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CHEM 1212 - Principles of Chemistry II
Chapter 16 - Spontaneity, Entropy, and Free Energy
16.1 Spontaneous Processes and Entropy
! a process is said to be spontaneous if it occurs without outside intervention ! spontaneous processes may be fast or slow ! thermodynamics tell us the direction of the process but not the speed ! thermodynamics only considers the initial and final states and does not require knowledge of the pathway between reactants ! see Figure 16. ! after many years of observation, scientists have concluded that the characteristic common to all spontaneous processes is an increase in a property called entropy , denoted by the symbol, S " the driving force for a spontaneous process is an increase in the entropy of the universe " entropy can be viewed as a measure of randomness or disorder " entropy is thermodynamic function that describes the number of arrangements (positions and/or energy levels) that are available to a system existing in a given state ! energy is closely associated with probability " see Figure 16. " see Figure 16. " see Table 16. " see Table 16. ! the type of probability we have been considering in this example is called positional probability because it depends on the number of configurations in space (positional microstates) that yield a particular state ! S solid < S liquid << S gas
16.2 Entropy and the Second Law of Thermodynamics
! in any spontaneous process there is always an increase in the entropy of the universe - this is the second law of thermodynamics ! energy is conserved in the universe, but entropy is not ! the second law can be paraphrased as follows; the entropy of the universe in increasing ! convenient to divide the universe into a system and the surroundings thus the change in the entropy of the universe is equal to the entropy of the system and the change in entropy of the surroundings ! if the change in the entropy of the universe is positive, the process is spontaneous in the direction written; if negative spontaneous in the opposite direction; if zero the process has no tendency to occur and the system is at equilibrium
16.3 The Effect of Temperature
! example, H 2 O(l) --> H 2 O(g); this is the system everything else the surroundings ! a mole of water has a volume of approximately 18 mL; a mole of gaseous water at 1 atm and 100 o^ C occupies a volume of approximately 31 liters; entropy increases in this system ! when heat is release to the surrounding (exothermic reaction), entropy of the surrounding is increased; the reverse occurs in endothermic reactions ! the sign of ) S univ tells us whether the vaporization of water is spontaneous or not ! have seen that ) S sys is positive and favors the process and ) S surr is negative and unfavorable; thus the components are in opposition; which controls the situation?; depends on the temperature ! at 1 atm, water changes spontaneously from liquid to gas at all temperatures above 100 oC; below 100 oC the opposite process (condensation) is spontaneous ! the central idea is that the entropy changes in the surroundings are primarily determined by heat flow ! an exothermic process in the system increases the entropy of the surroundings, because the resulting energy flow increases the random motions in the surroundings; this means that exothermicity is an important driving force for spontaneity ! the significance of exothermicity as a driving force depends on the temperature at which the process occurs ! the impact of the transfer of a given quantity of energy as heat to or from the surrounding will be greater at lower temperatures ! definition of ) S surr is ) S surr = -) H /T ! the minus sign is necessary because the sign of ) H is determined with respect to the reaction system, and this equation expresses a property of the surroundings; this mean if the reaction is exothermic,) H has a negative sign, but heat flows into the surroundings, ) S is positive ! see Table 16.
16.4 Free Energy
! so far have used S univ to predict the spontaneity of a process; however, another thermodynamic function is also related to spontaneity and is especially useful in dealing with the temperature dependence of spontaneity; the function is called the free energy , which is symbolized by G and defined by G = H - TS ; H is the enthalpy, T is the temperature in Kelvin, and S is the entropy ! for a process that occurs at constant temperature, the change in free energy () G ) is given by the equation, ) G = ) H - T ) S ! a process at constant T and P is spontaneous in the direction in which the free energy decreases; that the change in free energy must be negative ! now have two functions that can be used to predict spontaneity; the entropy of the universe, which applies to all processes; and free energy, which can be used for processes carried out at constant temperature and pressure; since so many chemical reactions occur under the latter conditions, free energy is the more useful to chemists
! the equilibrium position of a process represents the lowest free energy value available to a particular reaction system ! the free energy of a reaction system changes as the reaction proceeds, because free energy is dependent on the pressure of a gas or on the concentration of species in solution ! will deal with only the pressure dependence of the free energy of an ideal gas; the dependence of free energy on concentration can be developed using similar reasoning ! see text for derivation ! ) G = ) G o^ + RT ln ( Q ), where Q is the reaction quotient (from the law of mass action), T is the temperature (K), R is the gas constant, ) G o^ is the free energy change of for the reaction with all reactants and products at a pressure of 1 atm
The Meaning of ) G for a Chemical Reaction
! a value of ) G for a given reaction system tells us whether the products or reactants are favored under a given set of conditions, it does not mean that the system will proceed to pure products (if ) G is negative) or remain as pure reactants (if ) G is positive); instead, the system will spontaneously go to the equilibrium position, the lowest possible free energy available to it
16.8 Free Energy And Equilibrium
! from a thermodynamic point of view, the equilibrium point occurs at the lowest value of free energy available to the reaction system ! see Figure 16. ! recall ) G = ) G o^ + RT ln ( Q ), at equilibrium ) G = 0 and Q = K , then ) G o^ = - RT ln K " (1) when ) G o^ = 0 the system is at equilibrium when the pressures of all reactants and products are 1 atm, which means that K equals 1 " (2) when ) G o^ < 0 means that K > 1; the reaction will adjust to the right to reach equilibrium " (3) when ) G o^ > 0 means that K < 1; the reaction will adjust to the right to reach equilibrium ! see Table 16.
16.9 Free Energy And Work
! achieving the maximum work available from a spontaneous process can only occur via a hypothetical pathway; any real pathway wastes energy ! see Figure 16.
