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Nernst Equation

The Nernst equation relates the electrode potential or cell EMF to concentration, pressure, temperature, and reaction quotient for a redox reaction.

In one line: Nernst asks: balanced reaction first, quotient second, EMF last.

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Understand it

  • Standard EMF applies only under standard conditions.
  • When ion concentrations change, the reaction quotient changes and the cell EMF also changes.
  • At 298 K, the logarithmic form commonly used in Class 12 is E cell = E degree cell - (0.0591/n) log Q, where n is the number of electrons transferred and Q is the reaction quotient written from the balanced cell reaction.
  • For pure solids and liquids, activity is taken as one, so they are not included in Q.

Example

For Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), Q = [Zn2+]/[Cu2+]. Therefore E cell = E degree cell - (0.0591/2) log([Zn2+]/[Cu2+]).

Rule to remember

At 298 K: E cell = E degree cell - (0.0591/n) log Q.

For a half-cell Mn+ + ne- → M, E = E degree - (0.0591/n) log(1/[Mn+]), which can also be written as E = E degree + (0.0591/n) log[Mn+].

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For Daniell cell at 298 K, E degree cell = 1.10 V, [Zn2+] = 0.10 M, [Cu2+] = 1.0 M, and n = 2.

  1. 1Q = 0.10/1.0 = 0.10.
  2. 2E cell = 1.10 - (0.0591/2) log(0.10).
  3. 3Since log(0.10) = -1, E cell = 1.10 + 0.02955 = 1.12955 V.
  4. 4The cell EMF increases because product ion concentration is lower relative to reactant ion concentration.

Method you can reuse

  1. 1Balance the cell reaction.
  2. 2Count total electrons transferred to get n.
  3. 3Write Q using aqueous and gaseous species only.
  4. 4Substitute concentrations with units converted consistently.
  5. 5Calculate the logarithm and interpret whether EMF rises or falls compared with standard EMF.

Visual tip

A diagram is not required. A flow chart from balanced reaction to Q to substitution is more useful for numerical accuracy.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

For Zn + Cu2+ → Zn2+ + Cu, what concentration ratio appears in Q?

Think first, then show answer
Q = [Zn2+]/[Cu2+], because solids Zn and Cu are omitted.

Common wrong answer

A common wrong answer is using Q = [Cu2+]/[Zn2+] for the Daniell cell, which changes the sign of the correction term.

Don't mix this up

Students often put the concentration ratio upside down or use n as the coefficient of metal instead of the number of electrons transferred.

Exam tip

Write the balanced cell reaction before writing Q. This prevents most concentration-ratio and electron-number errors.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions ask for EMF under non-standard concentration, equilibrium constant relation, concentration cell EMF, or effect of dilution on electrode potential.
  1. 1

    Enough for 1 mark

    The Nernst equation relates the electrode potential or cell EMF to concentration, pressure, temperature, and reaction quotient for a redox reaction.

  2. 2

    Add for 2 marks

    Example: For Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), Q = [Zn2+]/[Cu2+]. Therefore E cell = E degree cell - (0.0591/2) log([Zn2+]/[Cu2+]).

  3. 3

    Add for 3 marks

    Standard EMF applies only under standard conditions.

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