Cell Potential Under Nonstandard Conditions (College Board AP Chemistry)

Deviations from standard conditions and cell potential

• Equilibrium arguments, such as Le Châtelier’s principle, do not apply to electrochemical systems because these systems are not in equilibrium
• For a standard cell where the concentrations are the same, the reaction quotient, Q, will be equal to 1

Reaction quotient, Q =

• Since we know that the standard cell potential is calculated at 1 M and 1 atm, we know that the value for Q (the reaction quotient) would have to be 1
• As a cell reaches equilibrium, the reaction quotient reaches the equilibrium constant, K, (Q = K ) and the magnitude of the cell potential decreases to zero
  • The cell is not creating a voltage and is now 'dead'

• A value for the cell potential of zero means that the reaction has reached equilibrium 
• If we change the concentration, we can change the magnitude of E_cell 
  • This is now no longer a cell operating under standard conditions!

Changing concentrations in a galvanic cell

Standard conditions in a Zn/Zn²⁺ Cu²⁺/Cu cell 

Zn (s) → Zn2+ (aq) + 2e–	Eo = -0.76 V	Oxidation
Cu2+ + 2e– → Cu (s)	Eo = +0.34 V	Reduction

E^o _cell = E^o_red - E^o_ox

E^o_cell = 0.34 - (-0.76) = 1.10 V

• If we change the concentrations to:

New Concentration	New Concentration
[Zn2+] = 5.00 M [Cu2+] = 1.00 M	[Zn2+] = 1.00 M [Cu2+] = 5.00 M
Q = 5	Q = 0.2
Ecell = 1.10 - 0.02 = 1.08 V which is now a lower value	Ecell = 1.10 - (-0.02) = 1.12 V which is now a higher value
This is a deviation that takes the cell further from equilibrium than Q = 1 will increase the magnitude of the cell potential relative to Eocell	This is a deviation that takes the cell closer to equilibrium than Q = 1 will decrease the magnitude of the cell potential relative to Eocell

Concentration Cells

• A voltage can be generated by constructing an electrochemical cell in which each compartment contains the same redox active solution but at different concentrations
• The voltage is produced as the concentrations equilibrate
• For example, if we look at the following cell containing two different concentrations of zinc sulfate solution 

Diagram to show two different concentrations of zinc sulfate in a concentration cell

Reduction occurs at the more concentrated half-cell and oxidation occurs at the less concentrated half-cell

• The two different reactions taking place are
  • Oxidation occurs in the less concentrated half-cell:
    • Zn²⁺ (aq) _{(0.50 M)} + 2e^– → Zn (s) 
  • Reduction occurs in the more concentrated half-cell:
    • Zn (s) → Zn²⁺ (aq) _{(1.00 M)} + 2e^–
• So for this reaction, E_cell will = 0
  • E^o_cell = E^o_red - E^o_ox
  • E^o_cell = -0.76 - (-0.76) = 0.00 V
• From the concentrations of the two different solutions of zinc sulfate, we can calculate the value for Q, or the reaction quotient
  • Q =
  • In this example Q = 
  • Solids are not included in this calculation
• Therefore, E_cell = 
• E_cell = 8.91 x 10^-3 V
• This is positive so is a spontaneous reaction
• As the concentrations of each half cell get closer together over time, the value for Q will increase and E_cell will decrease
  • When Q = 1 the reaction will be in equilibrium and E_cell will be equal to 0
  • If there is no difference in concentration, there is no longer a requirement for concentrations to equalise which creates the potential difference in the cell
• If E_cell = 0, then the cell is 'dead'