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Previously in Chem104: What determines reaction spontaneity? Entropy

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 + NaOH.

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Previously in Chem104: What determines reaction spontaneity? Entropy

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

  2. Hypothesis 1: Spontaneous reactions are exothermic HCl + NaOH Na+ + Cl- + H2O got warm so DHrxn <0  YES!!! Ba(OH)2.8H2O + 2NH4NO3 Ba(NO3)2 + 2NH3+ 10H2O got COLD so DHrxn> 0  NO!!! Conclusion 1: Spontaneous reactions can be exothermic or endothemic

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

  4. Hypothesis 2: Spontaneous reactions have increased entropy HCl (g) + NH3 (g) NH4Cl(s) So,J/K mol = 500 2(151) 150 2(70) 10(192) DSrxn = DSprdt - DSrgt Ba(OH)2.8H2O + 2NH4NO3 Ba(NO3)2 + 2NH3+ 10H2O DSrxn = [150 + 2(70) + 10(192)] - [500 + 2(151)] DSrxn = +432 J/K mol DSrxn> 0  YES!!! Entropy reagent gases >> Entropy solid prdt, DSrxn< 0  NO!!! Conclusion 2: Spontaneous reactions can have a decrease in entropy!

  5. Hypothesis 3: Reaction Spontaneity depends on entropy AND enthalpy HCl (g) + NH3 (g) NH4Cl(s) So,J/K mol = 187 193 94.6 DSrxn = DSprdt - DSrgt DSrxn = [94.6] - [187 + 193] DSrxn = - 285 J/K mol ENTROPY DECREASED DHof,kJ/mol = -92.3 -46.3 -315 DHrxn = DHprdt - DHrgt DHrxn = [-315] - [-92.3 + -46.3] DHrxn = - 176 kJ/mol ENTHALPY DECREASED Heat released goes to surroundings?!!

  6. Heat released to surroundings should increase DSSURR How much? Use this relationship of enthalpy and entropy: DSSURR = -DHsys / T So the addition of 176 kJ/mol heat to surroundings corresponds to: DSSURR = - (-176 kJ/mol)/ 289 = 0.591 kJ/K mol DSSURR = 591 J/K mol HCl (g) + NH3 (g) NH4Cl(s) And the net entropy change is: DSnet = DSSURR + DSSYS = DSUNIVERSE DSUNIVERSE= 591 - 285 J/K mol = 206 J/K mol THE ENTROPY of UNIVERSE INCREASED

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

  8. This is the fundamental requirement THE ENTROPY of UNIVERSE INCREASED This is the 2nd Law of Thermodynamics 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 Paul Grobstein’s version: The 1st Law: You can’t win. The 2nd Law: You can’t break even. The 3rd Law: You can’t leave the game.

  9. Chemists rarely use this: THE ENTROPY of UNIVERSE MUST INCREASE to predict what will happen Why?Using this fundamental relationship: DSTOTAL = DSSURR + DSSYS it’s too hard—impossible, really—to calculate DSSURR 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?”

  10. Blame it all on Josiah Gibbs. Josiah Willard Gibbs 1839-1903 This is how he figured it: “If the universe obeys:” DSUNIVERSE = DSTOTAL = DSSURR + DSSYS “And we can replace DSSURR :” DSTOTAL = -DHSYS / T + DSSYS “It’s all in terms of the system and we can measure it. Yeah!!”

  11. Blame it all on Josiah Gibbs: “It’s all in terms of the system. Yeah!!” DSTOTAL = -DHSYS / T + DSSYS “Now if we do some algebra:” T xDSTOTAL = -DHSYS + T DSSYS “And change the signs:” - T xDSTOTAL = DHSYS - T DSSYS “We can name the result after me!” -T xDSTOTAL = DGSYS = DHSYS - T DSSYS Gibbs Free Energy, DGSYS

  12. “Is this supposed to be an improvement?” Gibbs Free Energy, DGSYSDGSYS = DHSYS - T DSSYS How do I tell when a spontaneous event occurs? DSTOTAL > 0 is still the Law Since -T xDSTOTAL = DGSYS when DSTOTAL >0, DGSYS < 0 Spontaneous reactions & processes occur when Gibbs Free Energy is negative, DGSYS < 0

  13. “Interpretation, please!” DSTOTAL > 0 is still the Law if -T xDSTOTAL = DGSYS it means: the disorder in the universe came from the system Spontaneous reactions & processes occur when Gibbs Free Energy is negative, DGSYS < 0

  14. The best part? DGrxn is calculated exactly like DHrxn and DSrxn DGrxn = DGprdt - DGrgt Let’s do it!

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