Chem 2 Chp 16

• • more atoms = more degrees of freedom
  • number of atoms = number of degrees
• • greatest entropy = high molar mass and high number of atoms
• • goal of thermodynamics is to predict spontaneity
  • spontaneity: occurs without ongoing outside intervention
• • ehtalpy alone cannot predict spontaneity
• • entropy: measure of disorder or randomness of a system
• • S: thermo. func. that increases with number of energetically equivalent ways to arrange components of a system to achieve a particular state
  • S = k In w
  • k = 1.38 * 10^-23 J/K
  • w = number of microstates
• • microstate: each individual state of each individual particle
  • as long as pressure, volume, and temperature are constant, w remains unchanged
• • 2nd law: for any spontaneous process, the energy of the universe increases; greater dispersal or randomization of energy
  • delta s univ > 0
• • state function: delta s = s final - s initial
  • all that matters = beginning and final
  • path independent function
  • NOT work and heat
• Changes in State

  • solid -> liquid(increase in S)
  • liquid -> gas (large increase in S)
  • solid -> gas(large increase in S)
  • opposite direction = a decrease
• Distinguish between System and Surroundings

  • delta S univ = delta S sys + delta S surr
  • exothermic = increase of entropy of surroundings and decrease entropy of system
  • endothermic = decrease of entropy of surroundings and increase entropy of system
  • as temperature increases -> entropy of surroundings decreases
• Quantifying entropy changes in the surroundings

  • q sys (-): emits heat into surroundings -> increases entropy of surroundings
  • q sys (+): absorbs heat from surroundings -> decreases entropy of surroundings
  • Magnitude of delta S surr is proportional to magnitude of q sys
  • Magnitude of delta S surr is inversely proportional to temperature
• Gibbs Free Energy

  • delta G = delta H - T delta S
  • in order for G to be spontaneous delta S univ needs to be > 0
  • decrease G ( delta G > 0) -> spontaneous (-)
  • increase G ( delta G < 0) -> nonspontaneous (+)
• Gibbs Free Energy Cases

  • Case 1 : delta H (-) [exothermic] & delta S (+) [entropy increase] = spontaneous at all T
  • Case 2 : delta H (+) [endothermic] & delta S (-) [entropy decrease] = nonspontaneous at all T
  • Case 3 : delta H (-) [exothermic] & delta S (-) [entropy decrease] = spontaneous at low T & nonspontaneous at high T
  • Case 4 ; delta H (+) [endothermic] & delta S (+) [entropy increase] = nonspontaneous at low T & spontaneous at high T
• • only need to know delta S sys, delta H sys, and T to predict spontaneity
• • delta S rxn: standard entropy change for a reaction
• • 3rd law of thermo: entropy of a perfect crystal at absolute zero
  • nothing has an entropy of zero
• • more complex -> more motions allowed -> vibrations therefore more entropy
• • delta G f: change in energy when 1 mol of compound forms from its constituent elements in their standard states
• Stepwise Reaction Sequence

  • if multiplied -> delta G rxn is also multiplied
  • if reversed -> delta G rxn changes sign
  • if chemical equation can be expressed as a sum -> add all the free energies per step
• • Q is used for nonstandard conditions
  • if delta G is more negative than delta G0 = spontaneous
  • if delta G is less negative than delta G0 = nonspontaneous
• • at equilibrium -> K = Q & delta G rxn = 0
  • when K < 1 (reactant favored), InK is negative -> delta G0 = (+)
  • when K > 1 (product favored), lnK is positive -> delta G0 = (-)
  • when K = 1 (neither is favored), lnK = 0 -> delta G0 rxn = 0