# 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*. *p*‐ *V*‐ *T* 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