Molar latent heat of vaporization

Clausius-Clapeyron Equation. This equation was originally derived to describe the vaporization process of a pure liquid, but it can be also applied to other two-phase transitions of a pure substance. The Clausius-Clapeyron equation relates the variation of vapor pressure (P ) with absolute temperature (T) to the molar latent heat of vaporization, i.e., the thermal energy required to vajxirize one mole of the pure liquid ... 

However, to fully understand the design of the column, the material balance must be followed through the column. To simplify the analysis, it can be assumed that the molar vapor and liquid flowrates are constant in each column section, which is termed constant molar overflow. This is strictly only true if the component molar latent heats of vaporization are the same, there is no heat of mixing... 

Where T is the cell temperature, and AHV the molar latent heat of vaporization of the solvent. 

On the other hand, for nonequimolar distillation the p- may be set equal to the molar latent heats of vaporization... 

We can see from the results that the high flux correction is significant here. Also important is the effect of the unequal molar latent heats of vaporization resulting in a net mixture flux of... 

The second requirement (Eq. 11.5.25) is that the molar latent heats of vaporization of the constituent species be identical. Now, molar latent heats of many compounds are close to one another, but the differences are not zero. Let us examine the effect of such small differences in the latent heats on the interfacial rates of transfer. Example 11.5.1 demonstrates the importance of taking into account nonequimolar effects in distillation. 

The molar latent heats of vaporization may be taken to be equal. 

An alternative graphical methud for handling binaiy mixtures is thei of Ponchon3 and Savarii.3 and while more cumbersome to use than McCabe-Thiele, it allows for variations in the molar latent heat of vaporization and thus removes the principal assumption of the McCabe-Thiele method. As basic information it requires not only a y -Jc equilibrium relationship but also data on enthalpy of vaporizaiion as a function of composition, and, except for a few mixtures, such data are not trendily available. 

This is a situation frequently encountered in binary distillation operations when the molar latent heat of vaporization is similar for both components. In this case, NB = - Na = const., = N = 0. For an ideal gas mixture, equation (1-70) simplifies to... 

A packed-bed distillation column is used to adiabatically separate a mixture of methanol and water at a total pressure of 1 atm. Methanol—the more volatile of the two components—diffuses from the liquid phase toward the vapor phase, while water diffuses in the opposite direction. Assuming that the molar latent heat of vaporization is similar for the two components, this process is usually modeled as one of equimolar counterdiffusion. At a point in the column, the mass-transfer coefficient is estimated as 1.62 x 10-5 kmol/m2-s-kPa. The gas-phase methanol mole fraction at the interface is 0.707, while at the bulk of the gas it is 0.656. Estimate the methanol flux at that point. 

An alternative approximate solution to this problem can be obtained through the use of k -type coefficients. As mentioned in Example 2.3, the McCabe-Thiele method of analysis of distillation columns assumes equimolar counterdiffusion, which would justify the use of k-type coefficients regardless of the concentration levels. This would be exactly so only if the molar latent heats of vaporization of both components were equal. Although in this case there is a significant difference between the two heats of vaporization, we will show that the approximate solution is fairly close to the rigorous solution obtained above. It is easily shown that in this case, assuming steady-state equimolar counterdiffusion,... 

The two components have equal and constant molar latent heats of vaporization. 

Molar latent heat of vaporization at normal pressure... 

Vw and Vl are the specific molar volumes of saturated vapor and saturated liquid, respectively AHy is the molar latent heat of vaporization... 

Dunkel proposed to use a molar latent heat of vaporization as an additive value, describing intermolecular interactions. He represented it as a sum of the eontributions of latent heat of vaporization of individual atoms or groups of atoms at room temperature. 

The ratio of enthalpy differences, which appears in this equation and which we have denoted q, represents the molar heat of vaporization of the feed divided by the molar latent heat of vaporization of the binary system, assumed to be constant. Suppose, for example, that the feed consists of either saturated vapor or saturate liquid. Then the value of q will be 0 or 1, respectively, and for a partially vaporized feed it will lie somewhere between these two limits. The quantity q is therefore a dimensionless measure of the thermal quality of the feed. It turns out that q also enters into the construction of the locus of the points of intersection of the two operating lines of the enriching and stripping sections. That locus is represented by the expression... 

The above is often approximated in different ways. For example, when dealing with liquid-gas equilibria one frequently introduces the approximations Vi critical point, but at temperatures sufficiently high for the perfect gas approximation to hold. On defining L = Hg — Hi as the molar latent heat of vaporization of the liquid Eq. (2.3.3) assumes the approximate form... 

Enthdpy of feed as vapor at dew point - Actual feed enthalpy) Molar latent heat of vaporization of feed... 

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