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5.31: Untitled Page 93

  • Page ID
    18226
  • Chapter 5

    empirical expression for the vapor pressure is given by Antoine’s equation (Wisniak, 2001)

    B

    log ( p

    )  A

    (5‐22)

    A, vap

      T

    in which p

    is determined in mm Hg and T is specified in C. The coefficients A, vap

    A, B, and  are given in Table A3 of Appendix A for a variety of compounds.

    Note that Eq. 5‐22 is dimensionally incorrect and must be used with great care as we indicated in our discussion of units in Sec. 2.3.

    Figure 5‐3. pVT behavior of methane EXAMPLE 5.3. Vapor pressure of a single component

    In this example we wish to estimate the vapor pressure of methanol at 25 C using the Clausius‐Clapeyron equation. The heat of vaporization of methanol is

    H

     8 , 426 cal/mol at the normal boiling point of vap

    methanol, 337.8 K . The heat of vaporization is a function of temperature and pressure. The data given for the heat of vaporization is for the

    Two‐Phase Systems & Equilibrium Stages 167

    temperature T  337.8 K = 64.6 C . At this temperature, the vapor pressure of methanol is equal to atmospheric pressure. In order to estimate the vapor pressure at 25 C , we use the normal boiling temperature as the reference temperature. Normally we would compute the value of the heat of vaporization at 25 C using a thermodynamic relationship and then use an average value for

    H

    in Eq. 5‐21.

    vap

    However, in this example, we will estimate the vapor pressure at 25 C

    using the heat of vaporization at 64.6 C . All variables can be converted into SI units as follows:

    25 C + 273.16 K = 298.16 K

    (1)

    T

     337.8 K

    (2)

    o

    p

    ( T )  1 atm  101 , 300 Pa

    (3)

    M, vap

    o

    H

     (8426 cal/mol) ( 4 . 186 J/cal)  35 , 271 J/mol (4)

    vap

    Substitution of these results into Eq. 5‐21 gives

    p

    M, vap

    35 , 271 J

    1

    1

    

     101 , 300 Pa exp 

    /mol

    

    (5)

    3

     8.314 m Pa/mol K  298 2

    . K

    337 . 8 K 

     19 , 112 Pa

    Vapor pressures estimated using the Clausius‐Clapeyron equation can exhibit substantial errors with respect to experimental values of vapor pressure. This is caused by the fact that the assumptions made in the development of this equation are not always valid. The semi‐empirical equation known as Antoine’s equation has the advantage that it is based on the correlation of experimental values of the vapor pressure.

    EXAMPLE 5.4. Vapor pressure of single components using Antoine’s equation

    In this example, we determine the vapor pressure of methanol at 25 C

    using Antoine’s equation, Eq. 5‐22, and compare the result with the vapor pressure computed in Example 5.3. The numerical values of the

    168