Electrochemistry and the Nerst Equation

Objectives:

1. Measure the electrical potential of a zinc/iron battery cell at differing concentrations.

2. Construct an electrolytic cell.

Procedure:

Voltaic Cell

1. Prepare a 100mL of 0.1M Iron (II) Sulfate solution in a 150mL beaker and place the iron strip in the solution.

2. Prepare a 100mL of 0.1M Zinc Sulfate solution in a 150mL beaker and place the zinc strip in the solution.

3. Connect the beakers using the plastic bridge, which must be filled with a KCl solution and cotton wads on either end.

4. Place the positive end of the electrical meter on the Iron strip, and the negative on the end of the Zinc strip. The meter must be set to the 2V scale.

5. Record and then repeat the voltaic cell procedure using a solution of diluted Iron (II) Sulfate: 1mL of 0.1M.

Electrolytic Cell

1. Prepare a solution in a 150mL beaker containing 10g NaCl and 100mL of distilled water.

2. Insert two copper wire conductors.

3. Connect the power supply to the conductors.

4. Add phenolphthalein to the solution.

5. Set the power supply to two Volts.

6. Observe reaction.

Data Tables for Electrochemistry Lab:

Voltaic Cell

Note: The predicted voltage of 0.353 V in the original lab table appears to use older reference values for iron (about −0.41 V for Fe²⁺/Fe). Using the current OpenStax values (Fe²⁺/Fe = −0.447 V, Zn²⁺/Zn = −0.7618 V), the predicted standard cell potential is 0.315 V, as calculated below. The measured values are reported as recorded.

The Nernst Equation Explained

Standard cell potentials (E°) apply only under standard conditions, such as 1 M solutions at 25 °C. The Nernst equation shows how a cell’s potential changes when concentrations differ from standard values:

E_cell = E°_cell − (RT/nF) ln Q

• E_cell: the cell potential under the actual conditions (volts)
• E°_cell: the standard cell potential, E°_cathode − E°_anode
• R: the gas constant, 8.314 J/(mol·K)
• T: temperature in kelvin
• n: moles of electrons transferred in the balanced reaction
• F: Faraday’s constant, 96,485 C per mole of electrons
• Q: the reaction quotient, the ratio of product to reactant concentrations, each raised to its stoichiometric coefficient (pure solids are left out)

At 25 °C (298.15 K), RT/F multiplied by ln 10 is about 0.0592 V, so the equation is often written with base-10 logarithms:

E_cell = E°_cell − (0.0592 V/n) log Q

Worked Example: The Zinc/Iron Cell

Standard reduction potentials from the OpenStax table are:

• Fe²⁺ + 2e⁻ → Fe   E° = −0.447 V
• Zn²⁺ + 2e⁻ → Zn   E° = −0.7618 V

Iron has the less negative potential, so Fe²⁺ is reduced at the iron cathode and zinc is oxidized at the zinc anode. This is why the meter’s positive lead goes on the iron strip. The overall reaction is Zn + Fe²⁺ → Zn²⁺ + Fe, with n = 2.

E°_cell = −0.447 V − (−0.7618 V) = +0.315 V (more precisely, 0.3148 V)

The reaction quotient is Q = [Zn²⁺]/[Fe²⁺]. With both solutions at 0.1 M, as in the first trial, Q = 1 and log Q = 0. The Nernst equation therefore predicts E_cell = E°_cell ≈ 0.315 V. Equal concentrations give the standard potential even though they are not 1 M.

Now suppose the iron solution is diluted to 0.0010 M while the zinc solution stays at 0.10 M (an illustrative case; the lab procedure does not state the final iron concentration, so this is not the exact dilution used in the second trial):

• Q = 0.10/0.0010 = 100, so log Q = 2
• E_cell = 0.3148 V − (0.0592 V/2)(2) = 0.3148 V − 0.0592 V ≈ 0.256 V

Lowering the concentration of the reactant ion (Fe²⁺) lowers the cell potential. Each tenfold change in Q shifts a two-electron cell by about 0.030 V. This matches the direction seen in this lab, where the diluted iron solution gave a lower reading than the first trial. Measured values can also differ from predictions because of oxide films or impurities on the metal strips, small liquid-junction potentials at the salt bridge, and the fact that the Nernst equation strictly uses ion activities rather than molar concentrations.

For a related experiment on how temperature affects cell voltage, see The Effect of Temperature on Voltage in a Galvanic Cell.

Sources:

• OpenStax Chemistry 2e, 17.4: Potential, Free Energy, and Equilibrium
• OpenStax Chemistry 2e, Appendix L: Standard Electrode (Half-Cell) Potentials