Clausius-CIapeyron equation

Perry s Chemical Engineers Handbook, p. 2-61. lists the vapor pressure of ben2ene at 42.2 C as 200 mm Hg, so that the use of the Clausius-CIapeyron equation results in an estimation error of approximately 3.5%. 

Estimate the heat of vaporization from the Clausius-Ciapeyron equation or the Othmer piot. 

EXAMPLE 4.15 Heat of Vaporization from the Clausius-CIapeyron Equation... 

These equations, which relate the temperature dependence of the vapour pressure of a liquid to Atfvap, its enthalpy change per mole on vaporization, are called the Clausius-CIapeyron equations. Unlike the Clapeyron equation, they are not exact, as a number of approximations were introduced in their derivation, but they are nevertheless extremely valuable. 

In order to make possible a more systematic treatment of the subject and a fuller and better-adjusted consideration of recent advances, it has been found advisable to make somewhat extensive alterations in the now twenty-three-year-old general framework of the book. These changes affect, more especially, those chapters which deal with equilibria in one and two component systems. These chapters have not only been revised, but have been re-cast, re-arranged, and, to a considerable extent, rewritten. In these sections, the nature of the equilibria in intensively dried systems and the Smits theory of allotropy have also been discussed, although the limitations of space have necessitated brevity. Greater emphasis, also, has been laid on the applications of the Clausius-CIapeyron equation to the calculation of changes of equilibria with pressure and temperature. 

Product C has a fairly low vapor pressure, so we are concerned about the formation of a liquid phase in the reactor. The Clausius-CIapeyron equation well represents the vapor pressure of component C as a function of temperature... 

P4.2 Use the definite integral form of the Clausius-CIapeyron equation [Solution to Exercise 4.8(b)]. pi AvapT/ /I 1 ... 

When Pi and Pi are known, the Clausius-CIapeyron equation (Equation 9.4) has the form... 

Using dp/p = dln(p) and dT/T = —d(l/T), the connection between the equilibrium pressure of the gas phase p and the equilibrium temperature T can be expressed by the so-called Clausius-CIapeyron equation... 

The Clausius-CIapeyron equation (5.24) applies to phase equilibrium in singlecomponent systems where one phase is an ideal gas thus, the expression can describe phase equilibrium at evaporation and sublimation. Phase equilibrium between condensed phases is described by the Clapeyron equations (5.19) and (5.21), respectively. 

The Clausius-CIapeyron equation on the form (5.24) denotes the slope of an equilibrium curve depicted in a pT diagram. If, for example, we consider the phase equilibrium between water H20(/) and water vapour H20(g), then eqn. (5.24) denotes the tangential slope of the vapour pressure curve for water at any point given by the temperature T. 

The Clausius-CIapeyron equation shows the following characteristic property at the vapour pressure of the substances. Depicting the logarithm of the equilibrium vapour pressure (p) as ordinate and (1/T) as abscissa results in curves with the slope —AH/R. The curves will be almost rectilinear since AH is only slightly dependent on temperature. Such form of depicting is, for example, useful for experimental determination of AH for phase transformations in systems of matter. 

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