Understanding Spontaneity in Voltaic Cells: E, ∆G, w, Q’, K

Spontaneity in Voltaic Cells Relating E, ∆G, w,Q’, K

Eored + Eoox = Eo • Higher Eored means stronger oxidizer • Higher Eoox means stronger reducer • If Eo is positive , then the reaction is spontaneous.

∆G - It’s fun • ∆G is the available free energy - or energy available for work • By convention, we identify work which is negative with work which is being done by the system on the surroundings. And negative free energy change is identified as defining a spontaneous process. ∆G = -w • Work in a voltaic cell comes from e- movement (Q’)- The movement is from charge attraction (E). • So… w = Q’E

Q’ = (9.648x104 ) (number of moles (n)) • Q’ = nF • ∆G = -w so ∆G = -Q’E and ∆G = -nF E • E is in volts, so Q’E is in (coulomb volts) which is equal to Joules (J) the unit for ∆G

Example Zn + H+ → Zn2+ + H2 Half Reactions: Zn → Zn2+ + 2e- Eoox = 0.762v H+ + 2e- → H2 Eored = 0.000v Eo = 0.762v ∆G = -nF E = -2(9.648x104 )(0.762v) ∆G = -147000J = -147kJ

K means Equilibrium Konstant • Equilibrium means the reaction will also go in reverse: A + B ↔ C + D • If the reaction goes in reverse that will change the voltage (E) and the free energy (∆G)

∆G = -RT lnK R is a constant = 8.31 T is temperature in Kelvin (K) • If ∆G = -nF E then E = • So… E = lnK

If you have standard conditions (1atm, 25oC) then we know… • So Eo lnK

Understanding Spontaneity in Voltaic Cells: E, ∆G, w, Q’, K