Topic 2: Relevant revision

Question 1

• What is the general equation describing current in dynamic electrochemistry?

Answer 1

• i = nAFj
• i = current flowing upon voltage application
• A = electrode area (cm)
• F = Faradays constant (96845 C mol^-1)
• j = flux or reaction rate (mol cm^-2 s^-1)
• j is the rate of change of concentration (dC/dt)

Question 2

(IMP) What controls flux, j?

Answer 2

• j = k_xO*
• where O is the electronegative species that can be reduced to R by gaining an electron
• x is either the the mass transfer rate constant, k_t, or the intrinsic electron transfer constant, k^o
• The slowest k value controls the overall ror, so either process can dominate

Question 3

• (IMP) Normally electrochemical processes are …transfer controlled i.e k^o >> k_t. As a rule of thumb: To measure k^o –> …

Answer 3

Normally electrochemical processes are mass transfer controlled i.e k^o >> k_t. As a rule of thumb: To measure k^o –> k_t ≥ 10 k^o

Question 4

• What factors control mass transport, k_t

Answer 4

• Diffusion: movement of species down an always present concentration gradient. Majority of examples will be just diffusion controlled
• Convection: movement of species within a fluid due to a pressure/temperature gradient
• Migration: movement of ions in a charged field via electrostatics

Question 5

• Convection is generally ignored as it is minimised. How is convection minimised?

Answer 5

• By keeping change in pressure and temperature in the system 0
• If did want to introduce, could force convection using a pump/rotator

Question 6

• Why is migration ignored and what are the results of doing so?

Answer 6

• Migration is ignored as excess inert ions are added to the solution (e.g 0.1M KNO₃ – cant be reduced as high E_red)
• This increases solution conductivity (↓ R_soln, Ohmic drop = iR_soln, Ohmic drop ↓)
• DL thickness ∝ 1/electrolyte conc; therefore, decreasing size of double layer with ions means the potential due to electrostatic effects not felt until charged species are very close
• For this reason, migration can be discounted

Question 7

• Explain the origin of the diffusion rate constant. Use a graph to support your answer

Answer 7

• J is governed by k_t in a diffusion-controlled process
• 𝛿 is diffusion length

Question 8

• Draw a linear sweep voltammetry (LSV)and a corresponding Cyclic Voltammogram (CV) and the general process it is obtained

Answer 8

• Sweep electrode potential between two limits; lower where no electron transfer occurs; upper where species of interest is oxidised or reduced; CV then returns if cyclic
• LSV is one direction only (therefore half of plot 2)
• Voltammogram appears different for every species, acts as a fingerprint

Question 9

• What does the shape of the LSV depend on?

Answer 9

• Size of electrode
• Rate of electron transfer, k^o
• Chemical reactivity of electroactive species
• Voltage scnae rate, Vs^-1

Question 10

• Give a labelled example of a redox couple on a CSV on a large electrode and describe the potential to start a scan as well as the effect of increasing the scan rate applied in the sweep

Answer 10

• E = E^O’ ~ E_1/2
• E_1/2 half wave potential, use E^o’ as a guide as to what potential to use to start scan
• Which does it start from ?? reduction here?

Question 11

• What is the Randles Sevcik equation?

Answer 11

• Describes the peak current at a macroelectrode in this case
• i_p = 2.69E+05 n^3/2 A D^1/2 v^1/2 c*
• i_p – diffusion limited peak current at 298K
• D – diffusion coefficient (cm² s^-1)
• v – scan rate (Vs^-1)
• c* - concentration of species (mol cm^-3) – mol L^-1 = mol dm^-3 = mol cm^-3 * 1000

Question 12

• Why does peak current increase with increasing scan rate?

Answer 12

• i ∝ v^1/2 – as you scan faster, increase peak current

Question 13

• Derive an expression for k_t

Answer 13

• i = nAFk_tc= 2.69E+05 n^3/2 A D^1/2 v^1/2 c*
• k_t = 2.69E+05n^1/2D^1/2v^1/2/F
• means can also use v to change k_t as well as i_p

Question 14

• How can we use peak separation to predict i_p from the Randles-Sevcik equation?

Answer 14

Question 15

• How will increasing the scan rate change the size of diffusion layer profiles for a MACROscale electrode , draw them

Answer 15

• Flux depends on the size of the diffusion gradient