Entropy Changes in the System

Just as the enthalpy change of a reaction is the difference between the enthalpies of the products and reactants (Equation 5.12), the entropy change is the difference between the entropies of the products and reactants  

using 2 to represent summation and m and n to represent the stoichiometric coefficients of the reactants and products, respectively. Equation 18.7 can be generalized as follows  

The teim eguffitwAjm prc ess is dHliErem ftom Ihe term cherncd equHirkjm. Art equilibrium pnxess is one that we cause to occur by adding or removing energy from a system that is at equilibrium. 

The standard entropy values of a large number of substances have been measured in J/K mol. To calculate the standard entropy change for a reaction (A5° ), we look up the standard entropies of the products and reactants and use Equation 18.7. Sample Problem 18.2 demonstrates this approach. 

Recall that here per mole means per mole of reaction as written [M Section 5.6]. 

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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. 

This equation was originally arrived at by the French Engineer Sadi Carnot in 1824 during his investigation on the efficiency of heat engines. In terms of the heat and the entropy changes in the system, the second law may be expressed as follows ... 

To determine the sign of AStotai = ASsys + ASsurr/ we need to calculate the values of ASsys and ASsurr. The entropy change in the system equals the standard entropy of reaction and can be calculated using the standard molar entropies in Table 17.1. To obtain ASsurr = —AH°/T, first calculate AH° for the reaction from standard enthalpies of formation (Section 8.10). 

Predict the sign of the entropy change in the system for each of the following processes ... 

In order to usefully apply the second law, it will be necessary to be able to calculate both AS, the entropy change in the system of interest, and A,S sur, the entropy change of the surroundings. (Thermodynamic functions without the subscript sur can be assumed to refer to the system.) The mathematical form of our second law then becomes... 

Because it takes some practice to be able to use the recipes for calculating entropy changes in the system and surroundings, a few simple examples are presented here. 

Assume that region I in Figure 3.1 is an open system than can exchange both matter and energy with region II. The total entropy change in the system is... 

Entropy in this sense is different from the thermodynamic state function 5, which has a large reversible component, for instance as defined at phase transitions. An entropy change in the system is compensated for by an almost equal, but opposite change in the surroundings. 

The partition of the entropy change in the open system into two constitu ents, djS and dgS, makes it obvious that the thermodynamic properties of open and isolated systems are principally different. Even though the inequality diS/dt > 0 is satisfied, the total entropy of the open system can both increase and decrease because the value dgS/dt can be both positive and negative due to the exchange with the surroundings. The following probable situations of a total of entropy changes in the system illustrate the conclusion ... 

First we will consider the entropy changes accompanying chemical reactions that occur under conditions of constant temperature and pressure. As for the other types of processes we have considered, the entropy changes in the surroundings are determined by the heat flow that occurs as the reaction takes place. However, the entropy changes in the system (the reactants and products of the reaction) can be predicted by considering the change in positional probability. 

The connection between entropy and the spontaneity of a reaction is expressed by the second law of thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. Since the universe is made up of the system and the surroundings, the entropy change in the universe for any process is the sum of the entropy changes in the system (ASsys) and in the surroundings (ASsur,). Mathematically, we can express the second law of thermodynamics as follows ... 

Entropy Changes in the System Standard Entropy of Reaction (A5°xn)... 

The overall entropy change in the system and the surroundings is therefore... 

Where AS is the entropy change in the system and W the work. Eq corresponds to the maximum work that can be performed by transfer of heat Q in passing from temperature T to Tq. 

To improve on the cell model, two other classes of models were developed, namely, lattice-fluid and lattice-hole theories. In these theories, vacant cells or holes are introduced into the lattice to describe the extra entropy change in the system as a function of volume and temperature. The lattice size, or cell volume, is fixed so that the changes in volume can only occur by the appearance of new holes, or vacant sites, on the lattice. The most popular theories of such kind were developed by Simha and Somcynsky or Sanchez and Lacombe. ... 

Because nature always tends to proceed toward a more probable state, we can assert an equivalent form of the second law of thermodynamics In any spontaneous process, the total entropy change of the universe is positive, (ASu > 0). That this statement of the second law is equivalent to our original version is not at all obvious. But remember, energy that is not converted into work (a process that would decrease entropy) is transferred to the surroundings as heat. Thus the entropy of the surroundings increases, and the total entropy change in the system and surroundings is positive. 

We usually refer to the entropy change in the system simply as AS, so we ll drop the sys subscript. 

Many metals form sohd carbonates, such as CaC03. When carbonates are heated, gaseous CO2 can be driven off, leaving behind a metal oxide. What is the sign of the entropy change in the system for this type of chemical reaction Explain your answer. 

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