Electrochemistry | General Chemistry 3

Electrochemistry is studied in this chapter: electric energy and charge, electrochemical cells and their diagrams, Nernst equation, 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 in order to maintain the charge balance in the cell
 

Zinc-copper electrochemical cell:

The spontaneous chemical reaction is: Zn (s) + Cu2+ (aq) → Zn2+ (aq) + Cu (s)
Zn (s) and Cu (s) are the 2 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

A cell diagram is a 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 = νeFE0cellRT

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 =  νe0.02570 E0cell 

 


Nernst equation:

Relationship between the electromotive force of the cell and the reaction quotient ⇒ electrochemical cells can be used to determine the concentration of ions:
 

Ecell = E0cell  –  RTνeF  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  –  0.02570νe  ln Q

Half-Reaction E° Values

Relationship 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 directly measure the voltage of a single electrode but it can be determined by measuring the voltage difference between a standard electrode and the desired electrode 
⇒ in electrochemistry, a Standard Hydrogen Electrode (SHE) is used: 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 ⇒ SHE is the primary reference electrode
2 H+ (aq) + 2 e- → H2 (g)     [E0red = 0 V]

Faraday’s Laws

Electrolysis: process by which a chemical reaction occurs by the passage of an electric current through the solution. It is quantitatively described 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 Mνe

 

Faraday’s law of electrolysis:
 

m = ItF x Mνe

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