Coulometric Methods A Introduction 1 Coulometry

Coulometric Methods A. ) Introduction: 1. ) Coulometry: electrochemical method based on the quantitative oxidation or reduction of analyte - measure amount of analyte by measuring amount of current and time required to complete reaction < charge = current (i) x time in coulombs - electrolytic method external power added to system 2. ) Example: - Coulometric Titration of Cl- use Ag electrode to produce Ag+ Ag (s) ↔ Ag+ + e. Ag+ + Cl- ↔ Ag. Cl (ppt. ) - measure Ag+ in solution by 2 nd electrode - only get complete circuit when Ag+ exists in solution - only occurs after all Cl- is consumed - by measuring amount of current and time required to complete reaction can determine amount of Cl-

Typical coulometric titration cell. e. g. At the generator electrode (anode) Ag (s) Ag+ + e- (oxidation of silver to silver ion) At the cathode: Possible reaction cathode anode 2 H+ + 2 e- H 2 (g) (hydrogen evolution) Therefore, need sintered glass to separate the species generated in the other electrode (e. g. cathode, hydrogen gas) to prevent reactions with the “titration species” such as Ag+.

3. ) Based on Measurement of Amount of Electricity (or charge, in coulombs) Required to Convert Analyte to Different Oxidation State - Q = It where: for constant current with time Q = charge required (coulombs = amp. sec) I = current (amp. ) t = time of current (sec) for variable current with time: t Q= IIdt 0 Relate charge (coulombs, C) to moles of e- passing electrode by Faraday constant Faraday (F) = 96, 485 Coulombs (C)/mole e. F = 6. 022 x 1023 e-/ mole e- x 1. 60218 x 10 -19 C/ e- = 96, 485 Coulombs/mole e. If know moles of e- produced and stoichiometry of ½ cell reaction: Ag (s) ↔ Ag+ + e- (1: 1 Ag+/e-) gives moles of analyte generated, consumed, etc.

Example: Constant current of 0. 800 A (amps. ) used to deposit Cu at the cathode and O 2 at anode of an electrolytic cell for 15. 2 minutes. What quantity in grams is formed for each product? ½ cell reactions: Cu 2+ + 2 e 2 H 2 O To solve: Cu (s) 4 e- + O 2 + 4 H+ (cathode) (anode) Q = i. t Q = (0. 800 A)(15. 2 min) (60 sec/min) Q = 729. 6 C (amp. sec) amount Cu produced: =(729. 6 C)(1 mole e-/96, 485 C)(1 mole Cu/2 mole e-)(63. 5 g Cu/mole Cu) = 0. 240 g Cu amount of O 2 produced: =(729. 6 C)(1 mole e-/96, 485 C)(1 mole O 2/4 mole e-)(32. 0 g O 2/mole O 2) = 0. 0605 g O 2

4. ) Two Types of Coulometric Methods a) amperostatic (coulmetric titration) - most common of two b) potentiostatic Fundamental requirement for both methods is 100% current efficiency - all e- go to participate in the desired electrochemical process - If not, then takes more current over-estimate amount of analyte B) Amperostatic Methods (Coulometric Titrations) 1. ) Basics: titration of analyte in solution by using coulometry at constant current to generate a known quantity of titrant electrochemically - potential set by contents of cell - Example: Ag (s) ↔ Ag+ + e- for precipitation titration of Cl- To detect endpoint, use 2 nd electrode to detect buildup of titrant after endpoint.

2. ) Applications a) Can be used for Acid-Base Titrations - Acid titration 2 H 2 O + 2 e- ↔ 2 OH- + H 2 titrant generation reaction - Base titration H 2 O ↔ 2 H+ + ½ O 2 + 2 e- titrant generation reaction b. ) Can be used for Complexation Titrations (EDTA) Hg. NH 3 Y 2 - + NH 4+ + 2 e- ↔ Hg + 2 NH 3 +HY 3 - ↔ H+ + Y 4 c. ) Can be used for Redox Titrations Ce 3+ ↔ Ce 4+ + e. Ce 4+ + Fe 2+ ↔ Ce 3+ + Fe 3+

3. ) Comparison of Coulometric and Volumetric Titration a) Both Have Observable Endpoint - Current (e- generation) < serves same function as a standard titrant solution - Time < serves same function as volume delivered - amount of analyte determined by combining capacity - reactions must be rapid, essentially complete and free of side reactions b. ) Advantages of Coulometry - Both time and current easy to measure to a high accuracy - Don’t have to worry about titrant stability - easier and more accurate for small quantities of reagent < small volumes of dilute solutions problem with volumetric - used for precipitation, complex formation oxidation/reduction or neutralization reactions - readily automated c) Sources of Error - variation of current during electrolysis - departure from 100% current efficiency - error in measurement of current - error in measurement of time - titration error (difference in equivalence point and end point)

4. ) Change in Potential During Amperostatic Methods a) In constant current system, potential of cell will vary with time as analyte is consumed. - Cell “seeks out” electrochemical reactions capable of carrying the supplied current Cu 2+ + 2 e- ↔ Cu (s) initial reaction - Nernst Equation Ecathode = Eo. Cu 2+/Cu – 0. 0592/2 log (1/a. Cu 2+) Note: Ecathode depends on a. Cu 2+. As a. Cu 2+ decreases (deposited by reaction) Ecathode decreases.

- When all Cu 2+ is consumed, current is carried by another electrochemical reaction < generation of H 2 (g) if reduction 2 H+ + 2 e- ↔ H 2 (g) < breakdown of water if oxidation 2 H 2 O ↔ H 2 O 2 + 2 H+ + 2 e. H 2 O 2 ↔ O 2 + 2 H+ + 2 e- M 2+ + 2 e- M(s) (co-deposition) - Not a problem as long as : (1) other species don’t co-deposit (2) there isn’t a large excess of species being used in titrant generation vs. titrated analyte e. g. , Ag (s) vs. Cl- in solution (in Ag. Cl precipitation experiment)

C) Potentiostatic Coulometry 1. ) Basics: -detection of analyte in solution by using Coulometry at fixed potential to quantitatively convert analyte to a given form < current controlled by contents of cell. 2. ) Instrumentation requirements: - electrochemical/electrolysis cell - a potentiostat (apply the required potential/voltage to the system) - an integrator (analog or digital) for determination of the charged consumed Equivalent circuit Practical Circuit of a Potentiostat and an Electrochemical/Electrolysis Electrochemical cell

2) Advantages: - more specific than amperostatic coulometry < avoids redox of species that may interfere with constant current coulometry - can be used for over 55 elements without major interference 3) Disadvantages - does take longer than amperostatic titration < current (i) decreases with time < conversion becomes slower as less analyte around to oxidize or reduce It = Ioe-kt k = 25. 8 DA/Vd where: It = current at time t (A) I 0 = initial current (A) t = time (sec) *** typical values of D are in the range of 10 -5 cm 2/s *** typical values of d is 2 x 10 -3 cm D = diffusion coefficient (cm 2/s) A = electrode surface area (cm 2) V = volume of solution (cm 3) d = thickness of the surface layer where concentration gradient exists (cm)

Example (using the two equations): Deposition of Copper: Cu 2+ + 2 e- Cu (s) After 30 min, current decreases from the initial 1. 5 A to 0. 08 A By this time, approx. 96% of the copper has been deposited. 4) Other Applications of constant potential coulometry - electroplating, apply the correct potential, the “metal of interest” will be deposited. e. g. gold plated onto silver (vermeil) as jewelry e. g. zinc plated onto steel for anti-corrosion (zinc as “sacrificial cathodic coating”) The term "vermeil" refers to a silver item, containing no less than 92. 5% silver, that has been plated with a gold or gold alloy that is no less than 10 karat, to a thickness of not less than 2. 5 microns.