Differential heat of mixing

For equilibrium calculations we almost always use the partial molar Gibbs energy or chemical potential. But the partial volumes and enthalpies appear most often in the form of partial mass properties, and are used for calculations other than equilibrium. Wherever a dnt appears in this chapter (or elsewhere in this book) it could be replaced by 

Example 6.8 One Ibm of water at 200°F is added to a large mass of H2S04-water solution at 200°F and 60 wt% H2SO4. How much heat must be added or subtracted to keep the temperature constant at 200°F  

The quantity computed here is called the differential heat of mixing because it refers to adding a differential amount of pure material into a large amount of solution. If the amount 

FIGURE 6.8 Enthalpy-concentration diagram for sulfuric acid-water. The datum state is zero enthalpy for pure water and for pure sulfuric acid as liquids at 32°F = 0°C, and the pure species vapor pressure. The percentage is weight percent. (The data are from the International Critical Tables, as plotted in Hougen, O. A., K. M. Watson, and R. A Ragatz, Chemical Process Principles Charts. 1960, New York Wiley. Reprinted by permission of the estate of O. A. Hougen.) 

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Thus hf is equal to the heat absorbed (per mole of 1) when a small quantity 8ui of substance 1 is dissolved in the solution at constant T and p. For this reason it is often called the heat of solution of component 1, differential heat of mixing or partial molar heat of mixing." The partial molar heats may be determined readily from the heat of mixing h by the Bakhuis-Rooseboom method described in 3 of chap. I. 

The integral heat of mixing is, of course, the quantity directly measured in the calorimetric method However, the heat change on diluting a solution of the polymer with an additional amount of solvent may sometimes be measured in preference to the mixing of pure polymer with solvent In either case, the desired partial molar quantity AHi must be derived by a process of differentiation, either graphical or analytical. 

Materials that in themselves are normally stable, even under fire conditions Materials that exhibit an exotherm at temperatures greater than 500°C when tested by differential scanning calorimetry (DSC) Materials that do not react with water heat of mixing less than 30 cal/g Less than 0.01 W/mL... 

Differentiating the enthalpy equation with respect of N, will give the partial molar heat of mixing of component i, which in turn is related to the enthalpy interaction parameter,... 

Figure 9.11 Differential heats of ammonia adsorption versus coverage for various mixed oxides.

Figure 9.14 Differential heats of sulfur dioxide adsorption versus coverage on NiCuMgAI mixed oxides.

Figure 3 shows the differential heats of ammonia adsorption versus adsorbate coverage on sulfated binary mixed oxides. Both SZAl-2 and SZSi catalysts show similar... 

Figure 3. Differential heats of ammonia adsorption as a function of coverage on sulfated mixed oxides.

In ideal solutions, the pure solute and solvent mix with no heat of mixing, AH"" = 0, and the heat of dissolution is numerically equal to the heat of fusion. However, only a limited number of systems form ideal solutions. A less restrictive assumption is that the solution is represented by a regular solution model. This model assumes the heat of mixing is nonzero, but independent of solution composition and temperature (i.e., AH= constant) (Hildebrand and Scott 1950). For a regular solution the differential entropy of mixing is also assumed ideal (i.e., AS = —R In x). 

Strength of interaction between the carbonyl and the chlorine. Heats of mixing of two polymers, of course, provide a sum of all such energies of interaction. Differential scanning calorimetry measures the changes in heat capacity between the individual components and the blend. 

Kraflft point data were supplemented with calorimetric studies here also, but a Calvet calorimeter was used instead of a differential scanning calorimeter [16], The Calvet calorimeter yields data on heats of mixing when... 

Here, is the excess enthalpy (heat of mixing) and V is the excess volume (volume change of mixing). Both and V are subject to direct experimental determination. Taking the total differential of Eq. (7), and comparing the result with Eq. (8), we obtain the Gibbs-Duhem equation ... 

The partial or differential heat of solution, AH2, is the change in enthalpy when a very small amount of pure solute is added to a large amount of either solution or pure solvent. In the latter instance, the resultant quantity which is properly identified as the partial heat of solution at infinite dilution is sometimes referred to more simply as the heat of solution. For polymer solutions, AH 2 is often expressed as the heat absorbed per unit mass of solute added and can be found as the derivative of the integral heat of mixing ... 

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