Spontaneity, Entropy, and Free Energy

I. Spontaneous Processes and Entropy
A. A process is said to be spontaneous if it occurs without outside intervention. Remember that thermodynamics only considers the initial and final states and does not require knowledge of the pathway between reactants and products.
B. The driving force for a spontaneous process is and increase in the entropy of the universe S. Entropy can be viewed as a measure of randomness or disorder. Entropy is closely related to probability in that nature spontaneously proceeds toward the states that have the highest probabilities of existing. The probability of occurrence of a particular arrangement (state) depends on the number of ways (microstates) in which that arrangement can be achieved. This type of probability is called positional probability because it depends on the number of configurations in space that yields a particular state. Positional entropy increases in going from solid to liquid to gaseous state.
II. Entropy and the Second Law of Thermodynamics
A. The second law of thermodynamics states: in any spontaneous process there is always and increase in the entropy of the universe. The energy of the universe is constant but entropy is always increasing. DSuniv = DSsys + DSsurr. If the DSuniv is positive, the entropy of the universe increases, and the process is spontaneous in the direction written. If DSuniv is negative, the process is spontaneous in the opposite direction.
III. The Effect of Temperature on Spontaneity
A. If there is a exothermic reaction, the flow of energy into the surroundings increases the random motions of atoms and thereby increases the entropy of the surroundings. The sign of DSsurr is positive. An endothermic process creates the opposite effect; taking energy from the surroundings and decreasing the entropy; the sign of DSsurr is negative. The impact of the transfer of a given quantity of energy as heat to or from the surroundings will be greater at lower temperatures. The change in entropy of the surroundings equals the negative change in enthalpy divided by the temperature. Exothermicity is most important as a driving force at low temperatures.
IV. Free Energy
A. Free energy is defined as G and is equal to enthalpy minus temperature times entropy. A process is spontaneous in the direction in which the free energy decreases. The change in entropy of the universe equals the negative change in free energy divided by temperature.

V. Entropy Changes in Chemical Reactions
A. Lowering the number of independent units in the system leads to less positional disorder. Fewer molecules mean fewer possible configurations. The third law of thermodynamics states the entropy of a perfect crystal at 0K is zero. The change in entropy for a reaction is equal to the standard entropy values of the products minus the standard entropy values of the reactants. Generally, the more complex the molecule, the higher is the standard entropy value.
VI. Free Energy and Chemical Reactions
A. The more negative the value of DG, the further a reaction will go to the right to reach equilibrium. The standard free energy of formation is the change in free energy that accompanies the formation of 1 mole of that substance from its constituent elements with all reactants and products in their standard states.
VII. Free Energy, Pressure, and Equilibrium
A. A system at constant temperature and pressure will proceed spontaneously in the direction that lowers its free energy. The equilibrium position in a reaction represents the lowest free energy value available to a particular reaction system. The positional entropy is greater in a larger volume and therefore a smaller pressure. The free energy increases with pressure in the equation G = G' + RT*ln(P).
B. A reaction proceeds to the minimum free energy (equilibrium), which corresponds to the point where Gproducts = Greactants and DG = 0. The quantitative relationship between free energy and the value of the equilibrium constant is DG' = -RT*ln(K). K can now be related to enthalpy and entropy in the following equation: ln(K) = -DH'/R(1/T) + DS'/R.
VIII. Free Energy and Work
A. The maximum possible useful work obtainable from a process at constant temperature and pressure is equal to the change in free energy: wmax = DG. DG for a spontaneous process represents the energy that is free to do useful work. DG for a non-spontaneous process represents the work that must be done on the system for the reaction to occur. The amount of work obtained from a problem is always less than the maximum possible amount. A process that can return in full to its initial state is a reversible process. In reality, all real processes are irreversible. In other words, in any real cyclic process in the system, work is changed to heat in the surroundings, and the entropy of the universe increases.