Entropy = S Entropy is disorder or randomness

2nd Law of Thermodynamics Suniverse > 0 for spontaneous processes spontaneous = no external intervention Ssystem Ssurroundings positional disorder energetic disorder

Energetic Disorder P.E. K.E. random ordered a) endothermic reaction b)  random ordered reactants a) endothermic reaction b) exothermic reaction P.E. Hsystem 0 < products Hsurroundings 0 > Ssurroundings > 0

Ssurr depends on T Ssurr = - Hsystem (J/K) T heat  surroundings high T small effect low T relatively larger effect

Positional Disorder With 1 mole of gas, Not probable (1/2) (1/2) (1/2) = 1/64 With 1 mole of gas, Not probable

Positional Disorder Boltzman ordered states low probability low S RIP S = k ln W W = degrees of freedom Boltzman ordered states low probability low S disordered states high probability high S  Ssystem  Positional disorder Increases with number of possible positions (energy states) Ssolids < Sliquids << Sgases

Entropy (J/K) [heat entering system at given T] convert q to S Pext = 1.5 atm E = 0 w = -182 J q = +182 J T = 298 K E = 0 System 2 Pext = 0 atm w = 0 q = 0

 Pext = Pint + dP System 3 reversible process - infinitely slow wr= P1 = 6.0 atm P2 = 1.5 atm V1 = 0.4 L V2 = 1.6 L T1 = 298 K = T2 Pext = Pint + dP reversible process - infinitely slow V2 wr= - Pext  dV =- nRT dV V  = - nRT ln (V2/V1) V1

Ssystem Ssurr = - Hsystem Ssystem = qr = 1120 J T T 298 K System 1 Pext = 1.5 atm w = -182 J q = +182 J S = System 2 Pext = 0 atm w = 0 q = 0 S = System 3 Pext = Pint + dP wr = qr = S = -nRT ln (V2/V1) = - 1120 J + 1120 J 3.77 J/K 3.77 J/K 3.77 J/K Ssurr = - Hsystem T Ssystem = qr T = 1120 J 298 K

3rd Law of Thermodynamics Entropy of a perfect crystalline substance at 0 K = 0

Entropy curve S Temperature (K) gas liquid solid vaporization qr T fusion Temperature (K)

Entropy At 0K, S = 0 Entropy is absolute S  0 for elements in standard states S is a State Function Sorxn = nSoproducts - nSoreactants S is extensive

Increases in Entropy 1. Melting (fusion) Sliquid > Ssolid 2. Vaporization Sgas >> Sliquid 3. Increasing ngas in a reaction Heating ST2 > ST1 if T2 > T1. Dissolution Ssolution > (Ssolvent + Ssolute) ? 6. Molecular complexity number of bonds 7. Atomic complexity e-, protons and neutrons