# Electrochemistry | General Chemistry 3

Electrochemistry is studied in this chapter: the electric energy and charge, the electrochemical cells and their diagrams, the Nernst equation, the standard cell voltages of half reactions, the Faraday’s laws.

## 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) + Cu2+ (aq) → Zn2+ (aq) + Cu (s)
Zn (s) and Cu (s) are the two electrodes
Zn (s) → Zn2+ (aq) + 2 e-    [oxidation]   ⇒   Zn (s) is the anode
Cu2+ (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) + Cu2+ (aq) → Zn2+ (aq) + Cu (s)
The cell diagram is Zn (s) | ZnSO4 (aq) || CuSO4 (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 ΔGrxn (in J.mol-1):

ΔGrxn = ZEcell = - νeFEcell

Z = charge per mol (in C.mol-1)
νe = stoichiometric coefficient of the electrons in the 2 half reaction equations
F = Faraday’s constant = 96485 C.mol-1
Ecell = 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
νe = stoichiometric coefficient of the electrons in the 2 half reaction equations
F = Faraday’s constant = 96485 C.mol-1
E0cell = 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 =  $\frac{{\mathrm{\nu }}_{\mathrm{e}}}{0.02570}$ E0cell

Nernst equation:

Ecell = E0cell  –  $\frac{\mathrm{RT}}{{\mathrm{\nu }}_{\mathrm{e}}\mathrm{F}}$  ln Q

Ecell = electromotive force emf of the cell (in V)
E0cell = standard cell voltage (in V)
R = ideal gas constant = 8.314 J.mol-1.K-1
T = temperature (in K)
νe = 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: Ecell = E0cell  –  $\frac{0.02570}{{\mathrm{\nu }}_{\mathrm{e}}}$  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 E0cell, E0red and E0ox:

E0cell = E0red + E0ox

E0cell = standard cell voltage (in V)
E0red = standard reduction voltage (in V)
E0ox = standard oxydation voltage (in V)

For a particular half reaction: E0ox = - E0red

Cu2+ + 2 e- → Cu     [E0 = + 0.34 V]
Cu → Cu2+ + 2 e-     [E0 = - 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 1.0M H+ (aq) solution through which hydrogen gas is bubbled at P = 1.0 bar.

By convention, the voltage of the SHE is E0 = 0 V
⇒ 2 H+ (aq) + 2 e- → H2 (g)     [E0red = 0 V]

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

the mass of elements deposited at an electrode is directly proportional to the charge
⇒ m α Q

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 $\frac{\mathrm{M}}{{\mathrm{\nu }}_{\mathrm{e}}}$

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