Previously in Chem104: What determines reaction spontaneity? Entropy Today in Chem104: A recap The 2 nd Law & No Free Lunch What chemists really use- free energy Worksheet: “What’s keeping you alive?”

Hypothesis 1: Spontaneous reactions are exothermic HCl + NaOHNa + + Cl- + H 2 O got warm so  H rxn <0  YES!!! Ba(OH) 2. 8H 2 O + 2NH 4 NO 3 Ba(NO 3 ) 2 + 2NH H 2 O got COLD so  H rxn > 0  NO!!! Conclusion 1: Spontaneous reactions can be exothermic or endothemic

Next, we encountered ENTROPY ENTROPY: the concept An increase in disorder An increase in energy dispersal symbol S ENTROPY: its magnitude Depends on state of matter, solid< liquid<gas Depends on temperature Depends on complexity of molecule/matter calculated like enthalpy:  S rxn =  S prdt -  S rgt

Hypothesis 2: Spontaneous reactions have increased entropy HCl (g) + NH 3 (g)NH 4 Cl(s) Entropy reagent gases >> Entropy solid prdt,  S rxn < 0  NO!!! Ba(OH) 2. 8H 2 O + 2NH 4 NO 3 Ba(NO 3 ) 2 + 2NH H 2 O  S rxn > 0  YES!!! Conclusion 2: Spontaneous reactions can have a decrease in entropy!  S rxn =  S prdt -  S rgt  S rxn = [ (70) + 10(192)] - [ (151)]  S rxn = +432 J/K mol S o, J/K mol = 500 2(151) 150 2(70) 10(192)

Hypothesis 3: Reaction Spontaneity depends on entropy AND enthalpy HCl (g) + NH 3 (g)NH 4 Cl(s) Heat released goes to surroundings?!!  S rxn =  S prdt -  S rgt  S rxn = [94.6] - [ ]  S rxn = J/K mol S o, J/K mol =  H rxn =  H prdt -  H rgt  H rxn = [-315] - [ ]  H rxn = kJ/mol  H o f,k J/mol = ENTROPY DECREASED ENTHALPY DECREASED

HCl (g) + NH 3 (g)NH 4 Cl(s) Heat released to surroundings should increase  S SURR And the net entropy change is:  S net =  S SURR +  S SYS =  S UNIVERSE  S UNIVERSE = J/K mol = 206 J/K mol THE ENTROPY of UNIVERSE INCREASED How much? Use this relationship of enthalpy and entropy:  S SURR = -  H sys / T So the addition of 176 kJ/mol heat to surroundings corresponds to:  S SURR = - (-176 kJ/mol) / 289 = kJ/K mol  S SURR = 591 J/K mol

This is the fundamental requirement long version : a spontaneous change is accompanied by an increase in the total entropy of the system and the surroundings  S TOTAL =  S SURR +  S SYS THE ENTROPY of UNIVERSE INCREASED This is the 2 nd Law of Thermodynamics shorter version : total entropy change must be positive for a spontaneous reactions shortest version : the entropy of the universe is constantly increasing

This is the fundamental requirement Paul’s version : No Free Lunch This means, a spontaneous exothermic reaction is not just creating heat ( or energy). The price is Entropy—more disorder in the Universe.… or a greater distribution of energy THE ENTROPY of UNIVERSE INCREASED This is the 2 nd Law of Thermodynamics Paul Grobstein’s version : The 1 st Law: You can’t win. The 2nd Law: You can’t break even. The 3rd Law: You can’t leave the game.

Chemists rarely use this: Why? Using this fundamental relationship:  S TOTAL =  S SURR +  S SYS it’s too hard—impossible, really—to calculate  S SURR THE ENTROPY of UNIVERSE MUST INCREASE to predict what will happen So how do they predict what will happen? A new thermodynamic quantity was derived: Free Energy “wait a minute - how can you have free energy when you can’t have a free lunch?”

Blame it all on Josiah Gibbs. This is how he figured it: “If the universe obeys:”  S UNIVERSE =  S TOTAL =  S SURR +  S SYS “And we can replace  S SURR :”:”  S TOTAL = -  H SYS / T +  S SYS “It’s all in terms of the system and we can measure it. Yeah!!” Josiah Willard Gibbs

Blame it all on Josiah Gibbs: “It’s all in terms of the system. Yeah!!”  S TOTAL = -  H SYS / T +  S SYS “Now if we do some algebra:” T x  S TOTAL = -  H SYS + T  S SYS “And change the signs:” - T x  S TOTAL =  H SYS - T  S SYS “We can name the result after me!” - T x  S TOTAL =  G SYS =  H SYS - T  S SYS Gibbs Free Energy,  G SYS

“Is this supposed to be an improvement?” Gibbs Free Energy,  G SYS =  H SYS - T  S SYS How do I tell when a spontaneous event occurs?  S TOTAL > 0 is still the Law Since - T x  S TOTAL =  G SYS when  S TOTAL >0,  G SYS < 0 Spontaneous reactions & processes occur when Gibbs Free Energy is negative,  G SYS < 0

“Interpretation, please!”  S TOTAL > 0 is still the Law if- T x  S TOTAL =  G SYS Spontaneous reactions & processes occur when Gibbs Free Energy is negative,  G SYS < 0 it means: the disorder in the universe came from the system

The best part?  G rxn is calculated exactly like  H rxn and  S rxn  G rxn =  G prdt -  G rgt Let’s do it!