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  1. Liquid-Vapor Equilibria
    1. When a sample of liquid is placed in a closed container, it reaches equilibrium with its vapor: liquid <--> vapor

      dynamic equilibrium - two opposing processes are occuring at the same rate, no visible change.

      The pressure exerted by the vapor at equilibrium is referred to as the vapor pressure of the liquid. Vapor pressure depends upon the identity of the liquid and the temperature:

      vp water at 25oC = 24 mm Hg
      vp water at 100oC = 760 mm Hg

      vp benzene at 25oC = 92 mm Hg
      vp benzene at 80oC = 760 mm Hg

      Suppose one has a sample of H2O(l) in equilibrium with H2O(g) at 25oC, 24 mm Hg.

      If the volume of the container is increased, more liquid vaporizes, maintaining a constant pressure. If volume is decreased, some vapor condenses.

    2. Clausius-Clapeyron Equation:

      Clausius-Clapeyron Equation

      *Important: temperatures in the equation must be in kelvin.
      R=8.314 J / mol K

      q = m deltat Cp
      q = m deltaHf
      q = m deltaHvap
      Cp = specific heat, heat capacity

      The vapor pressure of 1-propanol at 14.7 oC is 10.0 torr. The heat of vaporization is 47.2 kJ / mol. Calculate the vapor pressure of 1-propanol at 52.8 oC.

      = 100.25 torr = P2

  2. Phase Diagrams
    Graph showing temperatures and pressures at which liquid, solid and vapor phases of a substance can exist.
    phase diagram

    Note that:
    -solid sublimes (passes directly to vapor) below triple point (0oC, 5 mm Hg for water; 115oC, 90 mm Hg for I2)

    -if line AD inclines toward P axis, melting point decreases as P increases. This behavoir is observed for water, where the liquid is the more dense phase.

    -more often, the solid is the more dense, AD tilts away from the P axis, and the melting point increases with pressure.

    Phase Changes
    The temperature of a substance remains constant during a phase change.

    How much energy does it take to convert 130 g of ice at -40oC to steam at 160oC?

    qtotal = ql + q2 + q3+....

    Cp ice = 2.1 J / g C Cp steam = 1.8 J / g C
    Hf of water = 6.0 kJ / mol Hvap = 43.9 kJ / mol

    Boiling Point - temperature at which vapor bubbles form in liquid.

    boiling liquid


    Hence, boiling point varies with applied pressure, P2.

    -When P2 = 760 mm Hg, bp H2O = 100oC (760 mm Hg, normal boiling point)
    -If P2 = 1075 mm Hg, bp H2O = 116oC
    -If P2 = 5 mm Hg, bp H2O = 0oC

    Critical Temperature - temperature above which liquid cannot exits. Critical pressure is the vapor pressure of the liquid at the critical temperature. In the above diagram, if you drew a line down from B, that would mark the critical temperature.

    O2: Critical T = -119oC. Liquid O2 cannot exist at room temperature, regardless of pressure.
    C3H8: Critical T = 97oC. Propane stored as a liquid under pressure at room temperature.

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