Liquids positional entropy

Negative A liquid (moderate entropy) combines with a solid to form another solid. Positive One mole of high entropy gas forms where no gas was present before. Positive One mole of high entropy gas forms where no gas was present before. Uncertain Same number of moles of gaseous products as of gaseous reactants. Negative Two moles of gas (and a solid) combine to form just one mole of gas. 

Equation (11.4) provides a convenient value for that constant. Planck s statement asserts that 5qk is zero only for pure solids and pure liquids, whereas Nernst assumed that his theorem was applicable to all condensed phases, including solutions. According to Planck, solutions at 0 K have a positive entropy equal to the entropy of mixing. (The entropy of mixing is discussed in Chapters 10 and 14). 

Lewis and Gibson [3] also emphasized the positive entropy of solutions at 0 K and pointed out that supercooled liquids, such as glasses, even when composed of a single element (such as sulfur), probably retain a positive entropy as the temperamre approaches absolute zero. For these reasons Lewis and Randall [4] proposed the following statement of the third law of thermodynamics ... 

This positive entropy change means that there is greater disorder in the product (HjO gas) than the reactant (HjO liquid). In terms of just entropy, the increase in entropy drives the reaction to the right, toward a condition of higher entropy. 

As you might expect, there is a large positive entropy change, corresponding to a large increase in randomness, on converting water from a liquid to a gas. 

The mixing of two gaseous substances, or of two non-polar liquids, are further examples of entropy-driven processes. These involve negligible enthalpy changes (no strong chemical bonds are formed or broken) but the increased randomness and disorder in the system lead to a positive entropy change. 

The positional entropy has been calculated (Hirschfelder et al., 1937 Lennard-Jones and Devonshire, 1939) to be approximately 8-12 J / K mol for most organic molecules. This number results from a mathematical expression of the probability of finding the centers of a particular number of liquid molecules arranged as they are in the solid. 

The vaporization process will be spontaneous at all temperatures at which AG° is negative. Note that AS° favors the vaporization process because of the increase in positional entropy, and AFP favors the opposite process, which is exothermic. These opposite tendencies will exactly balance at the boiling point of liquid Br2, since at this temperature liquid and gaseous Br2 are in equilibrium (AG° = 0). We can find this temperature by setting AG° = 0 in the equation... 

Liquids have more entropy than their corresponding crystalline forms. (Every atom or molecule in a crystal is in a prescribed position in the lattice in a liquid, positions of the particles may take on many different values consistent with the overall liquid nature.)... 

Positional probability is also illustrated by changes of state. In general, positional entropy increases in going from solid to liquid to gas. A mole of a substance has a much smaller volume in the solid state than it does in the gaseous state. In the solid state, the molecules are close together, with relatively few positions available to them in the gaseous... 

Positional entropy is also very important in the formation of solutions. In Chapter 11 we saw that solution formation is favored by the natural tendency for substances to mix. We can now be more precise. The entropy change associated with the mixing of two pure substances is expected to be positive. An increase in entropy is expected because there are many more microstates for the mixed condition than for the separated condition. This effect is due principally to the increased volume available to a given "particle" after mixing occurs. For example, when two liquids are mixed to form a solution, the molecules of each liquid have more available volume and thus more available positions. Therefore, the increase in positional entropy associated with mixing favors the formation of solutions. 

Some liquids may become glasslike rather than crystalline solids as the temperature is lowered. In this case, the molecules exhibit considerable randomness of arrangement and can be frozen in on further cooling so as to yield a positive entropy at 0°K. Both glycerol and ethanol can be cooled to yield positive entropies in this way. 

For the associated liquids Xq 2h/kT that points on essentially more value of positive entropy of activation AS. These values AS // , calculated accordingly to Eq. (66), represented in Table 1. For the homologous series of the w-alcohols is accurate observed the symbate dependence of AS on E. For the -alkanes such relationship isn t observed, since the values of AS for them are little and remain via the ranges of the inaccuracy of their determination based on experimental values x. ... 

Virtually since the beginning, however, a popular viewpoint has been to see entropy as a measure of disorder. Helmholtz used the word Unordnung (disorder) in 1882. This results from familiar relationships such as S > liquids > S soiids, and the universally positive entropy of mixing. We used this relationship in the previous section when we spoke of degree of mixed-upness. However the disorder analogy can involve a serious fallacy, as made clear by Lambert (1999 see also http //www.entropysite.com). 

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