Lecture 3: Nernst Equation and Spontaneous Reactions

Various Formulas Required for this Lecture

ΔG=nFE\Delta G = -nFE ΔG=nFE\Delta G = -nFE ΔG=nFE\Delta G^{\circ }=-nFE^{\circ }

ΔG=RTlnK\Delta G = -RTlnK

E=RTnFlnKE^{\circ }=\frac{RT}{nF}lnK


How to Find ΔG\Delta G

  1. Equilibrium constant
  2. EMF of the cell


n - # of electrons transferred in the reaction

ESU - electron static unit - each electron has a charge

E - at any condition

EE^{\circ } - at standard conditions

1 Faraday = 96,488 c/mol ee^{-} = The change of 1 mole, 6.0231023e6.023 \cdot 10^{23} e^{-}


ΔG\Delta G == n-n \cdot FF \cdot EE

J/mol == mole/mol \cdot J/V \cdot V

reactant reactant molemole^{-}


Nernst Equation

ΔG=nFE\Delta G = -nFE ΔG=nFE\Delta G^{\circ }=-nFE

ΔG=ΔG+RTlnQ\Delta G=\Delta G^{\circ }+RTlnQ

nFE=nFE+RTlnQ-nFE=-nFE^{\circ }+RTlnQ

E=ERTnFlnQE=E^{\circ }-\frac{RT}{nF}lnQ


At Equilibrium

Q=KQ = K

E=OE = O

ΔG=O\underbrace{\Delta G = O}

E=RTnFlnKE^{\circ }=\frac{RT}{nF}lnK


Spontaneous Reactions - will take place when a reduction half-reaction is paired with an oxidation half reaction lower on the table. If paired the other way the reverse reaction is spontaneous.

Example

F2+2II2+2FF_{2}+2I^{-}\rightarrow I_{2}+2F^{-} Spontaneous as written

Hg+2Ag+Hg2++2AgH_{g}+{2A_{g}}^{+}\rightarrow {H_{g}}^{2+}+2A_{g} Spontaneous as written

Cu2++2Il2+Cu{C_{u}}^{2+}+2I^{-}\rightarrow l_{2}+C_{u} Spontaneous in reverse

Cu2++2Cr2+Cu+2Cr3+{C_{u}}^{2+}+{2C_{r}}^{2+}\rightarrow C_{u}+{2C_{r}}^{3+} Spontaneous as written









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