Molecular disorder

The label liquid crystal seems to be a contradiction in tenns since a crystal cannot be liquid. However, tire tenn refers to a phase fonned between a crystal and a liquid, witli a degree of order intennediate between tire molecular disorder of a liquid and tire regular stmcture of a crystal. Wlrat we mean by order here needs to be defined carefully. The most important property of liquid crystal phases is tliat tire molecules have long-range orientational order. For tliis to be possible tire molecules must be anisotropic, whetlier tliis results from a rodlike or disclike shape. 

In this connection, in order to judge the level of these molecular rearrangements, the solid state X-ray structures of ferrocene and ferrocenium ion could be compared. Unfortunately, the molecular disorder caused by the rotation of the cyclopentadienyl rings in ferrocene means that the comparison procedure is far from simple and, in fact, the first results were interpreted in terms of a staggered conformation of the two cyclopentadienyl rings. It is now believed that the eclipsed conformation is the more stable (with a rotation angle of about 10°).2 However, as the rotational barrier is notably low (about 4 kJ mol-1), the conformation that one observes is probably that imposed by crystal packing forces. 

In this case, the decrease in entropy of the redox couple i.e. a decrease of the molecular disorder) is proposed to be due to the passage of the complex from the CuHIN4 square planar geometry to the usual octahedral geometry of Cu(II) complexes which requires the axial coordination of two solvent molecules (water). This reduces the disorder of the solvent molecules around the complex. 

Negative values for redox couple entropy have also been obtained for the Cu(II)/Cu(I) reduction, in aqueous medium, of the blue copper proteins stellacyanin, plastocyanin and azurin.14 The decrease in molecular disorder has been attributed in this case to the fact that the charge neutralization of the redox site (from + 1 to 0) favours the formation of hydrogen bonds between the solvent (water) and the copper centre.17... 

Simple thermodynamic considerations state that the reduction process is favoured (i.e. more positive cu(ii)/cu(p potential values are obtained) if the electron transfer is exothermic (AH° negative) and if the molecular disorder increases (AS° positive). It is therefore evident that the positive potential value for the reduction of azurin (as well as that of the most blue copper proteins) is favoured by the enthalpic factor. This means that the metal-to-ligand interactions inside the first coordination sphere (which favour the stability of the reduced form over the oxidized form) prevail over the metal complex-to-solvent interactions inside the second... 

Consider two liquid substances that are rather similar, such as benzene and toluene or water and ethylene glycol. When moles of the one are mixed with B moles of the other, the composition of the liquid mixture is given by specification of the mole fraction of one of them [e.g., Xa, according to Eq. (2.2)]. The energy or heat of the mutual interactions between the molecules of the components is similar to that of their self interactions, because of the similarity of the two liquids, and the molecules of A and B are distributed completely randomly in the mixture. In such mixtures, the entropy of mixing, which is a measure of the change in the molecular disorder of the system caused by the process of mixing the specified quantities of A and B, attains its maximal value ... 

Probably the most important reaction mechanism is the liquid-mediated process (Hi). This is because most drugs, even those not particularly susceptible to hydrolysis, become less stable as the surrounding moisture levels increase. It has been speculated that degradation proceeds via a thin film of moisture on the surface of the drug substance [23], However, studies have indicated that the moisture is concentrated in local regions of molecular disorder, rather than in thin films [24], These regions that are crystal defects or amorphous areas, equate to the reaction nuclei of mechanisms (i) and (ii). 

Correlation times and activation energy parameters obtained from different techniques may or may not agree with one another. Comparison of these data enables one to check the applicability of the model employed and examine whether any particular basic molecular process is reflected by the measurement or whether the method of analysis employed is correct. In order to characterize rotational motion in plastic crystals properly it may indeed be necessary to compare correlation times obtained by several methods. Thus, values from NMR spectroscopy and Rayleigh scattering enable us to distinguish uncorrelated and correlated rotations. Molecular disorder is not reflected in NMR measurements to this end, diffraction studies would be essential. 

Whenever a chemical reaction results in an increase in the number of molecules—or when a solid substance is converted into liquid or gaseous products, which allow more freedom of molecular movement than solids—molecular disorder, and thus entropy, increases. 

The positive sign of the 43.48 e.u. indicates that the reaction goes with an increase in entropy—that the products represent a state of greater molecular disorder than... 

The entropy of a substance can be given a precise mathematical formulation involving the degree of molecular disorder (Eq. 6-9). 

It follows from Eq. 6-9 that S = 0 when T = 0 for a perfect crystalline substance in which no molecular disorder exists. The third law of thermodynamics asserts that as the thermodynamic temperature T approaches 0 K the entropy S also approaches zero for perfect crystalline substances. From this it follows that at any temperature above 0 K, the entropy is given by Eq. 6-12. 

We consider, first, the mutual solubility of two nonpolar liquids, whose molecules have practically equal sizes, and equal attractive and repulsive forces. When they are brought into contact, thermal agitation will cause m ntnal diffusion until the two species are uniformly distributed. The mixing process has produced maximum molecular disorder, and therefore entropy, which is given by the expression, for 1 mole of solution,... 

To decide whether we need to worry about AS0 with regard to any particular reaction, we have to have some idea what physical meaning entropy has. To be very detailed about this subject is beyond the scope of this book, but you should try to understand the physical basis of entropy, because if you do, then you will be able to predict at least qualitatively whether AH° will be about the same or very different from AG°. Essentially, the entropy of a chemical system is a measure of its molecular disorder or randomness. Other things being the same, the more random the system is, the more favorable the system is. 

Different kinds of molecules have different degrees of translational, vibrational, and rotational freedom and, hence, different average degrees of molecular disorder or randomness. Now, if for a chemical reaction the degree of molecular disorder is different for the products than for the reactants, there will be a change in entropy and AS0 A 0. 

A spectacular example of the effect of molecular disorder in contributing to the difference between AH° and AG° is afforded by the formation of liquid nonane, C9H20, from solid carbon and hydrogen gas at 25° ... 

The high specific heat of water is connected with these changes. By the thermodynamic equation, AS = qn T (when S is the entropy and qn the amount of heat added reversibly at temperature, T), the high specific heat implies that, when water is heated over a given range of temperature, the increase in its entropy is greater than it would be for a normal liquid. The anomalous entropy increase is due to the unusual increase of molecular disorder. 

What do a melting ice cube and the reaction of barium hydroxide octahydrate have in common The common feature of these and all other spontaneous processes that absorb heat is an increase in the amount of molecular disorder, or randomness, of the system. The eight water molecules rigidly held in the Ba(OH)2 8 H20 crystal break loose and become free to move about in the aqueous liquid product similarly, the rigidly held H20 molecules in the ice lose their crystalline ordering and move around more freely in liquid water. 

The drawing shows ordered particles in a solid subliming to give a gas. Formation of a gas from a solid increases molecular disorder, so AS is positive. Furthermore, because we re told that the process is nonspontaneous, AG is also positive. Because the process is favored by AS (positive) yet still nonspontaneous, AH must be unfavorable (positive). This makes sense, since conversion of a solid to a liquid or gas requires energy and is always endothermic. 

Entropy, denoted by S, is a state function that measures molecular disorder, or randomness. The entropy of a system (reactants plus products) increases (AS is positive) for the following processes phase transitions that convert a solid to a liquid or a liquid to a gas reactions that increase the number of gaseous molecules dissolution of molecular solids and certain salts in water raising the temperature of a substance expansion of a gas at constant temperature. 

Both processes lead to an increase in molecular disorder, and the entropy increases. When we freeze water or condense steam, the signs of q and AS are reversed, reflecting the increase in molecular order. 

AS must be related to an increase in randomness or molecular disorder since in all the cases discussed where AH >0 the molecular state of the reaction products was more disordered than the reactants from which they were spontaneously formed ... 

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