Calculation heat of vaporization

The Clausius-Clapeyron equation implies that if we plot the natural log of the pressure of the gas phase versus inverse temperature, the slope of the resulting line is the heat of vaporization divided by the gas constant (R). A plot of In P (vapor pressure of water) versus inverse temperature is given in Figure 3. The calculated heat of vaporization (determined by multiplying the slope by R) is 10,400 cal/mol. The important aspect of Eq. (10) with regard to moisture sorption is the fact that increasing the temperature also increases the vapor pressure. 

Check the precision of the empirical relation proposed by Watson to calculate heats of vaporization. Take water as a test example. With boiling water at 100°C as the... 

Calculation of latent heats of fusion and sublimation are more difficult and less accurate than calculating heats of vaporization. Reid et al. (1987) summarized available methods. A crude but simple approximation for standard heats of formation is (Felder and Rousseau 1986)... 

According to Eq. (12.19), if In p or log o P is plotted against 1/T, a linear curve is obtained with a slope equal to — AH/R or — AH/2303R. The intercept at 1/T = 0 yields a value of AH/RTq. Thus, from the slope and intercept, both AH and Tq can be calculated. Heats of vaporization and sublimation are often determined through the measurement of the vapor pressure of the substance as a function of temperature. Figure 12.11 shows a plot of logio p versus 1/T for water Fig. 12.12 is the same plot for solid CO2 (dry ice). 

This value for the enthalpy of vaporization obtained with Option 3 is considerably higher than the one obtained with Option 2, as the flash calculation can take the temperature rise of the liquid into account. In this case, where a wide boiling mixture is regarded, even this incremental evaporation with the 0.001 vapor fraction causes a temperature rise in the liquid by 0.06 K, which has a considerable influence on the calculated heat of vaporization. For illustration, the mass balance is listed in Table 6.1 In fact, this example is an extreme one due to the wide boiling range. Usually, Option 2 should yield a better approximation and could be used for a rough check. Nevertheless, as there is no way to avoid the flash... 

Solution The fraction of liquid vaporized on release is calculated from a heat balance. The sensible heat above saturated conditions at atmospheric pressure provides the heat of vaporization. The sensible heat of the superheat is given by... 

To calculate the heat of vaporization, the Lee and Kesler method in article 4.3.1.3 is used. 

The nitrogen adsorption isotherm is determined for a finely divided, nonporous solid. It is found that at = 0.5, P/P is 0.05 at 77 K, gnd P/F is 0.2 at 90 K. Calculate the isosteric heat of adsorption, and AS and AC for adsorption at 77 K. Write the statement of the process to which your calculated quantities correspond. Explain whether the state of the adsorbed N2 appears to be more nearly gaslike or liquidlike. The normal boiling point of N2 is 77 K, and its heat of vaporization is 1.35 kcal/mol. 

The vapor pressure for the soHd at 25°C has been calculated from the value for the Hquid at 70°C and the heats of vaporization and fusion using the Clausius-Clapeyron relationship. 

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

Significant progress in the optimization of VDW parameters was associated with the development of the OPLS force field [53]. In those efforts the approach of using Monte Carlo calculations on pure solvents to compute heats of vaporization and molecular volumes and then using that information to refine the VDW parameters was first developed and applied. Subsequently, developers of other force fields have used this same approach for optimization of biomolecular force fields [20,21]. Van der Waals parameters may also be optimized based on calculated heats of sublimation of crystals [68], as has been done for the optimization of some of the VDW parameters in the nucleic acid bases [18]. Alternative approaches to optimizing VDW parameters have been based primarily on the use of QM data. Quantum mechanical data contains detailed information on the electron distribution around a molecule, which, in principle, should be useful for the optimization of VDW... 

Concerning the VDW parameters, the ability to directly apply previously optimized values makes convergence criteria unnecessary. If VDW parameter optimization is performed based on pure solvent or crystal simulations, then the heats of vaporization or sublimation should be within 2% of experimental values, and the calculated molecular or unit cell volumes should be also. If rare gas-model compound data are used, the references cited above should be referred to for a discussion of the convergence criteria. 

The cooling water (or other medium) must absorb enough heat to balanee the heat of vaporization and eondensate subcooling. Piping and hot wells must be sized based upon the maximum condenser requirement. The following example illustrates the method of calculating the quantity of eooling water for a specific service. 

A student is asked to calculate the amount of heat involved in changing 10.0 g of liquid bromine at room temperature (22.5°C) to vapor at 59.0°C. To do this, one must use Tables 8.1 and 8.2 for information on the specific heat, boiling point, and heat of vaporization of bromine. In addition, the following step-wise process must be followed. 

This equation can be used to calculate any one of the five variables (P Pb T2, Tt, and AHvap), knowing the values of the other four. For example, we can use it to find the vapor pressure (Pt) at temperature Tlt knowing P2 at T2 and the value of the heat of vaporization (Example 9.2). 

The calculations actually refer to the gaseous state. We may, however, disregard the small correction to the liquid state inasmuch as heats of vaporization of the polymer unit and of the monomer will be approximately the same. 

Maa (M2) developed a procedure for calculating the liquid surface temperature as a function of the time each liquid element is in contact with the vapor. He assumed that the latent heat of vaporization is transferred from the interior of the liquid to the interface by pure conduction. Consequently, the sole source of energy for vaporization is the sensible heat made available by a change in the liquid temperature. If exposure time is short, only the liquid near the surface will undergo a temperature change. The heat transfer within the liquid is modeled by... 

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