Applications Of Ideal Gases

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Applications Of Ideal Gases

• Relation such as pV nRT is equation of state
  gives relation between variables in a given
  state.
• Accuracy requires taking account of deviations
  from ideality
• e.g. ideal gas model ? gases cannot be liquefied

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Real Gases Deviations From Ideality

• Breakdown of ideal gas assumptions because of
  intermolecular forces
• long-range attractive force between molecules
• weak (van der Waals dispersion)
• from induced-dipole/induced-dipole force (these
  enable gases to liquefy)
• short-range repulsive force
• from Pauli Principle (cannot push molecules on
  top of each other, they would have same quantum
  numbers)
• finite size of molecules

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To Monitor Deviation...
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Size Of Non-Ideal Effects

• Deviation from ideality depends on
• type of molecule (strength of intermolecular
  forces) He has weakest forces, more polarizable
  molecules such as CO2 have bigger ones
• temperature (high T ? molecules move so fast they
  do not see intermolecular forces)
• pressure (all gases are ideal at sufficiently low
  pressures)

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cf Textbook - Figure 5.21, page 210
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Non-ideal Gas Equations Of State

• Simplest van der Waals equation of state
• ideal p ? V nRT

• a, b are parameters measured from experiment
• a (l2 atm mol2) b (l mol1)
• He 0.34 0.024
• CO2 3.59 0.042

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Example

• Find ideal and real (van der Waals) pressure of1
  mol of CO2 occupying 1.32 l at 48.0C.

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cf Textbook - Figure 5.26, page 209
Intermolecular forces lessen the force of
impact with the wall - real pressure is lower
P Pideal - a (n/V)2
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Virial Equation Of State

• van der Waals equation has problems e.g., value
  of b for He gt b for Ne, wrong way round (Ne
  bigger than He!)

• B, C are T-dependent
• Can be calculated from knowledge of
  intermolecular forces
• first to do this an Australian, John Barker
  (1969)