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.
Understanding Chemistry: The Nernst Equation
Voltage is a measure of how strongly a redox reaction can push electrons through an outside wire. Its deeper connection is to Gibbs free energy. A reaction with a more negative free energy change can provide more electrical work.
Cell potential is linked to that free energy per mole of electrons transferred. This is why the electron count matters.
If a balanced reaction transfers more electrons, the same overall free energy is spread across more charge. The voltage is therefore not simply multiplied by the coefficients in a balanced equation.
The Nernst equation adjusts the standard voltage by measuring the current chemical balance of the reaction. In its general form, cell potential equals standard cell potential minus the product of the gas constant, temperature, and the natural logarithm of the reaction quotient, all divided by the product of the electron count and Faraday constant. The reaction quotient must match the balanced overall cell reaction exactly.
Products go in the top part, reactants go in the bottom part, and each value is raised to its balanced coefficient. Pure solids and pure liquids are normally left out because their effective concentration changes very little. Students often lose marks by using a half reaction quotient when the question requires the full cell reaction.
The sign of the correction tells an important story. As products build up, the reaction quotient becomes larger. For a cell running in the written forward direction, its voltage falls because the reaction has less tendency to make more products.
If reactants are abundant and products are scarce, the voltage rises above its standard value. A negative calculated cell voltage means the reaction as written is not spontaneous under those conditions.
The reverse reaction would be favored. At equilibrium, there is no net electron flow through the circuit, even though particles still react in both directions at equal rates.
Concentration differences can produce a voltage even when both electrodes are made from the same material. In a concentration cell, ions tend to move from the more concentrated side toward the less concentrated side through the chemical changes at the electrodes. The cell runs until the difference becomes smaller.
This idea appears in ion selective electrodes used to measure pH, sodium levels, or fluoride levels. It matters in corrosion too.
Different oxygen or salt concentrations on one metal surface can create tiny electrochemical cells, causing some regions to corrode faster. When solving problems, first balance the redox equation, identify the electrons transferred, build the reaction quotient, then check whether the final voltage direction makes chemical sense.
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.