Spontaneous process entropy change

Another statement of the second law is this in any spontaneous process, the entropy of the Universe increases (AS. > 0). This statement is general, and it applies to any set of conditions. It is not confined to the special case of constant temperature and pressure, as is the statement that the free energy decreases in a spontaneous process. Entropy changes are particularly important in determining the energetics of protein folding. 

To sum up the situation, it may be concluded that the probability that all the molecules of a gas will remain in one part of the space available to them is extremely small under ordinary conditions. On the other hand, the probability of a virtually uniform distribution of the gas is large. The spontaneous process in which a gas, at constant temperature, fills uniformly the whole of the available volume is thus associated with a large increase in the probability of the system. In general, all spontaneous processes represent changes from a less probable to a more probable states and since such processes are accompanied by an increase of entropy, it is to be expected that there may be a connection between the entropy of a system in a given state and the probability of that state. 

Laws of Thermodynamics The laws of thermodynamics have been successfully applied to the study of chemical and physical processes. The first law of thermodynamics is based on the law of conservation of energy. The second law of thermodynamics deals with natural or spontaneous processes. The function that predicts the spontaneity of a reaction is entropy. The second law states that for a spontaneous process, the change in the entropy of the universe must be positive. The third law enables us to determine absolute entropy values. 

Consider a system which undergoes a spontaneous (irreversible) change from state A to state B within an adiabatic enclosure. Since the process is irreversible (spontaneous), the entropy change (Sg - S ) cannot be evaluated through Eq.3.10.1. 

Any change taking place which results in an increase in entropy has a positive entropy change (AS). Most spontaneous thermodynamic processes are accompanied by an increase in entropy. Entropy has units of Joules per degree K per mole. For representative values see table on p. 393. 

The relationship between entropy change and spontaneity can be expressed through a basic principle of nature known as the second law of thermodynamics. One way to state this law is to say that in a spontaneous process, there is a net increase in entropy, taking into account both system and surroundings. That is,... 

Notice that the second law refers to the total entropy change, involving both system and surroundings. For many spontaneous processes, the entropy change for the system is a negative quantity. Consider, for example, the rusting of iron, a spontaneous process ... 

Key Terms enthalpy, H free energy of formation, AG standard entropy change, AS° entropy, S spontaneous process standard free energy change, AG° free energy, G... 

The entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

The change in Gibbs free energy for a process is a measure of the change in the total entropy of a system and its surroundings at constant temperature and pressure. Spontaneous processes at constant temperature and pressure are accompanied by a decrease in Gibbs free energy. 

The following pictures show a molecular visualization of a system undergoing a spontaneous change. Account for the spontaneity of the process in terms of the entropy changes in the system and the surroundings. 

We see that the total change in entropy is a positive quantity for both these spontaneous processes, even though one process is exothermic and the other is endothermic. When this type of calculation is carried out for other processes, the same result is always obtained. For any spontaneous process, the total change of entropy is a positive quantity. Thus, this new state function of entropy provides a thermod3mamic criterion for spontaneity, which is summarized in the second law of thermodynamics ... 

In words, in any process that occurs at constant T and P, the free energy change for the system is negative whenever the total entropy change is positive that is, whenever the overall process is spontaneous. Defining a new function and imposing some restrictions provides a way to use properties of a system to determine whether a process is... 

When ammonium nitrate, NH jNOj, dissolves in water, it absorbs heat. Consequently, its standard enthalpy of solution must be positive. This means that the entropy change caused by ammonium nitrate going from solid to solution must increase for the process to proceed spontaneously. This is exactly what one would expect based on the concept of entropy as a measure of randomness or disorder. 

Solid ammonium nitrate is an orderly, crystalline substance, a state considerably less random than a solution of ions in water. In this case, the positive entropy change outweighs the enthalpy change. That is TAS > AH. The Gibbs free energy change is negative, so the process will proceed spontaneously. 

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... 

Hence, for an isolated system, the entropy of the system alone must increase when a spontaneous process takes place. The second law identifies the spontaneous changes, but in terms of both the system and the surroundings. However, it is possible to consider the specific system only. This is the topic of the next section. 

The total change in entropy is AY( 0iai), which must be positive for a spontaneous process. From Equation (4.8), we say... 

If ASsurroundings is sufficiently positive to make the total entropy change positive, the process will be spontaneous. 

While the first law allows us to calculate the energy change associated with a given process, it says nothing about whether or not the process itself will take place spontaneously. This is the province of the second law of thermodynamics and leads to the introduction of another state function, entropy, S. The entropy change in a system which moves from state 1 to state 2 is defined by... 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

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