The Nernst equation predicts the voltage of an electrochemical cell when the reactants and products are not at standard conditions. This matters because real batteries, sensors, and corrosion processes rarely operate with all solutes at 1 M and all gases at 1 atm. By connecting concentration to electrical potential, the equation explains why a cell voltage changes as a reaction proceeds.
It also shows how chemistry can create useful electrical energy from differences in chemical potential.
Key Facts
- Nernst equation at 25 °C: E = E° - (0.0592 V/n) log Q
- General Nernst equation: E = E° - (RT/nF) ln Q
- Q is the reaction quotient, built like K but using current concentrations or pressures.
- n is the number of moles of electrons transferred in the balanced redox reaction.
- At equilibrium, E = 0 and Q = K, so E° = (0.0592 V/n) log K at 25 °C.
- For a concentration cell at 25 °C, E = (0.0592 V/n) log(C_high/C_low) when the electrodes are identical.
Vocabulary
- Cell potential
- Cell potential is the voltage produced by an electrochemical cell due to the tendency of electrons to flow from anode to cathode.
- Standard cell potential
- Standard cell potential is the voltage of a cell when all aqueous species are 1 M, gases are 1 atm, and the temperature is usually 25 °C.
- Reaction quotient
- The reaction quotient Q describes the current ratio of product activities to reactant activities for a chemical reaction.
- Concentration cell
- A concentration cell is an electrochemical cell that produces voltage from a concentration difference between two otherwise identical half-cells.
- Salt bridge
- A salt bridge allows ions to move between half-cells so charge does not build up and stop electron flow.
Common Mistakes to Avoid
- Using K instead of Q in the Nernst equation is wrong because K applies only at equilibrium, while Q describes the cell under current conditions.
- Forgetting to balance electrons before choosing n is wrong because n must match the balanced overall redox reaction, not just one unbalanced half-reaction.
- Putting solids and pure liquids into Q is wrong because their activities are treated as 1 and do not appear in the reaction quotient.
- Reversing the concentration ratio in a concentration cell is wrong because electrons flow in the direction that reduces the concentration difference, so the high and low concentration terms must be placed consistently.
Practice Questions
- 1 A cell has E° = 1.10 V and transfers n = 2 electrons. At 25 °C, Q = 0.010. Use E = E° - (0.0592/n) log Q to find E.
- 2 A concentration cell uses identical Cu electrodes with Cu2+ concentrations of 1.00 M and 0.0100 M. For Cu2+ + 2e- -> Cu, calculate the cell potential at 25 °C.
- 3 Explain why the voltage of a galvanic cell decreases as it approaches equilibrium, using the terms Q, K, and E.