Entropy demand

Pure Substances A substance that contains no entropy is absolutely cold. In order to bring it up to room temperature at standard pressure, a certain amount of entropy is necessary. This can be generated internally or added from outside. The amount of entropy necessary varies from substance to substance. It is proportional to the amount of substance, so we relate the entropy required by a substance to the amount needed for 1 mol of substance. This quantity, which we were introduced to in Sect. 3.9, is called molar entropy. 

The values of the entropy at a point p, T (such as at standard conditions) can be converted to other p and T values if the gradients of the surfaces in the p and T directions are known at the former point, i.e., if dS/dp)j and (dS/dp) are known. The first coefficient describes the substance s loss of entropy by increase of pressure. The second one corresponds to its entropy capacity C, which we were introduced to in Sect. 3.9. 

Experiment 8.4 Cooling during dissolving ofNaNOs in water. Solid sodium nitrate is poured all at once into the water and subsequently, one stirs vigorously with a glass rod. A strong decrease in temperature can be observed. 

Distributing a tiny amount An of a substance inside a body results in a small change of entropy AS. The entropy change relative to the small amount of substance is used for defining a measure of the entropy demand of the substance  

To be exact, one must again deal with the limit of infinitesimally small additional amounts An of the substance, keeping pressure, temperature, and the amounts of all other substances constant in the process  

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The above two examples illustrate that the value of the partition function is an indicator for how many of the energy levels are occupied at a particular temperature. At T = 0, where the system is in the ground state, the partition function has the value q = 1. In the limit of infinite temperature, entropy demands that all states are equally occupied and the partition function becomes equal to the total number of energy levels. 

Cyclizations to form larger rings require the formation of a cyclic transition state from long-chain acyclic precursors which can adopt numerous conformations. This requirement implies a significant loss of entropy due to the coiling of the extended acyclic precursor. The increased entropy demands affect the rate of the intramolecular reaction substantially, as can be seen from the comparison of rate data for the formation of homologous lactones in the reaction of 305 306 (Scheme 2.113) ... 

Radical cyclizations usually comprise the central portions of radical clock scales. Cyclizations that produce low-strain five- and six-membered rings are exothermic, but the entropy demand in the transition states for these cyclizations results in reactions that are considerably slower than ring openings. Increasing the exo-... 

The amount of entropy contained in a portion of a mixture is obtained analogously to its volume from the amounts and entropy demands of its components, for example, components A and B ... 

In a chemical reaction, the substances involved produce new ones with changed entropy demands. Here, we are interested in the amount of entropy AS which is added or removed for compensation when a reaction takes place at constant pressure and constant temperature. Let us consider the reaction of 0.1 mol of iron and 0.1 mol of sulfur forming 0.1 mol of iron sulfide, at room conditions ... 

We see that exactly A5 = 0.1 Ct is lacking. This is what is needed to cover the entropy demands of the FeS produced by a conversion of A =0.1 mol. This amount of entropy AS must be introduced from outside if the iron sulfide is to be as warm at the end of the reaction as the iron and sulfur were before the process began. Without this added entropy, it would be colder. If the conversimi is multiplied, the required entropy multiplies correspondingly. 

This conversion-related quantity is called the molar reaction entropy ArS. In our example, the caveat for small A is unnecessary because only pure substances are participating in the reaction. However, if dissolved substances appear in the conversion formula, we can then only allow small additional conversions A for any arbitrary extent of the reaction. This is to ensure that the composition of the solution and, therefore, the entropy demands of the substances in it do not change noticeably. 

However, in contrast to the case of volume, the effects caused by the differing entropy demands of substances can be masked by others because energy is released in many processes which then generates entropy. In order to better understand the consequences of this circumstance, we will now deal with energy released or used by these processes. 

We have taken over this name for lack of a better one in order to distinguish between the effects caused by differences of entropy demands and those caused by entropy generation. In Eq. (8.25), the expression on the left represents the latent molar reaction entropy and the one on the right, the generated molar reaction... 

Unfortunately, the latent entropy becomes a problem because depending upon the type of substances, the entropy demands Sm and therefore the entropy content AS of the sample change in the reactor. A positive AS becomes noticeable as a negative contribution —AS in the calorimeter (Index ) so that not ASg but AS = ASg - AS = —ASe is measured there. 

In Chap. 9, which dealt with cross relations, we learned that the volume and entropy demands of a substance in a mixture can be derived from the pressure coefficient and the temperature coefficient a of chemical potential, meaning the derivatives of with respect to p and T at constant composition ... 

Volume Demand and Entropy Demand The temperature coefficient and the pressure coefficient of chemical potential fiu of a homogeneous mixture M are obtained by taking the derivative with respect to T or p. Based on the approach for a mixture of substances A, B, C,. .. 

Why are enzymes macromolecules The reason is that the active center must be of a defined or highly ordered geometry if it is to contain all the binding and catalytic amino acid residues in a correct alignment for optimal catalysis. This imposes a heavy entropy demand upon the system which can be compensated for at the expense of another already ordered region of the biopolymer (58). 

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