Entropy constant

The amount of heat released during a reaction is proportional to the amount of substance involved but the relationship is complicated in enzyme studies by secondary reactions. Although the use of entropy constants means that calorimetry theoretically does not require standardization, in many instances this will be necessary. The initial energy change can often be enhanced, giving an increase in the sensitivity of the method. Hydrogen ions released during a reaction, for instance, will protonate a buffer with an evolution of more heat. 

From measurements of the temperature dependency of the equilibrium constant, thermodynamic parameters may be deduced (section 3.4). Very few enthalpy and entropy constants have been derived for the distribution reaction MAj(aq) MA2(org) of neutral complexes such investigations give information about hydration and organic phase solvation. 

Schirmer et al. (7.) indicate that the constants and E j may be derived from physical or statistical thermodynamic considerations but do not advise this procedure since theoretical calculations of molecules occluded in zeolites are, at present, at least only approximate, and it is in practice generally more convenient to determine the constants by matching the theoretical equations to experimental isotherms. We have determined the constants in the model by a method of parameter determination using the measured equilibrium data. Defining the entropy constants and energy constants as vectors... 

Sj Molar constants for (T,VQ) - standard difference of entropy for 1 energy level only S Vector of entropy constants S ... 

Similarly, keeping entropy constant, so that we have an adiabatic process, we have... 

The first reason that led Latora and Baranger to evaluate the time evolution of the Gibbs entropy by means of a bunch of trajectories moving in a phase space divided into many small cells is the following In the Hamiltonian case the density equation must obey the Liouville theorem, namely it is a unitary transformation, which maintains the Gibbs entropy constant. However, this difficulty can be bypassed without abandoning the density picture. In line with the advocates of decoherence theory, we modify the density equation in such a way as to mimic the influence of external, extremely weak fluctuations [141]. It has to be pointed out that from this point of view, there is no essential difference with the case where these fluctuations correspond to a modified form of quantum mechanics [115]. 

For the calculation of the entropy constant S from kinetic considerations, see O. Sackur, Ann. d. Physik, 36, 958. 

Strictly speaking, the equation K =S is an extension of Boltzmann s theory, in so far as we have ascribed a definite value to the entropy constant. According to Boltzmann, the probabihty contains an undetermined factor, which cannot be evaluated without the introduction of new hypotheses. Boltzmann and Clausius suppose that the entropy may assume any positive or negative value, and that the change in entropy alone can be determined by experiment. Of late, however, Planck, in connection with Nemst s heat theorem, has stated the hypothesis that the entropy has always a finite positive value, which is characteristic of the chemical behaviour of the substance. The probabihty must then always be greater than unity, since its logarithm is a positive quantity. The thermodynamical probabihty is therefore proportional to, but not identical with, the mathematical probabihty, which is always a proper fraction. The definition of the quantity w on p. 15 satisfies these conditions, but so far it has not been shown that this definition is sufficient under all circumstances to enable us to calculate the entropy. 

Knowing the values of the entropy constants S and also the specific heats and their temperature coefiicients (i.e. /3, y,. ..) for all gases, we should be able to calculate the equilibrium constant K from the heat of the reaction for all gas reactions at all temperatures. The constants /3, y,. .. can be determined for each gas by direct measurements of the specific heats at different temperatures. The two laws of thermodynamics alone, however, do not enable us to express the entropy constants S in terms of experimental data. This has only recently been made possible by the discovery of Nernst s heat theorem (see Chapter XIV.). 

As long as we are ignorant of the values of the entropy constants S, the calculation of the equilibrium constant K from thermal data can only be carried out by actually determining K at a chosen temperature T, and then calculating the integration constant J from equation (9). When this has been done, however, we are in a position to predict the position of the chemical equilibrium, and hence the reactivity of the gases for all other temperatures. 

Thus Nernst s heat theorem enables us to calculate the entropy constant of a gas from its specific heat and from the vapour pressure curve of the condensed gas, and vice versa. Equation (166), however, involves the assumption that the specific heat of the gas can be expressed as a series of powers of T. 

The heat capacity Is estimated by comparison with mercurous chloride. The entropy Is estimated by comparison with the other mercurous and mercuric halides and use of additive entropy constants for the halogens from Kelley (2). 

The entropy at 298.15 was estimated by considering the additive entropy constants of Kelley (6) and Evans and Kubaschewski (7 ). The heat capacity was estimated in a similar manner by considering the heat capacities of the constituent elements and related compounds such as Mg, Og, MgO, P, 3 2 8 ... 

Sasaki, Y, Takagi, T., Kawaki, H. and Iwata, A. (1980). Novel Substituent Entropy Constant Oso represents the Molecular Connectivity x and its related Indices. Chem.Pharm.BulL, 31,330. 

Sasaki, Y., Takagi, T., Yamazato, Y, Iwata, A. and Kawaki, H. (1981). Utility of the Substituent Entropy Constants Ojo in the Studies of Quantitative Structure-Activity Relationships. Chem. Pharm.Bull.,29, 3073-3075. 

I recognized, of course, quite clearly that this could only be an approximate test. But if the regularities resulting from formula (77) were found to be actually confirmed in nature, this would constitute good support. As my colleague Planck once said to me in conversation, one cannot but assume that a law so general as this, that the entropy constant of matter is negligibly small at the absolute zero, is either as exactly true as the other Laws of Thermodynamics, or else is sometimes far removed from the truth. In spite of much search, no case has yet been found in which this... 

Of these the last condition, minimum Gibbs free energy at constant temperature, pressure and composition, is probably the one of greatest practical importance in chemical systems. (This list does not exhaust the mathematical possibilities thus one can also derive other apparently unimportant conditions such as that at constant U, S and , Eis a minimum.) However, an experimentalist will wonder how one can hold the entropy constant and release a constraint so that some other state function seeks a minimum. 

The third law of thermodynamics, like the first and second laws, is a postulate based on a large number of experiments. In this chapter we present the formulation of the third law and discuss the causes of a number of apparent deviations from this law. The foundations of the third law are firmly rooted in molecular theory, and the apparent deviations from this law can be easily explained using statistical mechanical considerations. The third law of thermodynamics is used primarily for the determination of entropy constants which, combined with thermochemical data, permit the calculation of equilibrium constants. 

When we want to remove the gas in keeping the total entropy constant and the molar volume constant, we get... 

Sackur-Tetrode constant (absolute entropy constant) ... 

Calculation of Entropy Constant-Pressure Path, No Phase Change... 

If the ideal law (46) is meant to apply to the entire concentration range, the entropy constants Ur and are equal, because in that case they simply represent the molar entropy of the pure polymer (x resp. x equal to 1). Writing = Ar — A r, the equation (47) then assumes the familiar form... 

In addition to the terms explained above, N2 represents the mol fraction of the solute, bi the co-volume of the solvent, Cvi the heat capacity and ii an entropy constant for a given normal state, both relating to the solvent. 

The situation is quite different in an open system or in an assembly of open systems, as is the case for a cell or an organism. In such an open system, the organism takes complex organic molecules from the environment, liberates free energy from these molecules, and rejects the products of the reaction. It can maintain its entropy constant and even decrease it so that its constituents become more ordered. It has been described as... 

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