Clausius Clapyron equation

Note that the temperature T in Equation 4-104 is the absolute temperature from the Clausius-Clapyron equation and is not associated with the heat capacity. 

If you plot the temperature and vapor pressure data given in Table 1, you reconstruct the liquid-vapor equilibrium line in the phase diagram of that liquid (Fig. 139). The equation of this line, and you might remember this from your freshman chemistry course, is the Clausius -Clapyron equation ... 

So if you want to know how the vapor pressure of a substance is going to vary with temperature, you can use the Clausius-Clapyron equation... 

From the normal boiling point of isobutyl alcohol (T° = 108.1°C,381.2K p°=760 torr), and one other vapor pressure measurement I found while doing research for this section (T=100°C, 373K p=570 torr), I ve gotten the heat of vaporization (AH), the heat needed to vaporize a mole of pure isobutyl alcohol itself. Using these two values in the Clausius-Clapyron equation, the AH for isobutyl alcohol is 10039.70 cal/mole. 

To show you how to use the Clausius - Clapyron equation, and to show you how well the equation fits over small temperature ranges. The calculated boiling point pressure for isobutyl alcohol (760.04 torr) is not very different from the normal boiling point pressure of 760.00 torr (0.005%). 

The P° s of Dalton - Raoult are vapor pressures taken at fixed temperatures. They are the p s in the Clausius - Clapyron equation found with a variation in temperature. Don t believe me Pick a vapor pressure and temperature pair from Table 1 for either liquid, and let these be p° and T° (and don t forget to use K, not °C). Now what happens when the unknown temperature (T) is the same as T° The (1/T — 1/T°) becomes zero, the entire exponent becomes zero, p° is multiplied by 1 (anything to the power zero is 1, eh ) and so... 

The next part is messy, but somebody s got to do it. I m going to use the vapor pressure-temperature data for the normal boiling points of both liquids in the Clausius-Clapyron equation. Why They re convenient, known vapor pressure-temperature points. When I do this, though, I exercise my right to use different superscripts to impress upon you that these points are the normal boiling points. So for liquid A, we have p and TJ if A is isobutyl alcohol,pi = 760 torr and T K = 101.8°C. For liquid B, we havep and T5 if B is isopropyl alcohol, p = 760 torr and T% = 82.3 °C. 

Using the new letters, above, and substituting the Clausius-Clapyron equation for every P° you get... 

The Clausius-Clapyron equation [Eq. (3.15)] is of incidental interest, because it states the molar relationship of water in a dispersion in equilibrium with its vapor—the definition of aw [Eqs. (2.1)—(2.5)] ... 

In Section 2.12 we introduced the accentric factor < > as a dimensionless correlating parameter in the theorem of corresponding states, and promised to explain it in this chapter. It is most easily explained in terms of Figure 5.4 and the Clausius-Clapyron equation. If the vapor-pressure data for some pure species form a straight line in Figure 5.4, then the equation of that line is... 

Exercise 7.3 The Clausius-Clapyron equation relates the latent heat of vaporization to temperature and vapor pressure according to the following equation ... 

Equation 11.14 has the Clausius-Clapyron assumptions built into it the more complex version without those assumptions is in [18, p. 640] (See Problem 11.36). 

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