Unit 9: Topic 8 - Cell Potential and Free Energy

Question 1

What kinds of redox reactions occur within electrochemical cells? What comes about as a result of these redox reactions?

Answer 1

• In an electrochemical cell, a reduction half reaction will occur at the cathode, and an oxidation half reaction will occur at the anode.
• As a result of the electromotive force caused by these redox reactions, electrons will flow through a wire from the anode to the cathode, converting chemical energy to electrical energy.
• The cell potential, denoted by E_cell, is the measure of the potential difference between two half cells in an electrochemical cell. The potential difference is caused by the ability of electrons to flow from one half cell to another. The cell potential is measured in volts(v) with a voltmeter.
• The substance being reduced would be the oxidizing agent, and the substance being oxidized would be the reducing agent. Another way to think of the cell potential is that it’s the difference between the potential for the reducing agent to become oxidized and the oxidizing agent to become reduced.

Question 2

What is the standard reduction potential and how can we use it to determine the thermodynamic favorability of an electrochemical cell?

Answer 2

• You will often be given a table of standard reduction potentials. They are essentially a long list of reduction half reactions and their corresponding potentials. In addition, the fact that they are standard reduction potentials means that all of the substances will be in their standard state conditions, which implies that all of the gases will be at 1atm, anything aqueous is at a concentration of 1.0 M, and the temperature is 25 degrees Celsius.
• The standard reduction potentials of the two half reactions that make up a electrochemical cell can be used to calculate its overall cell potential. If the overall standard cell potential is positive, then the overall reaction would be thermodynamically favored and therefore spontaneous.
• Similarly, if the overall standard cell potential is negative, then the overall reaction would be thermodynamically unfavored and therefore nonspontaneous. Since these type of reactions would be nonspontaneous, they require an externally-provided potential in order for the reaction to proceed, such as in the case of electrolytic cells. This also means that the substances involved in these reactions would be much better reducing agents and oxidation would be more favorable.

Question 3

How do you calculate the standard cell potential of an electrochemical cell?

Answer 3

• The overall cell potential can be calculated using the equation E_cell = E_red - E_oxid, where both E_red and E_oxid are standard reduction potentials.
• To determine which half reaction inside a galvanic cell will be oxidized or reduced, look at the signs of the reduction potentials of the half reactions. The half reaction with the more positive reduction potential will be reduced and the half reaction with the less positive reduction potential will be oxidized. Otherwise, the electrochemical cell will not be spontaneous, as it will result in a negative overall cell potential.

Question 4

Calculate the standard cell potential of a galvanic cell that uses the Ag / Ag+ and Sn / Sn2+ half-cell reactions. Write the balanced equation for the overall cell reaction that occurs. Identify the anode and the cathode.

E_Ag= +0.80V
E_Sn= −0.14V

Answer 4

• We are given that the standard reduction potential of silver is +0.80V and the standard reduction potential of tin is -0.14V. This means that the silver half cell will undergo reduction because it has a more positive reduction potential, and the tin half cell will undergo oxidation.
• Oxidation(anode): Sn(s)→Sn2+(aq)+2e− and reduction(cathode): Ag+(aq)+e−→Ag(s)
• Before combining the two half reactions, multiply the silver half reaction by 2 to obtain the same number of electrons as the tin half reaction. Thus, the overall reaction will be Sn(s)+2Ag+(aq)→Sn2+(aq)+2Ag(s)
• E_cell = E_red - E_oxid, where E_red = +0.80V and E_oxid = -0.14V. Thus, E_cell = +0.80V - (-0.14V) = +0.94V

Question 5

How can you link Gibbs free energy and the standard cell potential?

Answer 5

• The ideas of free energy and cell potential can be linked using the equation ΔGo = -nFEo, where ΔGo is the change in standard Gibbs free energy, n is the total number of moles of electrons being transferred in the overall redox reaction, F is the Faraday’s constant(96485 coulombs per mole of electrons, and Eo is the standard cell potential.
• Since n and F will both always be positive quantities, the sign of the standard Gibbs free energy change depends on the sign of the standard cell potential.
• If Eo > 0, then ΔGo < 0. Since ΔGo is negative, the reaction will be spontaneous.
• If Eo < 0, then ΔGo > 0. Since ΔGo is positive, the reaction will be nonspontaneous.