Constants composition

According to Equation 5.6, the interfacial tension can be assessed as the isothermal isobaric work required to reversibly expand the interface under constant composition of the system. Reversibility is easily satisfied with fluid interfaces. However, it is, with a few exceptions, impossible to extend a solid (S/L or S/G) interface reversibly. Furthermore, (crystalline) solids are usually not isotropic and the formation of new interfacial area by cleavage occurs along preferred (racks. 

Various procedures have been proposed to indirectly assess the interfacial tension of solids. None of them is unambiguous and we refrain here from discussing them. 

In most applications, it is the replacement of S/G by S/L, or vice versa, that is relevant, rather than the formation of new S or S/G. Hence, the quantities - y ) and (Ysl - Tsg) are of interest. These are operational quantities because exposure of a solid to a gas or liquid and replacement of a gas by a liquid at a solid easily reach equilibrium within the time scale of the measurement. This matter is discussed in more detail in Chapter 8. 

The requirement of constant composition poses a problem for solutions and other mixtures. When the interfacial area is extended, adsorption will occur at the newly formed interface. To relate the interfacial tension to the excess interfacial Gibbs (or, for that matter, Helmholtz) energy, adsorbed amounts and concomitant changes in the composition of the bulk phases have to be established, as has been discussed in Section 3.9 (Equation 3.77). Further elaboration on the relation between interfacial tension, adsorbed amounts, and composition of the bulk phase can be found in Chapters 7,11, and 14. 

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The system combines having three components and having constant composition, since the copolymer has the same composition as the homopolymer... 

When equations 54 and 58 through 60 are appHed to the special case of one mole of a homogeneous fluid of constant composition, n = 1, dn = 0, and these equations reduce to the following ... 

Because V = V T,P) foi a constant composition fluid, T and JPcan be considered independent variables, therefore... 

The batch-suspension process does not compensate for composition drift, whereas constant-composition processes have been designed for emulsion or suspension reactions. It is more difficult to design controUed-composition processes by suspension methods. In one approach (155), the less reactive component is removed continuously from the reaction to keep the unreacted monomer composition constant. This method has been used effectively in VT)C-VC copolymerization, where the slower reacting component is a volatile and can be released during the reaction to maintain constant pressure. In many other cases, no practical way is known for removing the slower reacting component. 

Minimum Reilux with Pinch Zone. There are some distillations where the minimum reflux does not occur at the intersection of the upper and lower operating lines and the q line. These cases arise when the equiUbrium is skewed from positive activity coefficients and when the operating line intersects the equiUbrium line in a 2one of constant composition, a pinch 2one, which is not at the line intersection. Figure 14 illustrates such a case. An example of such a pinch 2one in an ethanol—water column is available (37). 

Enthalpy and Entropy as Eunctions of T and P At constant composition the molar thermodynamic properties are functions of temperature and pressure (Postulate 5). Tmns... 

Equations (4-34) and (4-35) are general expressions for the enthalpy and entropy of homogeneous fluids at constant composition as functions of T and P. The coefficients of dT and dP are expressed in terms of measurable quantities. 

The general equations for constant-composition fluids derived in the preceding subsections reduce to very simple forms when the relations for an ideal gas are substituted into them ... 

Comparison with Eq. (4-20) provides an example of the parallelism that exists between the eqnaOons for a constant-composition sohiOon and those for the corresponding partial properties. This parallelism exists whenever the sohidon properties in the parent equation are related hnearly (in the algebraic sense). Thus, in view of Eqs. (4-17), (4-18), and (4-19) ... 

Note that these equations hold only for species in a constant-composition sohiOon. 

If written for 1 mole of a constant-composition solution, they become ... 

The relative volatiHties Ot) are defined by Eq. (13-33), is the mini-mum-reflux ratio (L v + i/D)min,. nd q describes the thermal condition of the feed (e.g., 1.0 for a bubble-point feed and 0.0 for a saturated-vapor feed). The Xi p values are available from the given feed composition. The 0 is the common root for the top-section equations and the bottom-section equations developed by Underwood for a column at minimum reflux with separate zones of constant composition in each section. The common root value must fall between 06/, and Ot/, where hk and Ik stand for heavy key and light key respectively. The key components are the ones that the designer wants to separate. In the butane-pentane splitter problem used in Example 1, the light key is /1-C4 and the heavy key is i-C. ... 

As an example, consider distilhug at constant composition the same mixture that was used to illustrate constant reflux. The following table is compiled ... 

Fixed-Bed Behavior The number of transitions occurring in a fixed bed of initially uniform composition before it becomes saturated by a constant composition feed stream is generally equal to the variance of the system. This introductory discussion will be limited to single transition systems. 

The kinetics of spinodal decomposition is complicated by the fact that the new phases which are formed must have different molar volumes from one another, and so tire interfacial energy plays a role in the rate of decomposition. Anotlrer important consideration is that the transformation must involve the appearance of concenuation gradients in the alloy, and drerefore the analysis above is incorrect if it is assumed that phase separation occurs to yield equilibrium phases of constant composition. An example of a binary alloy which shows this feature is the gold-nickel system, which begins to decompose below 810°C. 

Instant tea.s offer the consumer the convenience of rapid preparation it is sufficient to dissolve the product in hot water - to allow it to draw and to strain it is unnecessary - coupled with a uniform and constant composition. 

Tai, C.Y. and Chen, F.-B., 1998. Polymorphism of CaC03 precipitated in a constant-composition environment. American Institution of Chemical Engineers Journal, 44, 1790-1798. 

In the first version with a mobile phase of constant composition and with single developments of the bilayer in both dimensions, a 2-D TLC separation might be achieved which is the opposite of classical 2-D TLC on the same monolayer stationary phase with two mobile phases of different composition. Unfortunately, the use of RP-18 and silica as the bilayer is rather complicated, because the solvent used in the first development modifies the stationary phase, and unless it can be easily and quantitatively removed during the intermediate drying step or, alternatively, the modification can be performed reproducibly, this can result in inadequate reproducibility of the separation system from sample to sample. It is therefore suggested instead that two single plates be used. After the reversed-phase (RP) separation and drying of the plate, the second, normal-phase, plate can be coupled to the first (see Section 8.10 below). 

In the presence of a buffer with constant composition across the electrophoretic chamber, the angle of deflection (0) of the solute in the electric field is dependent upon the intrinsic electrophoretic mobility of the solute (p. ), the linear velocity of the buffer (v) and the current through the chamber (I) and can be described as [17] ... 

Thus, Ahj and Asj can be obtained by determining the pressure required to achieve a specified solubility at several different temperatures and constant composition, Xj. In the Henry s law region, Ahj and Asj can be found directly from the temperature... 

In batch operations, mixing takes place until a desired composition or concentration of chemical products or solids/crystals is achieved. For continuous operation, the feed, intermediate, and exit streams will not necessarily be of the same composition, but the objective is for the end/exit stream to be of constant composition as a result of the blending, mixing, chemical reaction, solids suspension, gas dispension, or other operations of the process. Perfect mixing is rarely totally achieved, but represents the instantaneous conversion of the feed to the final bulk and exit composition (see Figure 5-26). 

At minimum reflux, the regions in which the number of trays approaches infinity (called the pinch zones and region of constant compositions) are ... 

The membrane consists of a binary compound AVaBVb of constant composition. Ion activities in the solid state are 1. At the membrane surface the activities of A and B in the aqueous phase are given by the solubility product ... 

The law of constant composition This tells us that a compound always contains the same elements in the same proportions by mass. If the atom ratio of the elements in a compound is fixed (postulate 3), their proportions by mass must also be fixed. 

Two basic laws of chemistry are the law of conservation of mass and the law of constant composition. Which of these laws (if any) do the following statements illustrate ... 

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