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Unformatted text preview: Voltammetry Methods based on an electrolytic cell Apply potential or current to electrochemical cell & concentrations change at electrode surface due to oxidation & reduction reactions Can have 2 or 3 electrodes Stirred or unstirred solution Measure current or voltage In all electrochemical methods, the rate of oxidation & reduction depend on: 1) rate & means by which soluble species reach electrode surface (mass transport) 2) kinetics of the electron transfer process at electrode surface (electrode kinetics), which depend on: a) nature of the reaction b) nature of electrode surface c) temperature (we don't have much control over #2) Mass Transport or Mass Transfer
1) Migration movement of a charged particle in a potential field generally bad (important for conductance & electrophoresis) In most cases migration is undesirable and can be eliminated by adding a 100 fold excess of an inert electrolyte (i.e., electrochemically inert not oxidized or reduced) Inert electrolyte does the migrating, not the analyte Mass Transport or Mass Transfer
2) Diffusion movement due to a concentration gradient. If electrochemical reaction depletes (or produces) some species at the electrode surface, then a concentration gradient develops and the electroactive species will tend to diffuse from the bulk solution to the electrode (or from the electrode out into the bulk solution) Concentration polarization Reaction is A + eP Diagram for diffusion
Before power is turned on the analyte (A) is at its maximum concentration throughout the solution Product (P) is zero throughout Fick's Laws describe diffusion
1st Law Where J = flux of material i.e., moles passing a 1 cm2 plane at point x & time t (mol/cm2/sec) D = diffusion coefficient (cm2/sec) C = concentration t = time (sec) from when power is turned on x = distance from electrode surface (cm) Using an expression for Conservation of Mass And combining with Fick's First law gives Fick's Second Law Solving Fick's Laws for particular applications like electrochemistry involves establishing Initial Conditions and Boundary Conditions
Initial At t=0 i.e., before experiment starts, concentration is C & is same throughout the solution At t>0 the concentration at the electrode surface goes to zero the moment power is turned on Some distance away from the electrode surface at anytime t>0 the concentration is still C in the "bulk solution" unaffected by the electrode process Boundary 1 Boundary 2 Skipping to the Electrochemical Solution
Number of electrons Faraday's constant Electrode area Concentration Diffusion coefficient Time Current is the flux of electrons at the electrode surface Experiment showing how Cottrell equation describes current as a function of time Voltage applied to cell begins at V1 where no reaction occurs and is stepped up to V2 causing electrode process to begin and a current spike results. Current drops off with time according to the Cottrell equation since material must diffuse to the electrode surface in order to react. current (i) i time Quantity
Q I i E E R u z C j charge current current density electrical potential C A A m2 V Unit
coulomb ampere ampere per square metre volt volt siemens per metre ohm square metre per second volt farad per metre farad mole per square metre second potential difference V voltage conductivity resistance mobility charge number permittivity capacitance flux density note that S m1 m2 s1 V1 (none) F m1 F mol m2 s1 F = s second V C = J joule 11
a Mass Transport or Mass Transfer
3) Convection mass transfer due to stirring. Achieved by some form of mechanical movement of the solution or the electrode i.e., stir solution, rotate or vibrate electrode Difficult to get perfect reproducibility with stirring, better to move the electrode Convection is considerably more efficient than diffusion or migration = higher currents for a given concentration = greater analytical sensitivity Nernst Diffusion Layer Concept
for stirred solution & stationary electrode
Electrode Nernst diffusion Layer () (stagnant solution) Turbulent mixing region (bulk solution) Convective Mass Transport Electrode converts A + eP at surface Fick's first law applied to stagnant layer
= Cbulk  Csurface Cbulk  Csurface i = nFAD For stirred solutions i = nFAD Cbulk Mass Transport vs Electrode Kinetics
Experimentally rate of electron transfer is fast for many processes so can assume:  current depends only on mass transfer  surface concentrations are in equilibrium with applied potential as expressed by the Nernst equation Processes which satisfy these assumptions are known as electrochemically reversible A process may be reversible under one set of conditions and irreversible under other conditions. Process is more likely to be irreversible if  it involves a high current  employs a rapid potential scan If a process is irreversible, then the rate of reaction at the electrode surface (i.e., current) will be slower than predicted from mass transfer considerations alone ...
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 Fall '11
 Ryan

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