# Lecture 3: Nernst Equation and Spontaneous Reactions

### Various Formulas Required for this Lecture

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

﻿$\Delta G = -RTlnK$﻿

﻿$E^{\circ }=\frac{RT}{nF}lnK$﻿

#### How to Find ﻿$\Delta G$﻿

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

﻿$E^{\circ }$﻿ - at standard conditions

1 Faraday = 96,488 c/mol ﻿$e^{-}$﻿ = The change of 1 mole, ﻿$6.023 \cdot 10^{23} e^{-}$﻿

﻿$\Delta G$﻿ ﻿$=$﻿ ﻿$-n$﻿ ﻿$\cdot$﻿ ﻿$F$﻿ ﻿$\cdot$﻿ ﻿$E$﻿

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

reactant reactant ﻿$mole^{-}$﻿

### Nernst Equation

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

﻿$\Delta G=\Delta G^{\circ }+RTlnQ$﻿

﻿$-nFE=-nFE^{\circ }+RTlnQ$﻿

﻿$E=E^{\circ }-\frac{RT}{nF}lnQ$﻿

#### At Equilibrium

﻿$Q = K$﻿

﻿$E = O$﻿

﻿$\underbrace{\Delta G = O}$﻿

﻿$E^{\circ }=\frac{RT}{nF}lnK$﻿

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

﻿$F_{2}+2I^{-}\rightarrow I_{2}+2F^{-}$﻿ Spontaneous as written

﻿$H_{g}+{2A_{g}}^{+}\rightarrow {H_{g}}^{2+}+2A_{g}$﻿ Spontaneous as written

﻿${C_{u}}^{2+}+2I^{-}\rightarrow l_{2}+C_{u}$﻿ Spontaneous in reverse

﻿${C_{u}}^{2+}+{2C_{r}}^{2+}\rightarrow C_{u}+{2C_{r}}^{3+}$﻿ Spontaneous as written