# Electrochemistry | General Chemistry 3

## Electric Energy and Charge

SI units used in electrochemistry:

- Joule: J

- Coulomb: C

- Volt: V (1 V = 1 J.C^{-1})

- Ampere: A (1 A = 1 C.s^{-1})

**Electrical Energy U (in J):**

U = V x Z

V = voltage (in V)

Z = charge (in C)

**Electrical Charge Z (in C):**

Z = I x t

I = current (in A)

t = time (in s)

Chemical reactions can occur as a result of the passage of an electric current through a solution

## Electrochemical Cells

Oxidation-reduction reactions: electrons are transferred from one substance to another

⇒ oxidation-reduction reactions can be used to produce an electric current

**Electrochemical cell:**

Setup in which an electric current is obtained from a chemical reaction

It consists in 2 electrodes in solution, a salt bridge and an external circuit

Electrode: solid on the surface of which oxidation-reduction reactions occur

Cathode: electrode at which the reduction occurs

Anode: electrode at which the oxidation occurs

Salt bridge: provides an ionic current path between the 2 solutions with electrodes

Zinc-copper electrochemical cell:

The spontaneous chemical reaction is: Zn (s) + Cu

^{2+}(aq) → Zn^{2+}(aq) + Cu (s)

Zn (s) and Cu (s) are the two electrodes

Zn (s) → Zn^{2+}(aq) + 2 e^{-}[oxidation] ⇒ Zn (s) is the anode

Cu^{2+}(aq) + 2^{ }e^{-}→ Cu (s) [reduction] ⇒ Cu(s) is the cathode

## Cell Diagrams

Representation of an electrochemical cell

Zinc-copper electrochemical cell:

The spontaneous chemical reaction is: Zn (s) + Cu

^{2+}(aq) → Zn^{2+}(aq) + Cu (s)

The cell diagram is Zn (s) | ZnSO_{4}(aq) || CuSO_{4}(aq) | Cu (s)

By convention:

- metal electrodes are written at the ends of the diagram

- left-hand electrode: oxidation reaction ⇒ anode

- right-hand electrode: reduction reaction ⇒ cathode

- single vertical bars: boundaries of phases that are in contact

- double vertical bars: salt bridge

## Nernst Equation

Gibbs energy change of the reaction ΔG_{rxn} (in J.mol^{-1}):

ΔG_{rxn} = ZE_{cell} = - ν_{e}FE_{cell}

Z = charge per mol (in C.mol^{-1})

ν_{e} = stoichiometric coefficient of the electrons in the 2 half reaction equations

F = Faraday’s constant = 96485 C.mol^{-1}

E_{cell} = electromotive force emf of the cell (in V)

Relation between the equilibrium constant and the standard cell voltage:

ln K = $\frac{{\mathrm{\nu}}_{\mathrm{e}}{{\mathrm{FE}}^{0}}_{\mathrm{cell}}}{\mathrm{RT}}$

K = equilibrium constant

ν_{e} = stoichiometric coefficient of the electrons in the 2 half reaction equations

F = Faraday’s constant = 96485 C.mol^{-1}

E^{0}_{cell} = standard cell voltage (in V)

R = ideal gas constant = 8.314 J.mol^{-1}.K^{-1}

T = temperature (in K)

At T = 25°C: ln K = $\frac{{\mathrm{\nu}}_{\mathrm{e}}}{0.02570}$ E^{0}_{cell}

**Nernst equation:**

E_{cell} = E^{0}_{cell} – $\frac{\mathrm{RT}}{{\mathrm{\nu}}_{\mathrm{e}}\mathrm{F}}$ ln Q

E_{cell} = electromotive force emf of the cell (in V)

E^{0}_{cell} = standard cell voltage (in V)

R = ideal gas constant = 8.314 J.mol^{-1}.K^{-1}

T = temperature (in K)

ν_{e} = stoichiometric coefficient of the electrons in the 2 half reaction equations

F = Faraday’s constant = 96485 C.mol^{-1}

Q = reaction quotient

At T = 25°C: E_{cell} = E^{0}_{cell} – $\frac{0.02570}{{\mathrm{\nu}}_{\mathrm{e}}}$_{ } ln Q

Nernst equation: relation between the electromotive force of the cell and the reaction quotient

⇒ electrochemical cells can be used to determine the concentration of ions.

## Half-Reaction E° Values

Relations between E^{0}_{cell}, E^{0}_{red} and E^{0}_{ox}:

E^{0}_{cell} = E^{0}_{red} + E^{0}_{ox}

E^{0}_{cell} = standard cell voltage (in V)

E^{0}_{red} = standard reduction voltage (in V)

E^{0}_{ox} = standard oxydation voltage (in V)

For a particular half reaction: E^{0}_{ox} = - E^{0}_{red}

Cu

^{2+}+ 2 e^{-}→ Cu [E^{0}= + 0.34 V]

Cu → Cu^{2+}+ 2 e^{-}[E^{0}= - 0.34 V]

It is not possible to measure the voltage of a single electrode. However, we can determine this value by measuring the difference in voltage between a standard electrode and the desired electrode

In electrochemistry, we use a Standard Hydrogen Electrode (SHE):

nonreactive metal in a 1.0*M* H^{+} (aq) solution through which hydrogen gas is bubbled at P = 1.0 bar.

By convention, the voltage of the SHE is E^{0} = 0 V

⇒ 2 H^{+} (aq) + 2 e^{-} → H_{2} (g) [E^{0}_{red} = 0 V]

## Faraday’s Laws

Electrolysis: process by which a chemical reaction is made to occur by the passage of an electric current through the solution. It is described quantitatively by Faraday’s laws

First Faraday’s law:

the mass of elements deposited at an electrode is directly proportional to the charge

⇒ m α Q

Second Faraday’s law:

the mass of elements deposited / liberated at an electrode is directly proportional to the molar mass of the elements divided by the change in magnitude of the oxidation state of the substance

⇒ m α $\frac{\mathrm{M}}{{\mathrm{\nu}}_{\mathrm{e}}}$

**Faraday’s law of electrolysis:**

m = $\frac{\mathrm{It}}{\mathrm{F}}$ x $\frac{\mathrm{M}}{{\mathrm{\nu}}_{\mathrm{e}}}$

m = mass deposited as metal or evolved as gas (in g)

I = current (in A)

t = time (in s)

F = Faraday’s constant = 96485 C.mol^{-1}