# deltaG - Gibbs Energy G and Spontaneous Change The second...

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Gibbs Energy, Δ G , and Spontaneous Change The second law of thermodynamics gives us our criterion for a spontaneous (irreversible) process: in any spontaneous process the entropy of the universe ( Δ S univ ) increases, or mathe- matically Δ S univ = Δ S sys + Δ S surr > 0 Then Δ S univ = 0 reversible (equilibrium) process Δ S univ < 0 nonspontaneous process Since calculating Δ S univ is rather impractical we seek a criterion which is only dependent upon the system. Following the arguments given in class and summarized on p. 686-687 of the text we define a new state function, G , the Gibbs free energy G = H TS Then for the change in the Gibbs energy for a process at constant T and P Δ G = Δ H T Δ S (1) Note that since Δ G is a state function T and P need not remain constant during the process. The constant T , P requirement here just means that the initial and final T , P are the same. Whether they vary during the process is immaterial so long as the final T , P are brought back to the same initial values. So the criteria with reference to the system at constant temperature and pressure are Δ G < 0 spontaneous (2) Δ G = 0 equilibrium (reversible) Δ G > 0 nonspontaneous I. Standard Molar Gibbs Energy of Formation Just like for enthalpy we cannot know the absolute value of the Gibbs energy so we define a standard molar free energy of formation, Δ G o f . We choose the same standard states as for the standard enthalpy of formation: solids and liquids - pure material at P = 1 atm and a given T , gases - ideal gas behavior at 1 atm and a given T , dissolved species - 1 M (molar) under a pres- sure of 1 atm at a specified temperature. For a compound its Δ G o f is the change in Gibbs energy accompanying the reaction forming one mole of the pure material in its standard state at 298.15 K from the most stable forms of its constituent elements also in standard states at 298.15 K. For example, for CaCO 3 ( s ), Δ G o f [CaCO 3 ( s )] is the standard Gibbs energy change corresponding to the reaction

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-2- Ca( s ) + C( gr ) + 3/2 O 2 ( g ) CaCO 3 ( s ) Δ H o f (kJ mol 1 ) 0 0 0 -1206.9 Δ G o f (kJ mol 1 ) 0 0 0 -1128.8 S o (J mol 1 K 1 ) 41.6 5.686 205.0 92.9 The data below the reaction are from Appendix B, confirming that Δ G o f of the elements on the left is zero. This is exactly how the standard enthalpy of formation Δ H o f is defined.
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