Spontaneous change thermodynamics

The properties of a system at equilibrium do not change with time, and time therefore is not a thermodynamic variable. An unconstrained system not in its equilibrium state spontaneously changes with time, so experimental and theoretical studies of these changes involve time as a variable. The presence of time as a factor in chemical kinetics adds both interest and difficulty to this branch of chemistry. 

The common characteristic of any kind of dynamic equilibrium is the continuation of processes at the microscopic level but no net tendency for the system to change in either the forward or the reverse direction. That is, neither the forward nor the reverse process is spontaneous. Expressed thermodynamically,... 

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

In thermodynamics, entropy enjoys the status as an infallible criterion of spontaneity. The concept of entropy could be used to determine whether or not a given process would take place spontaneously. It has been found that in a natural or spontaneous process there would be an increase in the entropy of the system. This is the most general criterion of spontaneity that thermodynamics offers however, to use this concept one must consider the entropy change in a process under the condition of constant volume and internal energy. Though infallible, entropy is thus not a very convenient criterion. There have, therefore, been attempts to find more suitable thermodynamic functions that would be of greater practical... 

Of course, depending on the system, the optimum state identified by the second entropy may be the state with zero net transitions, which is just the equilibrium state. So in this sense the nonequilibrium Second Law encompasses Clausius Second Law. The real novelty of the nonequilibrium Second Law is not so much that it deals with the steady state but rather that it invokes the speed of time quantitatively. In this sense it is not restricted to steady-state problems, but can in principle be formulated to include transient and harmonic effects, where the thermodynamic or mechanical driving forces change with time. The concept of transitions in the present law is readily generalized to, for example, transitions between velocity macrostates, which would be called an acceleration, and spontaneous changes in such accelerations would be accompanied by an increase in the corresponding entropy. Even more generally it can be applied to a path of macrostates in time. 

A system can in principle undergo an indefinite number of processes under the constraint that energy is conserved. While the first law of thermodynamics identifies the allowed changes, a new state function, the entropy A, is needed to identify the spontaneous changes among the allowed changes. The second law of thermodynamics may be expressed as... 

The second law of thermodynamics (Clausius formulation) In isolated systems, spontaneous changes are always accompanied by a net increase in entropy. 

Table 5.1 summarizes the various constraint conditions and the associated thermodynamic potentials and second-law statements for direction of spontaneous change or condition of equilibrium. All of these statements are equivalent to Carnot s theorem ( dq/T < 0) or to Clausius inequality ([Pg.164]

Since some spontaneous reactions are exothermic and others are endothermic, enthalpy alone can t account for the direction of spontaneous change a second factor must be involved. This second thermodynamic driving force is nature s tendency to move to a condition of maximum randomness or disorder (Section 8.13). 

Thermodynamics is used to predict whether reactants have a spontaneous tendency to change into products. This tendency is associated with a decrease in the free energy or Gibbs energy of the system (G) to a minimum. As a consequence, the thermodynamic criterion for spontaneous change at constant temperature and pressure is AG < 0. Under standard conditions (concentrations = 1 M, and P = 1 atm), the standard Gibbs energy variation (AG°) is related with the equilibrium constant (A) by equation 11 ... 

In contrast to the conservation of internal energy (Eq. 2.1, the first law of thermodynamics), the entropy of the Universe always increases (Eq. 2.5), which is an alternative definition of the second law of thermodynamics. Inherent in the concept of entropy is a preferred direction for spontaneous change (AS rr > 0). For example, at 1 bar pressure, ice melts at 10°C, water freezes at —10°C, and not vice versa. A spontaneous process leads from a state of lower probability to a state of higher probability, and equilibrium is the state of maximum probability (Pitzer, 1995). 

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 ,. ... 

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... 

Any spontaneous change of substances that occurs in the natural environment advances with a decrease in exergy of the substances this is the law of exergy decrease in spontaneous processes in analogy to the law of affinity decrease in spontaneous processes. In contrast to energy which is always conserved in any processes due to the first law of thermodynamics, exergy is exempt from the law of conservation and so is the affinity. 

Let us prove the GlansdorGPrigogine theorem with an example of an arbitrary spatially homogeneous chemical reactive system. The internal parameters for such a system are the concentrations of intermediates of the stepwise chemical transformations. Any spontaneous changes of the system (and, as a result, changes in internal driving forces) relate namely to changes in the intermediate concentrations. Therefore, the partial force differential dxP may be substituted for by its full analogue related thermodynamic rushes (concentrations) of intermediates (a 1,. .., k) of the stepwise transformations ... 

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