Fixed surface concentration. t 1 < t 2 < t 3 C O. t 1 t 2 t 3. Concentration. Distance

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Jemima Walton
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1 Fixed surface concentration O * oncentration t 1 < t 2 < t 3 t 1 t 2 t 3 Distance

2 Fixed surface concentration onsider the t 1 < t 2 < t 3 * O concentration profile t 3 when t 1 t the sample 2 t 3 length is L. o (L, t 3 ) is no longer * O when the sample length is L. it does not meet the boundary condition o (, t) used to solve the Fick s 2 nd law. oncentration Distance L

5 Oxidation and Reduction equilibrium E (volts) The more positive the E value, the further the position of equilibrium lies to the right. That means that the more positive the E value, the more likely the substances on the left-hand side of the equations are to pick up electrons. A substance which picks up electrons from something else is an oxidising agent. The more positive the E value, the stronger the substances on the lefthand side of the equation are as oxidising agents. hlorine gas is the strongest oxidising agent (E = v). A solution containing dichromate(vi) ions in acid is almost as strong an oxidising agent (E = v). None of these three are as strong an oxidising agent as Au 3+ ions (E = v).

7 E = 0 F r e e G # oc (1 )nfe nfe E = E e n e r g y G # c G # a G # oa G # oc + nfe = G # c+ (1 )nfe nfe O + ne R Reaction oordinate ve shift in G leads to +ve shift in E Anodic oxidation facilitated

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9 Nernst Equation O + ne = R E = E o (RT/nF) (a R /a O ), E o =? E = E o (RT/nF) ( R / O ), E o = formal potential If the system follows the Nernst equation, the electrode reaction is often said to be thermodynamically or electrochemically reversible (or nernstian). Reversibility of a process ; one s ability to detect the signs of disequilibrium Rate of change of force driving the observed process vs. speed with which the system can reestablish equilibrium If the perturbation applied to the system is small enough, or if the system can attain equilibrium rapidly enough compared to the measuring time, thermodynamic relation will apply.

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11 ) ( ) (1 ) ( 0 0' 0' ) (0, ) (0, [ )] (0, ) (0, [ )] (0, ) (0, [ ) ( ) (0, ) (0, E E f R E E f O R b O f a c R b O f b f net a R b b c O f f e t e t nfak i t k t nfa k i i i nfa i t k t k v v v nfa i t k v nfa i t k v Input k f and k b equation, then we got the following equation

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13 nfak e E i e i i f ( E eq At Equilibrium conditions: the exchange current eq f ( E 0 E E O nfak eq 0' ) E 0' 0' nfak nfak (0, t ) e ) 0 0 RT ln nf [ 0 * O * R e ( O * O f ( E f ( E * O * R * (1 ) ) eq * O * R eq * R E 0' E ) 0' ) ] nfak (0, t ) e 0 R *: bulk concentration Nernst Equation 0 *= R * (1 ) f ( E eq E Both sides are raised to - power 0' Nernst equation at equilibrium can be derived from the kinetic equation when the reaction rate is assumed to be zero )

16 When diffusion of O and R in solution is considered, we have diffusion limited current i l

21 i = i c -i a If i c >> i a, i a can be ignored in calculating i. Suppose that i a /i c < 0.01 exp[{(1-)f/rt}/exp{(-f/rt)} = exp{(f/rt)} < 0.01 At 25, < -118 mv Similarly, if i a >> i c, i c can be ignored in calculating i. Suppose that i c /i a < 0.01, then at 25, > 118 mv In either case, ll > 118 mv

23 i = i c -i a If i c >> i a, i a can be ignored in calculating i. Suppose that i a /i c < 0.01 exp[{(1-)f/rt}/exp{(-f/rt)} = exp{(f/rt)} < 0.01 At 25, < -118 mv Similarly, if i a >> i c, i c can be ignored in calculating i. Suppose that i c /i a < 0.01, then at 25, > 118 mv In either case, ll > 118 mv

24 RT/F) Lni o - RT/F) Lni RT/F) Lni = RT/F) Lni o Lni = {RT/F) Lni o }/RT/F) {/RT/F)} Lni = Lni o {/RT/F)} Lni = Lni o F/RT)

25 Lead - Acid Battery

28 Lead-acid batteries Positive electrode: Lead dioxide (PbO 2 ) Negative electrode: Lead (Pb) Electrolyte: Solution of sulfuric acid (H 2 SO 4 ) and water (H 2 O) +ve electrode -ve electrode PbO 2 H 2 O H 2 O Pb H 2 O H 2 O H 2 O

29 Lead-acid batteries hemical reaction (discharge) +ve electrode Electron flow -ve electrode PbO 2 2e - O 2-2 Pb 2+ 2H 2 O 2H + 2H + SO 4 2- PbSO 4 H 2 SO 4 SO 4 2- H 2 SO 4 PbSO 4 Pb 2+ 2e - Pb H 2 O H 2 O H 2 O H 2 O H 2 O

30 Lead-acid batteries hemical reaction (discharge) Negative electrode Pb Pb e- Pb 2+ + SO 4 2- PbSO 4 Electrolyte 2H 2 SO 4 4H + + 2SO 4 2- Positive electrode PbO 2 + 4H + + 2e - Pb H 2 O Pb 2+ + SO 4 2- PbSO 4 Overall Pb + PbO 2 + H 2 SO 4 2PbSO 4 + 2H 2 O The nominal voltage produced by this reaction is about 2 V/cell. ells are usually connected in series to achieve higher voltages, usually 6V, 12 V, 24 V and 48V.

31 Battery Basics-ell hemistry Additional Reactions of Significance Oxygen Reaction ycle:: ½O 2 + Pb PbO PbO + H 2 SO 4 PbSO 4 + H 2 O Note: Oxygen reaction cycle is a benchmark characteristic of VRLA batteries. It is more pronounced with AGM than with gel constructions. Severe Overcharge Reaction: 2H 2 O O 2 + 4H + + 4e - Note: This results in water loss due to venting of O 2 and can be life limiting. Positive Grid orrosion: Pb + 2H 2 O PbO 2 + 4H + + 2e - Note: This results in water loss and can be life limiting.

Stability of water : As was noted in connection with the shaded region, water is subject to decomposition by strong oxidizing agents such as l 2 and by reducing agents stronger than H 2.

32 Stability of water : As was noted in connection with the shaded region, water is subject to decomposition by strong oxidizing agents such as l 2 and by reducing agents stronger than H 2. The reduction reaction can be written either as 2 H e H 2 (g) or, in neutral or alkaline solutions as H 2 O + 2 e H 2 (g) + 2 OH E + H /H2 = E o H + /H 2 + (RT / 2F) ln {[H + ] 2 / P H2 } at 25 and unit H 2 partial pressure reduces to E = E ph = ph Similarly, the oxidation of water H 2 O O 2 (g) + 4 H e is governed by the Nernst equation. E O2 /H 2 O = E o O 2 /H 2 O + (RT/4F) ln {P O2 [H + ] 4 } at 25 and unit H 2 partial pressure reduces to E = ph

40 Electrode at equilibrium Equilibrium Potential Measurement Potential Reference Electrode, RE Working Electrode, WE

41 Electrolytic cell harge : current flow Electron flow D power supply urrent flow Electron flow current ve +ve Working Electrode, WE ounter Electrode, E Zn e Zn Electron consumption athodic reduction u u e Electron generation Anodic oxidation D power supply determines the polarity of electrodes.

42 Working Electrode The Working Electrode is the electrode where the potential is controlled and where the current is measured. The Working Electrode serves as a surface on which the electrochemical reaction takes place. For batteries, the potentiostat is connected directly to the anode or cathode of the battery. Reference Electrode The Reference Electrode is used in measuring the working electrode potential. A Reference Electrode should have a constant electrochemical potential as long as no current flows through it. The most common lab Reference Electrodes are the Saturated alomel Electrode (SE) and the Silver/Silver hloride (Ag/Agl) electrodes. ounter (Auxiliary) Electrode The ounter, or Auxiliary, Electrode is a conductor that completes the cell circuit. The ounter Electrode in lab cells is generally an inert conductor like platinum or graphite. The current that flows into the solution via the Working Electrode leaves the solution via the ounter Electrode.

43 Potentiostat A potentiostat is an electronic instrument that controls the voltage difference between a Working Electrode and a Reference Electrode. Both electrodes are contained in an electrochemical cell. The potentiostat implements this control by injecting current into the cell through an Auxiliary or ounter electrode. In almost all applications, the potentiostat measures the current flow between the Working and ounter electrodes. The controlled variable in a potentiostat is the cell potential and the measured variable is the cell current. At a glance, a potentiostat measures the potential difference between the working and the reference electrode, applies the current through the counter electrode, and measures the current as an ir drop over a series resistor (R m in the Fig. 1). current Working Electrode, WE ounter Electrode, E Potential Reference Electrode, RE

44 What happens if the feedback is too slow in our Potentiostat? Hot shower in a bathroom Skin = Electrometer Hot/cold water knob = ontrol Amp Water is too hot Turn the knob to OLD 2 seconds later, you re freezing! Turn the water to HOT 2 seconds later, you re scalded! Turn the knob to OLD Repeat until water temperature is OK for a shower

45 Potentiostat An electronic instrument that measures and controls the voltage difference between a Working Electrode and a Reference Electrode. It measures the current flow between the Working and ounter Electrodes. I V S Potentiostat A ontrol Amp Three Primary omponents of a Potentiostat ontrol Amplifier: Supplies the power to maintain the controlled potential between the Working and Reference Electrodes. I/E onverter V i R m V v Electrometer ell Switch Electrometer: Measures the potential difference between the Reference and Working Electrodes. WE RE E urrent to Voltage onverter: Measures the current between the Working and ounter Electrodes.

Care of Computer-Controlled Potentiostats

Care of Computer-Controlled Potentiostats What is a Potentiostat? Potentiostat An electronic instrument that measures and controls the voltage difference between a Working Electrode and a Reference Electrode.