, and thus,
  greater speed. The particles will hit the walls
  more often. To keep the pressure constant, the
  volume would have to increase to compensate for
  the increased speed.
• I.e., At constant pressure, as temperature
  increases, the volume increases.

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The Kinetic Molecular Theory

• Avogadros Law
• Increase the number of gas particles at a given
  temperature would result in more collisions, and
  thus more pressure. To keep the pressure
  constant, the volume would have to increase.
• I.e., At some constant temperature and pressure,
  as the number of particles increase, the volume
  increases.

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The Kinetic Molecular Theory

• Daltons Law of Partial Pressures
• Since all gas particles are independent of each
  other, it doesnt matter what the identity of the
  individual particles are.
• The sum of the pressures of the individual gases
  would give the total pressure.

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The Kinetic Molecular Theory

• The Meaning of Temperature
• The Kelvin temperature indicates the average
  kinetic energy of gas particles
• Two different gases at the same temperature will
  have the same average kinetic energy
• From physics
• (KE)ave 3/2 RT
• This equation means, higher temperature, greater
  motion

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Real Gases

• No such thing as an ideal gas
• Real gases begin to behave like ideal gases under
  ideal conditions.
• at low pressures
• At high temperatures

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Real Gases

• Look at real gas behavior
• Graph of PV/nRT vs P
• For ideal gases, PV / nRT 1 at any pressure
• For real gases, PV / nRT approaches 1 at very low
  pressures (below 1 atm)

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Real Gases

• What is the effect of temperature when plotting
  PV / nRT vs. P?
• PV / nRT approaches 1 at low pressure and at high
  temperatures

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Real Gases

• Johannes van Der Waals
• Developed an equation for real gases
• Received a Nobel prize for his work

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Ideal Gases vs. Real Gases

• Volumeless
• Do not interact with each other

• Finite volumes
• Particles do take up space
• Volume of the gas is actually less than the
  volume of the container
• Particles do attract each other

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van der Waals Equation

• Correction factors for the ideal gas law
• Correct for the volume
• The actual volume of a real gas is
• V nb
• V volume of the container
• n moles of gas particles
• b constant, determined using experimental
  results

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van der Waals Equation

• Correction factors for the ideal gas law
• Correct for the attractive forces between
  particles
• Attractive forces would result in fewer, as well
  as slightly weaker collisions, resulting in less
  pressure.

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van der Waals Equation

• Pobs observed pressure
• P pressure expected from the ideal
• gas law
• Pobs P correction factor

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van der Waals Equation

• The correction factor for the attractive forces
  would also have to be experimentally determined.
• Depends on
• concentration of gas molecules (moles/liter or
  n/V)
• more gas molecules, more interactions
• Correction factor a(n/V)2
• a proportionality constant

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van der Waals Equation

• Pobs nRT a (n/V)2
• V nb
• Rearrange to get van der Waals equation
• Pobs a(n/V)2 x (V nb) nRT
• ( Pcorrected . Vcorrected nRT)

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van der Waals Equation

• A real gas becomes more like an ideal gas at low
  pressure
• Low pressure implies a large volume for the gas
  particlesthe volume of the gas becomes the
  volume of the container as the gas particles (nb
  becomes very small) get farther apart
• note that b is smaller when gas particles are
  smaller (b for He is 0.0237 L/mol while b for Xe
  is 0.0511 L/mol)

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van der Waals Equation

• A real gas becomes more like an ideal gas at high
  temperature
• High temperature means the gas particles have
  high kinetic energy and are moving past each
  other with greater speeds, giving the particles
  less of a chance to feel any attractive force.
  Pobs approaches Pideal

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Real Gases and Ideal Gases

• In summary, a real gas approaches the behavior of
  an ideal gas
• at low pressure (large container)
• at high temperature
• when the gas experiences few attractive forces
  (the more nonpolar the particle, the weaker the
  attractive forces)