Criteria of spontaneity

Thus far we have observed that the Gibbs and Planck functions provide the criteria of spontaneity and equilibrium in isothermal changes of state at constant pressure. If we extend our analysis to systems in which other constraints are placed on the system, and therefore work other than mechanical work can be performed, we find that the Gibbs and Helmholtz functions also supply a means for calculating the maximum magnitude of work obtainable from an isothermal change. 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

Equation 2.2-8 indicates that the internal energy U of the system can be taken to be a function of entropy S, volume V, and amounts nt because these independent properties appear as differentials in equation 2.2-8 note that these are all extensive variables. This is summarized by writing U(S, V, n ). The independent variables in parentheses are called the natural variables of U. Natural variables are very important because when a thermodynamic potential can be determined as a function of its natural variables, all of the other thermodynamic properties of the system can be calculated by taking partial derivatives. The natural variables are also used in expressing the criteria of spontaneous change and equilibrium For a one-phase system involving PV work, (df/) 0 at constant S, V, and ,. ... 

From the above discussion, it is dear why the choice of surfactants for ECs is still made on a trial and error basis. Once this choice is made, an extensive work is required to optimise the composition to produce an acceptable product that satisfies the criteria of spontaneous emulsification and stability under practical conditions. In many cases, it is also essential to add other components such as... 

Starting with equation (5.48) we can derive four equations that provide the criteria for spontaneity or equilibrium in a system under a specific set of conditions. To derive the first equation, we use the first law to write... 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

Many of the electrochemical techniques described in this book fulfill all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-defined and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difficult to implement. For this type of process, hydro-dynamic techniques become important, where mass transport is controlled by convection as well as diffusion. 

The chapter also outlines the criteria for equilibrium in terms of the Gibbs function and chemical potential, together with the criteria for spontaneity. 

The choice of species and strain to be used in a carcinogenicity study is based on various criteria including susceptibility to tumor induction, incidence of spontaneous tumors, survival, existence of an adequate historical data base, and availability. 

If the temperature and volume are constant, and if the only constraint on the system is the pressure of the environment. Equation (6.106) and Equations (7.1) through (7.6) provide the criteria of equilibrium and spontaneity. The equality in Equation (7.1) apphes to a reversible change, and as no exchange of work occurs with the environment, the reversible change must be in a system at equilibrium. Similarly,... 

CRITERIA OF EQUILIBRIUM AND SPONTANEITY IN SYSTEMS 213 SO that the chemical potential is also... 

By Ames criteria, a chemical must be considered mutagenic if, at a dose of lOOy per plate, it more than doubles the number of spontaneous revertants, either with or without metabolizing microsomes. 

The basic question in all of thermodynamics is A certain system is under such and such constraints, what is the equilibrium state that it can go to spontaneously The amazing thing is that this question can be answered by making macroscopic measurements. Thermodynamics does not deal with the question as to how long it will take to reach equilibrium. We now have seven criteria for equilibrium in a one-phase system with one species and only PV work. The criteria of equilibrium provided by these thermodynamic potentials are (dt/)S K n 0, (dH)SPn < 0, (d/4)r K 0, (dG)rp <0, (dC/[/r])s v >(1 < 0,... 

The reason for going into this much detail on all of the thermodynamic potentials that can be defined for a one-phase, one-species system and the corresponding criteria for spontaneous change is to illustrate the process by which these thermodynamic potentials are defined and how they provide criteria for... 

NOTE 2 The criteria are based on the self-ignition temperature of charcoal, which is 50°C for a sample cube of 27 rrf. Substances and mixtures with a temperature of spontaneous combustion higher than 50°C for a volume of 27 m should not be assigned to this hazard class. Substances and mixtures with a spontaneous ignition temperature higher than 50°C for a volume of 450 litres should not be assigned to hazard Category 1 of this hazard class. 

---