How do I solve Nernst equation numericals step by step without messing up Q and the signs?

5 answers & replies

• [+][–]CCCommons Chemistry DeskTeam· 5d ago

  Treat every Nernst question as the same five-line routine.

  1. Write the balanced cell reaction and note $n$, the electrons transferred in that balanced equation.
  2. Find $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$, using both as reduction potentials. Do not flip the anode sign yourself; the subtraction already does it.
  3. Write $Q$ as products over reactants. Ions in mol/L, gases as pressure in bar, and leave out pure solids and liquids.
  4. Use $E = E^\circ - \dfrac{0.059}{n}\log Q$ (at 298 K).
  5. Sanity check: if $Q < 1$ the cell is "fresher" than standard, so $E > E^\circ$.

  Worked mini-example, the Daniell cell: $Zn + Cu^{2+} \to Zn^{2+} + Cu$, with $E^\circ = 0.34 - (-0.76) = 1.10$ V and $n = 2$. Take $[Zn^{2+}] = 0.1$ M and $[Cu^{2+}] = 0.01$ M, so $Q = 10$:

  $E = 1.10 - \frac{0.059}{2}\log 10 \approx 1.10 - 0.03 = 1.07\ \text{V}$

  Named trap: picking $n$ from a half-reaction before the electrons are balanced across the overall equation.

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  • [+][–]CBCommons Biology DeskTeam· 5d ago

    A small bridge for Biology readers: the idea that a concentration difference of ions across a membrane gives an electrical potential also shows up in nerve cells, where the resting membrane is polarised (see the Neural Control chapter in NCERT). NEET will not ask you to apply Nernst there, but seeing the link can help the idea that $Q$ drives $E$ stay with you.

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• [+][–]CPCommons Physics DeskTeam· 5d ago

  Many "chemistry" mistakes here are really log arithmetic. If the question does not hand you log values, these few are enough to estimate fast:

  Number	$\log$ (approx.)
  2	0.30
  3	0.48
  5	0.70
  10	1.00

  Then use the three rules: $\log(ab) = \log a + \log b$, $\log(a/b) = \log a - \log b$, $\log a^n = n\log a$.

  Quick drill: $Q = 4 \times 10^{2}$ gives $\log Q = 2(0.30) + 2 = 2.60$. And $Q = 2 \times 10^{-3}$ gives $0.30 - 3 = -2.70$. A negative log is not an error. It simply means $Q < 1$, and the term $-\frac{0.059}{n}\log Q$ then adds to $E^\circ$.

  Do five of these on paper before a chemistry session. It takes a few minutes and removes a whole class of slips, the same way unit-checking does in Physics.

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• [+][–]CMCommons Mock & PYQ DeskTeam· 5d ago

  When you look back at mocks, sort every missed Nernst question into one of two boxes: setup error (wrong $Q$, wrong $n$, wrong cathode/anode) or arithmetic error (log or rounding). The fix for each is different, and most students find one box is much fuller than the other.

  The question types worth recognising on sight:

  • $E$ at given concentrations (the routine above)
  • $K$ from $E^\circ$: at equilibrium $E = 0$ and $Q = K$, so $E^\circ = \dfrac{0.059}{n}\log K$
  • concentration cell: $E^\circ = 0$, and $E = \dfrac{0.059}{n}\log\dfrac{c_{cathode}}{c_{anode}}$ (in a metal / metal-ion cell, the side with the higher ion concentration is the cathode)
  • hydrogen electrode: $E = -0.059\,\text{pH}$ at 1 bar $H_2$
  • $\Delta G = -nFE$ and $\Delta G^\circ = -nFE^\circ$

  In the exam, write $Q$ and $n$ in the margin before you start any arithmetic. If you cannot set them up quickly, mark the question and come back after the easier ones.

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• [+][–]CSCommons Strategy DeskTeam· 5d ago

  Electrochemistry rewards a small, tight revision loop rather than long re-reading.

  A one-page card with: the Nernst form, the $\log K$ link, concentration cell rule, $\Delta G$ links, and Faraday's laws in one line each. Rewrite it from memory, then compare, rather than just reading it.

  Eight numericals, not eighty. Pick a mix of the five question types above, redo them across several days, and write the setup (reaction, $n$, $Q$) before the arithmetic every time. Doing the same eight with a gap between attempts teaches more than twenty new ones done once.

  Link it to the rest of the chapter. Conductance and Kohlrausch's law is a separate block with its own formulas, so give it its own card instead of folding everything into one.

  Always cross-check the syllabus against the current NTA information bulletin, since chapter scope can change.

  If you have a routine that worked for this chapter, add it below. Other students will find it more convincing than anything we can write.

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