Molecular interpretation entropy

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. 

Over a long period of time experimental results on amphiphilic monolayers were limited to surface pressure-area ( r-A) isotherms only. As described in sections 3.3 and 4, from tc[A) Isotherms, measured under various conditions, it is possible to obtain 2D-compressibilities, dilation moduli, thermal expansivities, and several thermodynamic characteristics, like the Gibbs and Helmholtz energy, the energy cmd entropy per unit area. In addition, from breaks in the r(A) curves phase transitions can in principle be localized. All this information has a phenomenological nature. For Instance, notions as common as liquid-expanded or liquid-condensed cannot be given a molecular Interpretation. To penetrate further into understanding monolayers at the molecular level a variety of additional experimental techniques is now available. We will discuss these in this section. 

From Equation 13.9 we see that the entropy of a gas increases during an isothermal expansion (V2 > Vi) and decreases during a compression (V2 < Vt). Boltzmann s relation (see Eq. 13.1) provides the molecular interpretation of these results. The number of microstates available to the system, H, increases as the volume of the system increases and decreases as volume decreases, and the entropy of the system increases or decreases accordingly. 

The entropy increases when a solid melts or a liquid vaporizes, and it decreases when the phase transition occurs in the opposite direction. Again, Boltzmann s relation provides the molecular interpretation. When a solid melts or a liquid vaporizes, the number of accessible microstates O increases, and thus the entropy... 

Thus, 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. 

The first molecular interpretation was attempted by Eley (1939, 1944). Eley assumed that the process of solution can be viewed as a two-step process first, the creation of a cavity that can accommodate the solute, and second, the introduction of the solute into this cavity. Thus, schematically, the process is depicted in Fig. 3.1. For each thermodynamic quantity of solution, say the standard enthalpy and entropy, one can write... 

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. 

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