CHEM 3500 / Topic 5: Electrochemistry

Cell: → cell parts, cell setup, Ecell ; Electrode: → double layer, electrode potentials, ideal electrodes, reference electrodes ; Electrolyte: → ion transport, migration, conductivity ; Method: → potentiometry, voltammetry (mostly L17) ; Equation: → Nernst, the Ecell calc

Cell: How do you get the cell potential from the two electrode potentials? (L16 s9)

> Ecell = E_cathode − E_anode (cathode = reduction, anode = oxidation)

> Galvanic (spontaneous) → Ecell > 0

> Nernst for the cell: Ecell = E°cell − (RT/zF) · ln Q

∴ Ecell = cathode − anode, + means spontaneous

Cell: What is required in an electrochemical cell?

> Redox reaction: something gets oxidized, something gets reduced

> Anode: the electrode where oxidation happens

> Cathode: the electrode where reduction happens

> Electrolyte: the ion-conducting stuff between the two electrodes (ions move thru here)

> External circuit = e⁻-conducting wire between the two electrodes (e⁻ move thru here)

Cell: What does a voltammetry setup need, and what is the Luggin capillary for? (L17 s23–24)

> Potentiostat + WE + CE + RE (in a Luggin capillary) + electrolyte

> CE = Pt mesh / gauze (large area to carry current)

> Luggin capillary → RE tip right next to the WE

> Frit → separates catholyte (around cathode) + anolyte (around anode) → ions pass, CE products don't reach the WE ( my reasoning)

∴ 3 electrodes + potentiostat; RE measured close to the WE

Electrode: What is the electrochemical double layer, and how does it form? (L16 s5, Skoog 22A-5)

> Electrode = conductor in an electrolyte

> Metal (Fe) → some Fe²⁺ dissolve → e⁻ left in metal → surface (-)

> (-) surface attracts (+) ions → (-) layer (metal) + (+) layer (solution) = double layer

> → electric field forms at the interface

> IHP → oriented solvent dipoles + ions touching the surface

> OHP → closest approach of solvated ions

> Diffuse layer → ions spread out → bulk solution

> Double layer acts like a capacitor → ↑ surface area → ↑ capacitance → ↑ non-Faradaic current (review sheet)

∴ conductor in solution → charge separates at the interface → double layer + electric field

Electrode: How are electrode potentials measured, and what is the common reference? (L16 s6)

> Interfacial potential difference → can't be measured directly

> → measure vs. a reference electrode (voltmeter between the 2 electrodes)

> Common reference = NHE → H₂ → 2H⁺ + 2e⁻

> E° = 0 V @ pH 0, p(H₂) = 1 atm, 298 K

∴ electrode potentials are always relative → reported vs. a reference (NHE = 0 V)

Electrode: What is the standard electrode potential (E°)? (L16 s7)

> E° = reduction potential of the electrode (cathode) vs oxidation potential of the reference electrode (anode)

> Standard conditions → all species a = 1 (c = 1 M, p = 1 atm)

> T must be stated (normally given, usually 298 K)

∴ E° = reduction potential vs reference, all a = 1

Electrode: What are ideal polarized vs ideal non-polarized electrodes, and which one should a reference electrode be? (L16 s18, s20)

> Ideal polarized → potential changes, current stays 0 (flat line on the current vs E plot)

> Ideal non-polarized → current changes, potential stays fixed (vertical line)

> Neither exists in reality

> Reference electrode → ideal non-polarizable → stable E with little dependence on T, c, and current

> Purpose of reference → current-independent (stable) reference value for E measurements (midterm review Q)

∴ Reference = non-polarizable → E doesn't move

Electrode: How do the Ag/AgCl and SCE reference electrodes work? (L17 s3–4)

> Ag/AgCl: AgCl + e⁻ ⇌ Ag + Cl⁻ → Ag wire coated with AgCl in KCl, frit to the sample

> SCE: Hg₂Cl₂ + 2e⁻ → 2Hg + 2Cl⁻ → Hg / Hg₂Cl₂ in saturated KCl

> Both: E = E° − (RT/F) ln[Cl⁻] → E depends only on [Cl⁻]

> Fixed [Cl⁻] (e.g. 1.0 M or saturated KCl) → fixed, stable E

∴ Fixed [Cl⁻] = stable reference E

*Electrode: What are the 4 types of metallic sensing electrodes? (L17 s6)

> 1st kind → its own cation (e.g. Cu²⁺ + 2e⁻ ⇌ Cu)

> 2nd kind → ion that forms a precipitate / complex with the metal (e.g. AgCl + e⁻ ⇌ Ag + Cl⁻ → senses Cl⁻)

> 3rd kind → competing cation in a complex / solubility equilibrium (e.g. Hg(EDTA)²⁻ + Ca²⁺ + 2e⁻ ⇌ Hg + Ca(EDTA)²⁻)

> Inert metal (Pt) → redox equilibrium in solution (e.g. Fe(CN)₆³⁻ / Fe(CN)₆⁴⁻)

∴ Type = what the electrode responds to

Electrode: How does a pH glass membrane work, and what else is needed to measure pH? (L17

s7–9, Rev)

> Ionically conductive glass membrane → known [H⁺] inside (filling), unknown [H⁺] outside (sample)

> Gl–O⁻ + H⁺(aq) ⇌ Gl–OH on both surfaces → different [H⁺] → membrane potential (E_b)

> E_b = (RT/zF) ln(a₁/a₂) → E_b = 0.0592 V − 0.0592 V · pH (inside a = 0.1)

> Also needed: 2 reference electrodes (stable, known E), one on each side

> Measured potentiometrically at zero current

∴ H⁺ binding on glass → membrane potential → pH

Electrolyte: Why must the electrolyte transport both charge and mass? (L16 s11)

> Charge: e⁻ flow anode → cathode through the wire → (+) charge builds up at the anode, (−) at the cathode

> Ions move to cancel the buildup (anions → anode, cations → cathode) → circuit closed

> Mass: reaction uses up X at the electrode surface

> Fresh X brought in + products moved away → reaction keeps going

> No transport → charge piles up / surface runs out of X → current stops

∴ Charge transport closes the circuit, mass transport feeds the reaction

Electrolyte: How does the electrolyte transport charge and mass? (L16 s11)

> J = −D∇c − (zF/RT)·D·c·∇φ + ∇(c·u)

> Diffusion → concentration gradient (∇c) → high c → low c

> Migration → potential gradient (∇φ) → only charged X (z ≠ 0)

> Convection → bulk flow of solution (u) (e.g. stirring)

∴ Diffusion + migration + convection = mass transport

Electrolyte: Why do we add a supporting electrolyte? (L16 s14)

> Supporting electrolyte = high c of non-reacting salt (e.g. KCl) → only carries charge

> Few ions → ↑ ionic resistance → potential (∇φ) lost in the solution

> ↑ ions → ↑ charge carriers → ↓ resistance → ↓ potential lost

> J = −z·u·c·∇φ → ↑ c → same J with a smaller ∇φ

∴ Supporting electrolyte ↓ resistance → ↓ potential lost

Electrolyte: Why is KCl the most common electrolyte salt, and what if you used NaCl? (L17 s5, Rev)

> Junction = 2 electrolytes of different c meet → ions diffuse at different speeds → charge separation → junction potential (adds error to Ecell)

> K⁺ and Cl⁻ have very similar diffusivities → minimal junction potential

> NaCl → Na⁺ ≠ Cl⁻ diffusivity → bigger junction potential → must be measured + adjusted for

∴ KCl = similar diffusivities = minimal junction potential

Method: What is the measurement principle of potentiometry, and what are its components? (L16 s16, s19)

> Current-less (zero current) measurement of electrode potential vs a reference → quantitative c of redox species (via Nernst)

> Sensing / indicator electrode = cathode → its E depends on X

> Reference electrode = anode → stable, known E

> Electrolyte between them + voltmeter to read E

∴ Potentiometry = E of the sensing electrode vs the reference at zero current → c of X

Method: Why must potentiometric measurements be current-less? (L16 s17)

> Current flows → system no longer at equilibrium → measured E changes

> e.g. ↑ potential → pulls e⁻ away from the electrode → Fe → Fe²⁺ + 2e⁻ runs → current flows to re-equilibrate

> Nernst only holds at equilibrium → E only reflects c of X at zero current

∴ Current disturbs equilibrium → wrong E → measure at zero current

Method: What steps does X go through to react at an electrode? (L17 s17)

> Mass transfer → bulk to surface (diffusion, migration, convection)

> Chemical reaction → X changes form if needed (Ox → Ox′)

> Physical state change → e.g. adsorption on the electrode

> Electron transfer → Ox + ne⁻ → Red

> Red leaves by the same steps in reverse

∴ Bulk → surface → electron transfer → back out

Method: How does a potentiostat work, and what does each electrode do? (L17 s21)

> WE → where the reaction of interest happens

> RE → stable reference; potentiostat measures E between WE and RE

> CE → completes the circuit; potentiostat drives + measures current between WE and CE

> Adjusts WE–CE power until WE/RE potential = the set value

> No current through the RE → RE potential stays stable

∴ E measured vs RE, current flows WE ⇌ CE

Method: What is the difference between Faradaic and non-Faradaic current? (L17 s22)

> Faradaic → charge transfer across the electrode interface → redox reaction (e.g. Fe → Fe²⁺ + 2e⁻) → the signal

> Non-Faradaic → polarization of the interface, no charge transfer → double layer charges like a capacitor → background

∴ Faradaic = e⁻ cross (reaction); non-Faradaic = interface charges (no reaction)

Method: How does cyclic voltammetry work and what do you read from it? (L17 s28–31)

> Apply E swept linearly forward + back → measure current

> ↑ E → electrode more (+) → electrode pulls e⁻ from X → X loses e⁻ → X oxidized (electrode = e⁻ taker)

> ↓ E → electrode more (−) → electrode pushes e⁻ into X → X gains e⁻ → X reduced

> Oxidation peak (i_p^a, E_p^a) on the forward sweep + reduction peak (i_p^c, E_p^c) on the back sweep

> E½ → identifies the redox species; i_p → concentration

> Reversible → fast kinetics, peaks fixed vs scan rate, ΔE_p = 59 mV / z (25 °C)

> Irreversible → slow kinetics, peaks shift outward at ↑ scan rate, ΔE_p > 59 mV / z

∴ E½ = which X, i_p = how much X, ΔE_p = how fast

Method: What is anodic stripping voltammetry (ASV) and when is it used?

> For trace metals (10⁻⁹–10⁻¹⁰ M)

> Step 1: hold cathodic E for a set time → metals deposit on WE (preconcentration ↑)

> Step 2: scan E positive → deposited metals oxidize (strip) → measure i

> Each metal strips at its own E → Pb + Cd resolved; charge (area) ∝ amount

∴ Trace Pb/Cd in soil → ASV: deposition = ↑ sensitivity + leaves the matrix behind

Equation: How do you balance a redox half-reaction in acidic solution? (L16 s4 + gen chem)

> Balance all atoms except O + H

> Balance O → add H₂O

> Balance H → add H⁺

> Balance charge → add e⁻ to the more positive side

> Full reaction → multiply half-reactions so e⁻ match → add → cancel

> e.g. 2MnO₂ + 2H⁺ + 2e⁻ → Mn₂O₃ + H₂O

> No condition given → assume acidic

∴ atoms → O (H₂O) → H (H⁺) → charge (e⁻) → check atoms + charge

Equation: How do you balance a redox half-reaction in basic solution? (L16 s4 + gen chem)

> Balance as if acidic first

> Add OH⁻ to both sides = # of H⁺

> H⁺ + OH⁻ → H₂O

> Cancel the H₂O on both sides

> e.g. 2MnO₂ + H₂O + 2e⁻ → Mn₂O₃ + 2OH⁻

> Basic → Q says basic/alkaline or gives OH⁻ (NaOH, KOH)

∴ basic = acidic method + OH⁻ to kill the H⁺ + cancel the extra H₂O

Equation: How do you balance equations, generally?

> Put a letter in front of every species

> Write one equation per element (left count = right count)

> For redox, ↑ a charge equation too

> Set one letter = 1 → solve the rest → scale up to whole numbers

Equation: How do you get an electrode potential at non-standard conditions? (L16 s8)

> Nernst: E = E° − (RT/zF) · ln(∏ a_red^ν_red / ∏ a_ox^ν_ox)

> z = number of e⁻ exchanged per reaction; F = 96,485 C mol⁻¹; R = 8.315 J K⁻¹ mol⁻¹; T in K

> ↑ a_red → ↑ ratio → ↓ E, ↑ a_ox → ↑ E

> All a = 1 → ln 1 = 0 → E = E°

∴ Nernst corrects E° for the real activities

Equation: How is the cell's ΔE related to the free energy of the reaction? (L16 s10)

> ΔG = −z · F · ΔE (ΔE measured at zero current, reversible)

> ΔE = driving force of the reaction → same thing as ΔG, just written as a voltage

> ΔE + → ΔG − → spontaneous (galvanic)

> ΔE − → ΔG + → not spontaneous

> +E electrode = takes e⁻ (reduced, cathode); lower E = gives e⁻ (oxidized, anode)

∴ +ΔE = −ΔG = spontaneous

Equation: How do ions migrate, and how does migration give current? (L16 s13)

> J = −z · u · c · ∇φ (u = ion mobility, ∇φ = electric field gradient)

> Anode → (+) charges formed / (-) consumed; cathode → (-) charges formed / (+) consumed

> Cations (supporting) → cathode, anions (supporting) → anode → cancels the charge buildup

> i = J · z · F → ↑ J = ↑ current density

∴ Migration = ions pulled by the field → carries the current

*Equation: What does the Butler–Volmer equation describe? (L17 s18)

> i = i₀ · [e^{(α_a zF(E − E_eq)/RT)} − e^{(α_c zF(E_eq − E)/RT)]}

> 1st term = oxidation (E > E_eq), 2nd = reduction (E < E_eq)

> E = E_eq → i = 0 (equilibrium, no net current)

> i₀ = exchange current → ↑ i₀ = faster e⁻ transfer kinetics (between electrode and X @ its surface)

∴ Current ↑ exponentially as E moves away from E_eq

Equation: How do you get a diffusion coefficient (D) from voltammetry? (L17 s33–34, Final Q18)

> Randles–Sevcik: i_p = 0.4463 · zFAc · √(zFvD / RT) (v = scan rate, A = area, c = concentration)

> Run CV at several scan rates → plot i_p vs √v → straight line

> Slope → solve for D

> Tafel (s32): ln i = ln i₀ + (α_a zF / RT) η → intercept = ln i₀ (kinetics)

∴ Vary scan rate → i_p vs √v → D

Signal: What is S/N and how do you estimate it from data or a plot? (L3 s6–7)

> S/N = mean / standard deviation = 1 / RSD

> Discrete data → s = √(Σ(xᵢ − x̄)² / (n − 1))

> Plot → s ≈ (noise max − noise min) / 5

> ↑ S/N → ↑ signal (mean) or ↓ noise (s)

∴ S/N = mean / s; plot noise span ≈ 5s

Noise: How does ensemble averaging improve S/N, and how many scans do you need? (L3 s12, Rev)

> Average n repeat measurements → S/N ↑ by √n

> n = ((S/N)₂ / (S/N)₁)² (e.g. 5 → 25 needs n = 25)

∴ S/N ∝ √n

Noise: What causes noise, and which hardware method fixes each? (L3 s8–11, s14, Rev)

> Instrumental: thermal → ↓ T, ↓ resistance; shot → fewer junctions; flicker → good connections

> Environmental (power lines, EM) → grounding + Faraday cage (grounded metal housing → induced currents drain to ground)

> Sample: vibrations → isolation table; T / humidity → environmental chamber

∴ Match the noise source to its fix

Circuit: How do voltage and current dividers work? (L3 s21–24, L4 s10–13, Rev)

> Series (voltage divider) → same I through all, V splits: (Vin − V2) / R1 = V2 / R2

> Parallel (current divider) → same V across all, I splits: 1/R = 1/R1 + 1/R2, I = V / R per branch

> Always V = I · R

∴ Series splits V, parallel splits I

Circuit: How do you minimize loading error from meters? (L4 s7, s14, Final Q2)

> Ammeter → in series → needs LOW impedance

> Voltmeter → in parallel → needs HIGH impedance

> Meters draw or block current → they change the circuit they measure

∴ Ammeter low Z in series, voltmeter high Z in parallel

Signal: How do you find ADC resolution or the bits needed? (L4 s23, s25, Final Q3)

> 2ⁿ bins (n = bits) → resolution = range / 2ⁿ

> e.g. 0–6 V, 8-bit → 6 / 256 = 23 mV

> Bits needed → smallest n with 2ⁿ ≥ range / resolution (0–12 V at 0.01 V → 1200 → n = 11)

∴ ↑ bits → smaller bins → better resolution

Calibration: Blank vs dummy vs standard vs control vs internal standard vs standard addition? (L2 s12–20)

> Blank → sample matrix without X (e.g. solvent in cuvette)

> Dummy → instrument run with nothing in it (e.g. empty IR holder)

> Standard → artificial X to calibrate; control → artificial sample close to real

> Internal standard → different signal, added equally to all → corrects stimulus / intake / dilution fluctuations

> Standard addition → same X added to the sample → extrapolate to 0 signal

∴ All of them reduce systematic (non-random) errors