Nernst Equation

In-depth explanation of Nernst Equation

The Nernst equation gives the cell potential under nonstandard conditions as E = E° - (RT/nF) ln Q, where Q is the reaction quotient. At 25 C this simplifies to E = E° - (0.0592/n) log Q. As the cell discharges, the concentration of products increases and Q grows, so the potential falls until it reaches zero at equilibrium. The equation shows how concentration affects the voltage of batteries and sensors. It is the basis for pH measurement with glass electrodes. Mastering it connects electrochemistry with chemical equilibrium.

Going deeper: Nernst Equation

Key ideas: E = E standard - (RT/nF) ln Q. At 25 C this is E = E standard - (0.0592/n) log10 Q. For the Zn/Cu cell n = 2, so E = 1.10 - 0.0296 log([Zn2+]/[Cu2+]); with 0.010 M Cu2+ and 1.0 M Zn2+ E falls to 1.04 V. Each tenfold change in an ion concentration shifts a half-cell by 0.0592/n V.

Common mistakes and connections: Mistakes: placing products and reactants upside down in Q, using ln with the 0.0592 factor (it is for log10), forgetting n, and including solids or pure liquids in Q. It explains why E falls as a battery discharges and underlies pH electrodes and concentration cells.

Visualization of Nernst Equation

The Nernst equation shows how voltage falls as the reaction quotient Q rises; at Q = 100 the Zn-Cu cell gives 1.04 V and reaches 0 at equilibrium. The interactive lesson shows this as a live animation or chart.

Worked example and use case

For a zinc-copper cell with [Zn2+] = 1.0 M and [Cu2+] = 0.010 M, Q = 100 and E = 1.10 - 0.0296 × log(100) = 1.04 V.

Where Nernst Equation fits in Acids, Bases & Electrochemistry

Nernst Equation is topic 55 of 105 in Acids, Bases & Electrochemistry.

Related topics

• Cell PotentialIntermediate
• Electrochemical SeriesIntermediate
• Spontaneity from Cell PotentialIntermediate
• Cell Potential and Free EnergyAdvanced
• Cell Potential and EquilibriumAdvanced
• Concentration CellsAdvanced

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