Lectures 1–2 Practice: Electrochemical Cells and the Nernst Equation

Ten short problems that examine Lectures 1 and 2 together, in the formats you may meet in the assessment: sorting, true or false, reading cell notation, choosing an equation, looking up data, finding a mistake, reading a graph, a multi-step calculation and working backwards. Each problem is labelled with the lecture it draws on. They start with the ideas and build up to the calculations, so begin with Problem 1. Each answer is checked as you go, and the working is shown once each step is correct.

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Equation sheet

Cell notation: anode | anode solution || cathode solution | cathode (|| is the salt bridge)
E°_cell = E°(cathode) − E°(anode); E° values are never multiplied by coefficients
Nernst equation: E_cell = E°_cell − (RT/nF) ln Q
At 298.15 K: RT/F = 0.02569 V, so E_cell = E°_cell − (0.02569 V/n) ln Q
Or with log₁₀: E_cell = E°_cell − (0.0592 V/n) log₁₀ Q
Q = [products] / [reactants], each raised to the power of its coefficient; solids count as 1
ΔG = −nFE_cell; ΔG° = −nFE°_cell
ln K = nFE°_cell / RT; at equilibrium Q = K and E_cell = 0
F = 96,485 C mol⁻¹; R = 8.314 J K⁻¹ mol⁻¹; ln x = 2.303 log₁₀ x

Key terms, if this is new to you

Anode and cathode: Oxidation takes place at the anode and reduction at the cathode, in every kind of cell.
Galvanic and electrolytic cells: A galvanic cell runs a spontaneous reaction and delivers electrical work (E_cell > 0). An electrolytic cell uses a power supply to drive a non-spontaneous reaction (E_cell < 0).
Salt bridge: Joins the two half-cells and carries ions, keeping each solution electrically neutral. Electrons travel through the external wire.
Standard hydrogen electrode (SHE): The reference electrode, 2H⁺ + 2e⁻ → H₂, whose potential is defined as 0 V. Every E° in the table is measured against it.
Standard conditions: All dissolved species at 1 M, gases at 1 bar, at a stated temperature (usually 298.15 K). E°_cell applies only under these conditions.
Reaction quotient, Q: The ratio of product to reactant concentrations at any moment, written like an equilibrium constant. It changes as the cell runs.
Equilibrium constant, K: The value Q reaches when the reaction stops. A large K means the reaction goes almost to completion.
Electrons transferred, n: The number of electrons that pass from the anode to the cathode for the cell reaction as written, for example 2 for Zn + Cu²⁺ → Zn²⁺ + Cu.
Spontaneous: A reaction that can proceed without an energy input: ΔG < 0 and E_cell > 0.
Concentration cell: A cell with the same couple in both half-cells but at different concentrations. E°_cell = 0, so its whole voltage comes from the ln Q term.

About the values

Standard reduction potentials are those in the Lecture 1 table and slides, at 298.15 K.
All problems are at 298.15 K unless stated otherwise, so RT/F = 0.02569 V and 2.303RT/F = 0.0592 V.
Concentrations are used in place of activities, as in the lectures. Solids have an activity of 1 and gases enter Q as their pressure in bar.
Small rounding differences are accepted, so you do not need to match every decimal place.
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