Entropy, Free Energy, and the Second Law of Thermodynamics

1 The Entropy of an Isolated System Always Increases in Any Spontaneous Process 424 

2 The Entropy Change for a Process Can Be Calculated Using the Thermodynamic Definition of Entropy 432 

3 The Third Law of Thermodynamics Allows Us to Determine Absolute Entropies 440 

4 The Spontaneity of a Process at Constant Temperature and Pressure Is Governed by the Gibbs Free Energy 446 

5 The Mixing of Pure Substances Leads to an Increase in the Entropy and a Decrease in the Gibbs Free Energy 456 

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Chapter 8 Entropy, Free Energy, and the Second Law of Thermodynamics... 

The basic principles of thermodynamics are treated together in Chapters 7 Thermochemistry Energy in Chemical Reactions, and 8, Entropy, Free Energy, and the Second Law of Thermodynamics. This... 

Why Do We Need to Know This Material The second law of thermodynamics is the key to understanding why one chemical reaction has a natural tendency to occur bur another one does not. We apply the second law by using the very important concepts of entropy and Gibbs free energy. The third law of thermodynamics is the basis of the numerical values of these two quantities. The second and third laws jointly provide a way to predict the effects of changes in temperature and pressure on physical and chemical processes. They also lay the thermodynamic foundations for discussing chemical equilibrium, which the following chapters explore in detail. 

It follows from the second law of thermodynamics that the optimal free energy of a hydrocarbon-water mixture is a function of both maximal enthalpy (from hydrogen bonding) and minimum entropy (maximum degrees of freedom). Thus, nonpolar molecules tend to form droplets with minimal exposed surface area, reducing the number of water molecules affected. For the same reason, in the aqueous environment of the hving cell the hydrophobic portions of biopolymers tend to be buried inside the structure of the molecule, or within a lipid bilayer, minimizing contact with water. 

The second law of thermodynamics states that the total entropy of a system must increase if a process is to occur spontaneously. Entropy is the extent of disorder or randomness of the system and becomes maximum as equilibrium is approached. Under conditions of constant temperature and pressure, the relationship between the free energy change (AG) of a reacting system and the change in entropy (AS) is expressed by the following equation, which combines the two laws of thermodynamics ... 

That this should be so is a corollary of the Second Law of Thermodynamics which is concerned essentially with probabilities, and with the tendency for ordered systems to become disordered a measure of the degree of disorder of a system being provided by its entropy, S. In seeking their most stable condition, systems tend towards minimum energy (actually enthalpy, H) and maximum entropy (disorder or randomness), a measure of their relative stability must thus embrace a compromise between H and S, and is provided by the Gibb s free energy, G, which is defined by,... 

Early chemists thought that the beat of reaction, —AH. should be a measure of the "chemical affinity" of a reaction. With the introduction of the concepl of netropy (q.v.) and ihe application of the second law of thermodynamics lo chemical equilibria, it is easily shown that the true measure of chemical affinity and Ihe driving force for a reaction occurring at constant temperature and pressure is -AG. where AG represents the change in thermodynamic slate function, G. called Gibbs free energy or free enthalpy, and defined as the enthalpy, H, minus the entropy. S. times the temperature, T (G = H — TS). For a chemical reaction at constant pressure and temperature ... 

The First Law of Thermodynamics Any Change in the Energy of a System Requires an Equal and Opposite Change in the Surroundings The Second Law of Thermodynamics In Any Spontaneous Process the Total Entropy of the System and the Surroundings Increases Free Energy Provides the Most Useful Criterion for Spontaneity... 

The existence of an energy balance is not sufficient to answer all questions about a chemical reaction. Does a given reaction take place at all If so, to what extent does it proceed Questions relating to the processes and extent of chemical reactions require the introduction of some new thermodynamic functions which, like E and //, are properties of the state of the system. These new functions are entropy, S, and Gibbs free energy, G. In order to answer these and other questions, a mathematical statement of the second law of thermodynamics is required ... 

We know that the concept of entropy is the fundamental consequence of the second law of thermodynamics. There are two other functions, which utilize entropy in their derivations. These two functions are free energy function and work function. These functions like the internal energy, heat content and entropy are fundamental thermodynamic properties and depend upon the states of the system only. 

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