# 1 Gibbs Free Energy and Spontaneity and the meaning of the universe…

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1 Gibbs Free Energy and Spontaneity and the meaning of the universe…

2 Relationship Between  S surr & H Water  S Surr q(system)   S surr affected by heat transfer into or out of closed system Entropy of the surroundings will be affected only by the heat transferred into or out of any closed system. Heat added to surroundings: K.E. surr increases; Molecules are moving faster. K.E. surr increases; Molecules are moving faster. Disorder increases since there is more randomness Disorder increases since there is more randomness Entropy increases. Entropy increases. Note: q p = -  H sys   S surr

3 Heat flow; Temperature Dependent Remember that heat transfer is temperature dependent. Heat will transfer more efficiently with changes at low temperature than at high temperature. i.e., 100€ to an International College student is worth more than to Raul. @ High temperature, molecules are already moving fast, an extra 10°C will not increase their velocities as much as molecules at very low temperature. -  H sys =  S surr units: J. Tmol K Therefore since:  S univ =  S sys +  S surr  S univ =  S sys -  H sys T

4  S univ and Spontaneity Criteria for Spontaneity in terms of the system:  S univ =  S sys +  S surr  S univ =  S sys -  H sys T  S univ  H sys (-)  S univ  H sys (-) (+) Spontaneous  S sys (+) (+) Spontaneous  S sys (+) Spontaneous

5 Spontaneity in terms of T  S univ Criteria for Spontaneity in terms of the system:  S sys +  S surr =  S univ (1)  S sys -  H sys =  S univ (2) T Note rearranging eqn. 2 -T  S sys +  H sys = -T  S univ -T  S sys +  H sys = -T  S univ J. Willard Gibbs realized that -T  S univ can be defined as a new function provided that  T = 0

6 J. Willard Gibbs The Free Energy change (  G) is a measure of spontaneity of a process and of the useful energy available from such a process. J. Willard Gibbs (1839-1903) was not particularly well known in his day, nor is his name widely recognized today, yet he is considered by some to be among the greatest scientists ever born in America. He was awarded th first doctorate in engineering granted in the United States, by Yale University. Gibbs became a professor of mathematical physics at Yale when he was 32 years old and began to publish a series of papers related to thermodynamics and equilibrium. Perhaps because his work was so theoretical, it was largely unappreciated at the time, though its great value was recognized by James Clerk Maxwell. Gibb’s work, if not his name, remains current and vital to this day.

7  G and Spontaneity Defining a new State function  G: -T  S univ  -T  S univ  =  G@  T,  P= 0 Consider  G = - T  S univ  G 0  G = 0@ equilibrium  S univ = 0  G > 0nonspontaneous  S univ 0nonspontaneous  S univ < 0 (rev is spontaneous)

8  G: Pictorial View  H sys  S sys Gibbs’ Free Energy can be defined in terms of the enthalpy of the system (  H sys ) and the entropy of the system (  S sys ) -T  S univ =  H sys - T  S sys =  G  G =  H - T  S  G < 0  G > 0  G = 0 @ equilb Forward reaction occur Spontaneous in forward direction Reverse reaction occur nonspontaneous in forward direction  G < 0  G > 0 See later that :  G  Keq or Q

9  G: Equations of Free Energy Gibbs’ Free Energy can be used to determine the Standard free energy (°) of formation  G =  H - T  S  G° f =  H° f - T  S° f ° Standard State f -formation from elements If data is not for formation process, then equation is slightly adjusted according to:  G° =  H° - T  S° Or from tabulated thermodynamic data:  G° rxn =  n  G° f (prod) -  n  G° f (react)

1010  G: Evaluation of Free Energy Consider the calculation for the following reaction: CH 3 OH (g) + O 2 (g)  CO 2 (g) + H 2 O (g) Determine  G°rxn 2 CH 3 OH (g) + 3 O 2 (g)  2 CO 2 (g) + 4 H 2 O (g)  H° rxn - 201.20-393.5-241.82   S° rxn + 237.6205.0-213.6-188.83   G° rxn - 161.90-394.4-228.57  Evaluate by:  G° rxn =  H° rxn - T  S° rxn  X° rxn =  n  X° f (prod) -  n  X° f (react) Or  G° rxn =  n  G° f (prod) -  n  G° f (react)

1 Effect of temperature on Free Energy Temperature influence on Free Energy and Spontaneity both  H,  S (+)  G =  H-T  S both  H,  S (+) (1000) (1) lg. # sm. # What is the sign of  G ? Temperature will dictate outcome of  G. T low : Temperature small  H-T  S   G (+) dominates negligiblenonspontaneous T high : Temperature large  H-T  S   G (-) negligible dominatesspontaneous

1212 Temperature Relationship and  G Consider Temperature affect on thermodynamic parameters  H-T  ST  G Spontaneity + a - +all -spon: T not impt - b + -all +nonspon: T not impt - c - -low -spon:  H impt - d - -high +nonspon :  S impt + e + +low +nonspon :  H impt + f + +high -spon:  S impt From this table, a spontaneous process can be made nonspontaneous i.e., c & d by increasing Temperature. i.e., c & d by increasing Temperature.

1313 Spontaneity: Example Example : (c) N 2 F 4(g)  2NF 2 (g)  H° - T  S°  G° (c) N 2 F 4(g)  2NF 2 (g)  H° - T  S°  G° 85 kJ 198 J/K @ T Low  H° dominates  G° (+)  Nonspontaneous @ T High  S° dominates  G° (-)  Spontaneous Example : (c) What temp will spontaneity switch for the reaction: (c) What temp will spontaneity switch for the reaction: N 2 (g) + 3H 2(g)  2NH 3 (g)  H° - T  S°  G° N 2 (g) + 3H 2(g)  2NH 3 (g)  H° - T  S°  G° - 92 kJ -198.5 J/K - 92 kJ -198.5 J/K @ T Low  H° dominates  G° (-)  Spontaneous @ T High  S° dominates  G° (+)  Nonspontaneous To go from spontaneous to nonspontaneous,  G° = 0 … T = - 92kJ = 463.5 K below spontaneous -0.198 kJ / K above, nonspontaneous -0.198 kJ / K above, nonspontaneous

1414 Phase Change Process What determines the spontaneity of a phase change?  H:s l g  S:s l g Two factors competing: Which dominates will determine phase change. Note: In a phase change: s  l is at equilib. or  G° = 0 or  G° = 0 0 =  H° - T  S°  H° = T  S° With signs for  H &  S are the same T =  H°  S°  S° Endo  H(+) Exo  H(-)  S(+)  S(-)  S(+)

1515 Free Energy and work Science and Technology use physical and or chemical processes because these can do work. Economics: To make money €, the work to be preformed must be a possibility and efficient.  G provides information on spontaneity:  G (+) or (-) provides information on the spontaneity of the process @  P,  T = 0 Wasting time:  G is useful because it prevents the wasted effort on process with no inherent tendency to occur.  G isn’t whole story, Kinetics also important: Note that thermodynamically favorable process may still not occur to any appreciable extent because of the Kinetics. - It makes sense to find a catalyst to speed up the reaction. - It makes sense to find a catalyst to speed up the reaction. - Prevents wasting time and resource of seeking a catalyst on a reaction that won’t even work. - Prevents wasting time and resource of seeking a catalyst on a reaction that won’t even work.

1616  G Equations  G°  n  G° prod -  n  G° reaction  H° -   S° - RT ln K eq  G - RT ln Q

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