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The Nernst Equation and Cells Away from Standard Conditions

A tabulated electrode potential applies only at one set of concentrations. The Nernst equation converts it to any composition, which turns a cell into an instrument for measuring concentration.

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What a learner can do afterwards

  • Writes the reaction quotient for a cell reaction and substitutes it into the Nernst equation with the right electron count
  • Calculates the potential of a concentration cell and explains why it is not zero
  • Converts a standard cell potential into an equilibrium constant and states the link to Gibbs energy
  • Explains why the quotient should strictly contain activities and when the concentration form is good enough

1 · Read

A table potential assumes every solute sits at 1 M, but your cell rarely does. You correct it with E equals E standard minus R T over n F times ln Q. You write Q from the balanced cell reaction with each species raised to its stoichiometric power, and you read n from the balanced half reactions. If you miscount n or swap a power, the voltage shifts.

Try it together

Take a concentration cell with the same metal on both sides. E standard is exactly zero, yet you still measure a voltage because the ion concentrations differ. Oxidation runs in the dilute half cell while reduction runs in the concentrated one, evening the two sides out. As Q drifts toward 1 the voltage fades to zero, and the same ratio gives a smaller voltage when more electrons move.

You can turn a standard potential into an equilibrium constant because minus n F times E standard equals minus R T times ln K. A positive E standard means K sits above 1, so products dominate at equilibrium, while a negative one means reactants win. As your cell runs down, Q approaches K and E falls to zero.

Good to know

Strictly speaking Q holds activities, not concentrations. In dilute solutions the two match closely enough that concentrations work fine. In concentrated brines that shortcut fails, so you reach for activities there.

You correct the standard potential with Q and n, read concentration cells from Q alone, link E standard to K, and use activities when solutions are concentrated.

2 · Watch

Take it off screen

Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.

Where it sits

Then practise

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The Nernst Equation and Cells Away from Standard Conditions · Science, ages 21 to 22 · LightMySky