Nils Walter: Chem 260The spontaneity of chemical reactionsAtkins, Chapter 4Reaction: 2 H2(g) + O2(g) →→→→2 H2O(l)⇒⇒⇒⇒∆∆∆∆rStotal= ∆∆∆∆rSsys+ ∆∆∆∆rSsurr= +1590 J K-1mol-1∆∆∆∆rS = ΣΣΣΣννννSm(products) -ΣΣΣΣννννSm(reactants)Here: ∆rS = 2Sm(H2O, l) - {2Sm(H2, g) + Sm(O2, g)}= -317 J K-1mol-1Would not be spontaneous!? 1111920298572−−−+=−−=∆−=∆molKJKmolkJTHSrsurrrBut... Is spontaneous!!!Nils Walter: Chem 260The hydrophobic effect: Water entropy drives protein foldingThe hydrophobic side chains of a protein collapse on the way to the functional native structureNils Walter: Chem 260The Gibbs free enthalpy (“Gibbs energy”)To judge whether a chemical reaction is spontaneous, we need to consider entropy changes in both system and surroundings⇒⇒⇒⇒Josiah Willard Gibbs (1839-1903; theoretician @ Yale):Definition: G = H - TS THSSSSsyssurrsystotal∆−∆=∆+∆=∆(@ constant p, T)all state functions⇒⇒⇒⇒G is a state function (no memory of path) H, S are extensive ⇒⇒⇒⇒G is extensive (increases with n) ⇒⇒⇒⇒change in G: ∆∆∆∆G = ∆∆∆∆H - T ∆∆∆∆S = -T ∆∆∆∆Stotal(@ constant p, T) ⇒⇒⇒⇒The Gibbs free enthalpy calculates changes in entropy of both system and surroundings from system parameters aloneNils Walter: Chem 260Spontaneity∆∆∆∆G = ∆∆∆∆H - T ∆∆∆∆S = -T ∆∆∆∆Stotal(@ constant p, T) 2nd law of thermodynamics:∆∆∆∆Stotal≥≥≥≥0 (J K-1)⇒⇒⇒⇒ ∆∆∆∆G ≤≤≤≤0 (J) (@ constant p, T)“In a spontaneous change at constant temperature and pressure, the Gibbs energy decreases”Nils Walter: Chem 260∆∆∆∆G describes the maximumnon-expansion work @ constant p, Tinfinitesimal changes of G: dG = dH - TdS (2nd law)⇒⇒⇒⇒dG = dU + pdV - TdS⇒⇒⇒⇒dG = dw + dq + pdV - TdS⇒⇒⇒⇒dG = -pexdV + dw’ + dq + pdV - TdSexpansion worknon-expansion workFor reversible changes: p = pexand dq = TdS⇒⇒⇒⇒dG = dw’rev= dw’max; overall: ∆∆∆∆G = w’maxand dH = dU + pdV (@ constant p)and dU = dw + dq (1st law)and dw = -pexdV + dw’Nils Walter: Chem 260Meaning of the Gibbs energyAtkins: “If we know ∆∆∆∆G of a reaction, then we know the maximum non-expansion work that we can do by harnessing the reaction in some way at constant pressure and temperature”G = H - TSH = measure of the total energy that can be obtained from the system as heatTS = measure of the energy that is stored in the random motion of molecules in the system⇒⇒⇒⇒Difference (= G) becomes the energy stored in the orderly motion and arrangement of the molecules in the systemNils Walter: Chem 260Sample problem:A hard-working human brain, perhaps one that is grappling with physical chemistry, operates at about 25W. What mass of glucose must be consumed to sustain that power output for an