Entropy aqueous systems

Now, let s look at a polymeric system. To begin with, the motion in polymer chains is hindered. The massive size of the polymer itself and the intermolecular forces within the chains create an inflexible system, especially when compared to the aqueous systems with which we are most familiar. Secondly, the entropy of mixing is not actually as great as that seen in typical solution formation. Polymers are inherently highly entropic, so the benefit of mixing them together is modest. Therefore, any two polymers that form a miscible blend depend primarily... 

Criss, C.M. Cobble, J.W., "Thermodynamic Properties of High Temperature Aqueous Systems. IV Entropies of the Ions up to 200°C and the Correspondence Principles", JACS, 1964, 86,... 

In aqueous systems, the enthalpy change due to micellization is usually positive, and micelliza-tion is driven by entropy change. Explain the reason for the positive entropy change. 

Let us denote the entropy of the maximum-degassed aqueous system by 5. Then, insofar as the residual entropy 85 is greater than 0, in the first, linear approximation we have 85 5 — 5. In the case of an isochoric process the work VAp can be represented as... 

In the linear approximation A5 = A5 in the same approximation at V const the change of internal energy can be estimated as AU = CyAT. Substituting expressions (502) and (507) with regard to explicit forms of 85 and AU into Eq. (506), we derive the expression for the entropy of the maximum-degassed associated aqueous system... 

From here on we shall call the maximum-associated aqueous system maximum-structured, whereas the bound energy 6SAT can be spoken of as of structurization potential Ay.. The calculation of the value Ay from formula (506) shows that Aa RAT, where R is the gas constant. The calculation of the entropy from formula (508) yields the estimate 5 5 — R (the 5 versus T plot is presented in Fig. 32). 

Let us put S = S I 5.S and substitute this expression into Eq. (514). Then combining Eqs. (514) and (513), and taking Eq. (507) into account, we obtain the expression for estimating the entropy of a maximum-degassed disordered aqueous system ... 

Car-Parrinello methods contrasted wilhslalic (0 Ktemperature) computational quantum mechanical methods They can treat entropy accurately without the need to use models such as the harmonic approximation for degrees of freedom of atomic motions. They can be used to sample potential energy surfaces on picosecond time scales, which is essential for treating liquids and aqueous systems. Tliey can be used to sample reaction pathways or other chemical processes with a minimum of a priori assumptions. In addition, they can be used to find global minima [in conjunction with methods of optimization such as simulated annealing (Kirkpatrick et at, 1983)] and to step out of local minima. 

The data available (mainly for aqueous systems) indicate that the negative values of AG nic are due mainly to the large positive values of AS C. A// nic is often positive and, even when negative, is much smaller than the value of 7 A.S nic. Therefore, the micellization process is governed primarily by the entropy gain associated with it, and the driving force for the process is the tendency of the lyophobic group of the surfactant to transfer from the solvent environment to the interior of the micelle. 

In contrast to aqueous systems, micelle formation in non-polar media is driven by the benefit in energy rather than by an increase in entropy. The replacement of polar group - hydrocarbon interaction (as in the case of dissolution) with the interaction between polar groups upon their association into micellar core is thermodynamically beneficial. The benefit in energy upon association of polar groups is so large, that even at low concentrations true surfactant solutions contain small pre-micellar associates rather than individual surfactant molecules. 

It might be expected that just below the UCFT, the enthalpies associated with the contact and free volume dissimilarities should impart enthalpic stabilization. Conversely, just above the LCFT (if accessible), the combinatorial entropy of mixing should give rise to entropic stabilization. Flocculation on cooling appears to result from the free volume contribution. This may explain why such flocculation is not always readily achieved in aqueous systems of this type. 

An analogous situation could also arise in the case of membrane separation of a concentrated mixture of CaCl2 and HCl, if the selectivity of the membrane would permit to clearly reject the Ca ions while easily transporting water, CP ions, and protons. Note that such spontaneous separation of two components must proceed with a decrease in entropy of the aqueous system. 

Millcro has also used the correspondence principle method to evaluate ionic volumes in NMP as well as in methanol. Similar to the case for entropies, ionic volumes in the non-aqueous system are plotted against the absolute 5n(aq) values, and the Vi (X) for the non-aqueous system assigned so that values for both cations and anions fall on the same line. The volumes can be expressed, similar to eqn. 2.11.36, as... 

Estimations based on eqn. 2.11.36 or 2.12.10 assume that the constants a and b are known. When this is not the case, approximate estimates of a and b can probably be made, assuming that one can estimate the amount of structure in a solvent relative to those for which entropy data are already available. By interpolating between solvents one can then estimate the constant a from those listed in Table 2.11.13. With the exception of DMSO and DMF, the b constants in Table 2.11.13 for the non-aqueous systems are not too widely different, so it seems reasonable that an average of these values may give a fair estimate of b for other organic solvents. Fortunately, in eqn. 2.12.10 is not extremely... 

It has been pointed out by Adamson (34) and others (35,36) that the entropy-related chelate effect, as manifested in the stability constants, disappears when unit mole fraction replaces unit molality as the standard state of solutes in aqueous systems. On this basis the stability constants assumed for the model compounds in Table II (20) would have to be equivalent in magnitude regardless of the number of chelate rings formed. On the other hand the relative degrees of dissociation of the model compounds in Table II remain an experimental fact, with the larger concentration unit giving smaller numerical concentrations for the solutions illustrated, thus compensating for the disappearance of the chelate effect in the numerical values of the stability constants. 

Keywords Aqueous systems bibliography biochemical systems enthalpy data entropy data equilibrium data excess properties Gibbs energy data heat capacHy data partial molar properties review articles thermochemistry thermodynamics. 

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