Entropy changes

How can we use the fact that any spontaneous process is irreversible to make predictions about the spontaneity of an unfamiliar process Understanding spontaneity requires us to examine the thermodynamic quantity called entropy, which was first mentioned in Section 13.1. In general, entropy is associated either with the extent of randomness in a system or with the extent to which energy is distributed among the various motions of the molecules of the system. In this section we consider how we can relate entropy changes to heat transfer and temperature. Our analysis will bring us to a profound statement about spontaneity that we call the second law of thermodynamics. 

The entropy, S, of a system is a state function just like internal energy, E, and enthalpy, H. As with these other quantities, the value of S is a characteristic of the state of a system. 

For the special case of an isothermal process, AS is equal to the heat that would be transferred if the process were reversible, divided by the absolute temperature at which the process occurs  

Although there are many possible paths that can take the system from one state to another, only one path is associated with a reversible process. Thus, the value of is uniquely defined for any two states of the system. Because S is a state function, we can use Equation 19.2 to calculate AS for any isothermal process between states, not just the reversible one. 

How do we reconcile the fact that S is a state function but AS depends on q, which is not a state function  

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Any change taking place which results in an increase in entropy has a positive entropy change (AS). Most spontaneous thermodynamic processes are accompanied by an increase in entropy. Entropy has units of Joules per degree K per mole. For representative values see table on p. 393. 

If tlie entropy change in step (2) could be at times greater than zero and at other times less than zero, every neighbouring state y<, yC,. ywoiild be accessible, for there is no restriction on the adjustment of volumes in... 

By the standard methods of statistical thermodynamics it is possible to derive for certain entropy changes general formulas that cannot be derived from the zeroth, first, and second laws of classical thermodynamics. In particular one can obtain formulae for entropy changes in highly di.sperse systems, for those in very cold systems, and for those associated, with the mixing ofvery similar substances. 

The most fiindamental of cluster properties are the bond strengths and entropy changes for the process [125]... 

The entropy change AS for a temperature change from to T2 can be obtained from the following integration... 

B2.4.2). The slope of the line gives AH, and the intercept at 1/J= 0 is related to A imimolecular reaction, such as many cases of exchange, might be expected to have a very small entropy change on gomg to the transition state. However, several systems have shown significant entropy contributions—entropy can make up more than 10% of the barrier. It is therefore important to measure the rates over as wide a range of temperatures as possible to obtain reliable thennodynamic data on the transition state. 

Prediction of solubility for simple ionic compounds is difficult since we need to know not only values of hydration and lattice enthalpies but also entropy changes on solution before any informed prediction can be given. Even then kinetic factors must be considered. 

In this discussion, entropy factors have been ignored and in certain cases where the difference between lattice energy and hydration energy is small it is the entropy changes which determine whether a substance will or will not dissolve. Each case must be considered individually and the relevant data obtained (see Chapter 3), when irregular behaviour will often be found to have a logical explanation. 

Steinberg, I. Z., Scheraga, H. A. Entropy changes accompanying association reactions of proteins. J. Biol. Chem. 238 (1963)172-181. 

Water-soluble globular proteins usually have an interior composed almost entirely of non polar, hydrophobic amino acids such as phenylalanine, tryptophan, valine and leucine witl polar and charged amino acids such as lysine and arginine located on the surface of thi molecule. This packing of hydrophobic residues is a consequence of the hydrophobic effeci which is the most important factor that contributes to protein stability. The molecula basis for the hydrophobic effect continues to be the subject of some debate but is general considered to be entropic in origin. Moreover, it is the entropy change of the solvent that i... 

What enthalpy difference would lead to a 25-75% mixture of syn and skew rotamers of 1-butene Neglect any entropy change. 

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

Equation (3.7) gives a simple procedure for evaluating the entropy change accompanying a change of state. At the normal boiling point of a liquid, for example, the heat is absorbed reversibly and equals the heat of vaporization AH,. Since T is constant, the entropy of vaporization is AH,/T. For benzene, for example, AS, = (30.8 k J mol" )/353 = 87 J K mol. ... 

A moment s reflection will convince us that these probabilities can be used as thermodynamic probabilities in Eq. (3.21) to calculate the entropy change on stretching ... 

In the volume elements describing individual subchains, the x, y, and z dimensions will be different, so Eq. (3.32) must be averaged over all possible values to obtain the average entropy change per subchain. This process is also easily accomplished by using a result from Chap. 1. Equation (1.62) gives the mean-square end-to-end distance of a subchain as n, 1q, and this quantity can also be written as x + y + z therefore... 

This expression gives the average entropy change per chain to get the average for the sample, we multiply by the number v of subchains in the sample. The total entropy change is... 

In writing Eq. (8.41), we have clearly treated Aw as a contribution to enthalpy. This means we neglect volume changes (AHp jj. versus AUp jj.) and entropy changes beyond the configurational changes discussed in the last section (AGp jj. versus AH jj.). In a subsequent development it is... 

This situation does not improve greatly with increasing temperature, because the entropy change is small. At 2000 K (1727°C) and 101.3 kPa (1 atm), the hydrogen mole fraction at equihbrium is 0.036 at 3000 K (2727°C) the hydrogen mole fraction is about 0.2 (154). 

Second Law of Thermodynamics. The entropy change of any system together with its surroundings is positive for a real process, approaching zero as the process approaches reversibiUty ... 

A heat engine is a device operating in cycles that takes in heat, from a heat reservoir at temperature Tp, discards heat, to another heat reservoir at a lower temperature T, and produces work. A heat reservoir is a body that can absorb or reject unlimited amounts of heat without change in temperature. Entropy changes of a heat reservoir depend only on the absolute temperature and on the quantity of heat transferred, and are always given by the integrated form of equation 4 ... 

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