Molecular interpretation of entropy

We emphasized earlier that thermodynamics is a branch of science which can be. developed without any regard to the molecular nature of matter. The logical arguments employed do not require any knowledge of molecules, yet in the understanding of thermodynamics, many of us find it helpful to interpret thermodynamic principles in the light of molecular structure. 

In specifying a thermodynamic state we ignore the positions and velocities of individual atoms and molecules. However, any macroscopic property is in fact the result of the position and motion of these particles. At any instant we could define the microscopic state of a system in principle which means that we would specify the position and momentum of each atom. An instant later, even though the system might remain in the same macroscopic state, the microscopic state would be completely different, since at ordinary temperatures molecules change their positions at speeds of the order of 10 - cm per second. 

a system at equilibrium remains in the same macroscopic state, even though its microscopic state is changing rapidly. There are an enormous number of microscopic states consistent with any given macroscopic state. This concept leads us at once to a molecular interpretation of entropy entropy is q measure of how many different nncroscqpii stqte arje, agivenmqavscopic state. 

Thus far we have considered a mere fifty-two cards if we consider the vast number of molecules (6.02 x 10 in a mole) the likelihood of a net decrease in entropy is obviously much more remote. 

In light of this, it is easy to predict what kinds of entropy changes will occur when various processes take place. Suppose, for example, that we increase the temperature of a gas. The range of molecular speeds becomes more extended, since a larger proportion of the molecules have speeds which differ from the most probable value. Thus there is more disorder at a higher temperature, and the entropy is greater. 

In general, any irreversible process results in an increase in total entropy, whereas any reversible process results in no overall change in entropy. This statement is known as the second law of thermodynamics. 

The sum of the entropy of a system plus the entropy of the surroundings is everything there is, and so we refer to the total entropy change as the entropy change of the universe, AS niy. We can therefore state the second law of thermodynamics in terms of two equations  

Because spontaneous processes are irreversible, we can say that the entropy of the universe increases in any spontaneous process. This profound generalization is yet another way of expressing the second law of thermodynamics. 

The rusting of iron is spontaneous and is accompanied by a decrease in the entropy of the system (the iron and oxygen). What can we conclude about the entropy change of the surroundings  

The second law of thermodynamics tells us the essential character of any spontaneous change—it is always accompanied by an increase in the entropy of the universe. We can use this criterion to predict whether a given process is spontaneous or not. Before seeing how this is done, however, we will find it useful to explore entropy from a molecular perspective. 

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Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

THE MOLECULAR INTERPRETATION OF ENTROPY AND THETHIRD LAW OFTHERMODYNAMICS On the molecular level, we learn that the entropy of a system is related to the number of accessible microstates. The entropy of the system increases as the randomness of the system increases. The third law of thermodynamics states that, at 0 K, the entropy of a perfect crystaiiine soiid is zero. 

SECTION 19.3 The Molecular Interpretation of Entropy and the Third Law of Thermodynamics... 

Equation (18.1) provides a useful molecular interpretation of entropy, but is normally not used to calculate the entropy of a system because it is difficult to determine the number of microstates for a macroscopic system containing many molecules. Instead, entropy is obtained by calorimetric methods. In fact, as we will see shortly, it is possible to determine the absolute value of entropy of a substance, called absolute entropy, something we cannot do for energy or enthalpy. Standard entropy is the absolute entropy of a substance at 1 atm and 25°C. (Recall that the standard state refers only to 1 atm. The reason for specifying 25°C is that many processes are carried out at room temperature.) Table 18.1 lists standard entropies of a few elements and compounds Appendix 3 provides a more extensive listing. The units of entropy are J/K or J/K mol for 1 mole of the substance. We use joules rather than kilojoules because entropy values are typically quite small. Entropies of elements and compounds are all positive (that is, S° > 0). By contrast, the standard enthalpy of formation (A//f) for elements in their stable form is arbitrarily set equal to zero, and for compounds, it may be positive or negative. 

Equation 8.1 is a statistical definition of entropy. Defining entropy in terms of probability provides a molecular interpretation of entropy changes as well as allowing for the cglpw iqj enfpja plangi fip qip H such as that of an ideal gas. In... 

Equation (18.1) provides a useful molecular interpretation of entropy, but is normally not used to f-nlenlate the entropy of a system because it is difficult to determine the... 

The concept of entropy was developed so chemists could understand the concept of spontaneity in a chemical system. Entropy is a thermodynamic property that is often associated with the extent of randomness or disorder in a chemical system. In general if a system becomes more spread out, or more random, the system s entropy increases. This is a simplistic view, and a deeper understanding of entropy is derived from Ludwig Boltzmann s molecular interpretation of entropy. He used statistical thermodynamics (which uses statistics and probability) to link the microscopic world (individual particles) and the macroscopic world (bulk samples of particles). The connection between the number of microstates (arrangements) and its entropy is expressed in the Boltzmann equation, S = kin W, where W is the number of microstates and k is the Boltzmann constant, 1.38 x 10 JK L... 

It is often claimed, with some justification, that statistical theory explains the basis of the second law and provides a mechanistic interpretation of thermodynamic quantities. For example, the Boltzmann expression for entropy is S = ks In W, where W is the number of ways the total energy is distributed among the molecules. Thus entropy in statistical theory is connected to the availability of microstates for the system. In classical theory, on the other hand, there are no pictures associated with entropy. Hence the molecular interpretation of entropy changes depends on statistical theory. 

An alternative argument asserts that increases in spatial configurations are all essentially just manifestations of increases in energetic configurations, and that the molecular interpretation of entropy can be understood by only considering the latter. For more information, see F.L. Lambert, J. Chem. Ed, 84(9), 1548 (2007). 

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