Phase Diagrams

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Phase Diagrams

• Continued

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• Get last two slides

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The Clapeyron Equation

• A one-component system with phases a and b in
  equilibrium
• This condition implies several things
• PaPb
• mamb
• TaTb
• Coexistence curves
• change T or P
• one phase disappears
• change T and P simultaneously
• keeping mamb, then the two phases
• will exist in equilibrium

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The Clapeyron Equation

• So, if we change T and P simultaneously keeping
  mamb, then
• dP/dT is a total derivative.
• Only one constraint, DG0 (the two phases must
  remain in equilibrium.

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Enthalpy Relationships

• At the triple point,
• This is because it takes the same amount of heat
  to vaporize a solid irrespective of which way it
  occurs.

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Problem 1

• What is the change in the boiling point of water
  at 100 oC per change in atmospheric pressure (in
  Pa)?
• Given
• DHvap40.69kJ/mol
• Vsteam30.199x10-3m3/mol
• Vwater0.019x10-3m3/mol

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Problem 1
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The ClauiusClapeyron Equation

• If a vapor obeys the ideal gas law, then the
  Clapeyron equation for sublimation/vaporization
  process may be simplified
• molar vol. of liquid negligible relative to molar
  vol. of gas.
• Therefore

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The ClauiusClapeyron Equation

• Rearrangement of the equation gives
• Integrating gives

A plot of ln(P/Po) vs 1/T is linear
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The ClauiusClapeyron Equation