Lectures 3–4 Practice: Current, Electron Energy and Overpotential

Eleven short problems that examine Lectures 3 and 4 together, in the formats you may meet in the assessment: sorting, true or false, choosing an equation, step-by-step and multi-step calculations, working backwards and finding a mistake. 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

Current is the rate of flow of charge: i = q/t, so q = it (1 A = 1 C s⁻¹)
Moles of electrons = q/F; moles of metal = q/(zF)
Mass = moles × M; 1 mA h = 3.6 C
Fermi level: E_F = −4.44 eV − eE (E in V vs SHE)
Level of a couple: −4.44 eV − eE_eq
Nernst: E_eq = E° + (RT/nF) ln[Mⁿ⁺]
Overpotential: η = E − E_eq; η < 0 reduction, η > 0 oxidation
Electrolytic cell: supply voltage ≥ |E°_cell|; E_F(cathode) − E_F(anode) = eV
Current density = current ÷ area (mA cm⁻²)

Key terms, if this is new to you

Open and closed circuit: On open circuit no current flows and no net reaction occurs. When the circuit is closed, current flows and the cell reaction runs.
Current: The rate of flow of charge, in amperes (C s⁻¹). At an electrode it measures the rate of the electrode reaction.
Faraday constant, F: The charge on one mole of electrons, 96,485 C mol⁻¹.
Fermi level, E_F: The energy of the highest-energy electrons in the electrode. A more negative potential raises it.
Equilibrium potential, E_eq: The potential at which oxidation and reduction run at equal rates, so no net current flows; from the Nernst equation.
Overpotential, η: How far the applied potential is from E_eq. It sets which reaction wins and how fast the net reaction goes.

About the values

F = 96,485 C mol⁻¹; molar masses: Zn 65.38, Cu 63.55, Ag 107.87, Li 6.94 g mol⁻¹.
Standard reduction potentials are those in the Lecture 1 table, at 298.15 K, where RT/F = 0.02569 V.
The absolute potential of the SHE is taken as 4.44 V, so an electron at 0 V vs SHE has an energy of −4.44 eV (IUPAC).
Small rounding differences are accepted, so you do not need to match every decimal place.
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