3 Slides Per Page

10/9/2020

Lecture #3 of 26

Looking forward… our review of Chapter “0” ● Cool applications ● Redox half-reactions ● Balancing electrochemical equations ● History of electrochemistry and Batteries

● IUPAC terminology and Ecell = Ered – Eox ● Thermodynamics and the Nernst equation ● Common reference electrodes ● Standard and Absolute potentials ● Latimer and Pourbaix diagrams

● Calculating Ecell under non-standard state conditions ● Conventions

RECALL: Daniell (galvanic) Cell (1836) 66

No more H2 from the (primary) battery! anode cathode oxidation reduction

Chemist, Meteorologist

Half-reactions are physically separated!

2+ – 2+ – Zn (s) → Zn (aq) + 2e Cu (aq) + 2e → Cu (s) John Frederic Daniell (1790–1845) NET REACTION: Zn (s) + Cu2+ (aq) → Zn2+ (aq) + Cu (s) from Wiki

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Voltage Produced by Galvanic Cells 67

The difference in electric potential between the anode and the cathode is called: ✓ Cell potential ✓ Cell voltage ✓ emf (electromotive force)

This should be –0.76 V! Cell Diagram (we will discuss this soon) Zn (s) + Cu2+ (aq) Cu (s) + Zn2+ (aq) [Cu2+] = 1 M and [Zn2+] = 1 M Zn (s) | Zn2+ (aq, 1 M) || Cu2+ (aq, 1 M) | Cu (s) anode salt bridge cathode

EXAMPLE: What is the (standard) potential of a galvanic cell 68

consisting of a Cd electrode in a 1.0 M Cd(NO3)2 solution and a Cr electrode in a 1.0 M Cr(NO3)3 solution? Which half-reaction is reducing? 2+ – 0 Cd (aq) + 2e Cd (s) E = -0.40 V Cd2+ will get reduced to Cd Cr3+ (aq) + 3e– Cr (s) E0 = -0.74 V Cr will get oxidized to Cr3+ More negative of the two … thus, it is reducing Anode (oxidation): Cr (s) Cr3+ (1 M) + 3e– x 2 Cathode (reduction): 2e– + Cd2+ (1 M) Cd (s) x 3 2Cr (s) + 3Cd2+ (1 M) 3Cd (s) + 2Cr3+ (1 M) 0 0 0 Ecell = Ecathode – Eanode 0 Ecell = -0.40 V – (-0.74 V) 0 Ecell = +0.34 V (positive = spontaneous, since ∆퐺 = −푛퐹퐸) … if your answer is negative then you switched the anode/cathode in the galvanic cell

Electrochemistry: 69 conventions… oh, conventions! Cathode – electrode where catholyte species are reduced Anode – electrode where anolyte species are oxidized

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Electrochemistry: 70 conventions… oh, conventions! Cathode – electrode where catholyte species are reduced Anode – electrode where anolyte species are oxidized

Does a Negative/Positive Electrode = Cathode or Anode?… It depends!

For the discharging (galvanic) battery, label the anode and the cathode.

http://autoshop101.com/

Electrochemistry: 71 conventions… oh, conventions! Cathode – electrode where catholyte species are reduced Anode – electrode where anolyte species are oxidized

Does a Negative/Positive Electrode = Cathode or Anode?… It depends!

For the charging (electrolytic) battery, label the anode and the cathode.

e– e–

This is a generator (AKA power supply) cathode anode

http://autoshop101.com/

Electrochemistry: 72 conventions… oh, conventions! Positive electrode – positively charged; immersed in the posolyte Negative electrode – negatively charged; immersed in the negolyte … I’m not kidding! … Sheesh!… … Take-home message: For batteries, don’t call electrodes anodes and cathodes (but naming convention used by most is for discharge)

e– e– e– e–

anode cathode cathode anode

http://autoshop101.com/

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Chemist, Meteorologist The Daniell Cell (1836)

low impedance to measure current – –

Icell John Frederic Daniell (1790–1845) from Wiki As drawn, current flows for < 1 sec and then stops due to Zn Cu lack of charge neutrality… … capacitive charging Zn(s) Zn2+(aq) Cu2+(aq) Cu(s)

Zn | Zn2+(aq) || Cu2+(aq) | Cu

Chemist, Meteorologist The Daniell Cell (1836)

Now it works = “electrochemistry”! low impedance to measure current – –

Icell John Frederic Daniell + Ai (1790–1845) from Wiki As drawn, current flows B – i for < 1 sec Salt bridge and then contains an inert, stops due to Zn redox inactive Cu lack of charge salt solution neutrality… (electrolyte) … capacitive charging Zn(s) Zn2+(aq) Cu2+(aq) Cu(s)

Zn | Zn2+(aq) || Cu2+(aq) | Cu

The Daniell Cell (1836) Quick Quiz * Name the cell type * Identify the anode * Identify the cathode low impedance to measure current * Name the – – electrode signs Icell + * primary galvanic cell Ai … Ultimately, this cell will have fully discharged, and at which point it will B – i be at equilibrium

(ΔG = Ecell = 0)… (A/–) (C/+) Zn Cu … Then, any direction of polarization bias will result Zn(s) Zn2+(aq) Cu2+(aq) Cu(s) in electrolytic function (i.e. Zn | Zn2+(aq) || Cu2+(aq) | Cu charging)!

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76 Quick Check on Your Understanding

You try!

(a) What is the standard Ecell for a galvanic cell based on zinc and silver?

Ecell = +0.80 V – (-0.76 V) = 1.56 V

(b) If one wanted to electrolytically charge the cell from part a (before any reactions took place), what potential would one have to provide?

Ebias < –1.56 V… such that Ecell + Ebias < 0 (this is the observed value)

77 International Union of Pure and Applied Chemistry (IUPAC)

(Accepted) Nomenclature and Terminology that you’ve learned, but may have forgotten

• Coulomb (in units of C = A·s) is the unit of charge (96,485 C are in a mole of singly charged species = Faraday constant, F ≈ 96,500 C/mol ≈ 105 C/mol) differentiate, with respect to time integrate, over time • Electricity is the flow of current (I; in units of A = C/s) and is negative (cathodic) or positive (anodic) depending on the direction and sign of the current-carrying species (e.g. e–, H+) • (Electrode) (electric) potential (V or E; in units of V = J/C) is written as a reduction

This relates to Gibbs free energy as ΔG = –RT ln K = –nFEcell (electrical work per mole), and… … partial molar Gibbs free energy is the electrochemical potential (휇ҧ, in units of J/mol) ➢ Chemical potential (휇, in units of J/mol) ➢ Galvani/Inner (electric) potential (ϕ, in units of V) … and in summary, 휇ҧ = 휇 + 푧퐹ϕ Also, standard state is a solvent, a solid, and a species at unit activity (~1 M solutes, ~1 bar gases) Also, E = IR (Ohm’s law) when resistance is constant

• Galvanic cells produce power (in units of W = A x V = C/s x J/C = J/s) by spontaneous redox reactions

• Electrolytic cells require a power input to drive redox reactions; thus, the reactions are thermodynamically unfavorable • A battery has an anode/anolyte and a cathode/catholyte, but these descriptors change depending on whether the battery is being discharged(Sources (galvanic): B&F, M3LC or charged course (electrolytic); textbook, negative electrode/negolyte and positive electrode/posolyte are better and http://goldbook.iupac.org/)

78 International Union of Pure and Applied Chemistry (IUPAC)

(Accepted) Nomenclature and Terminology that you’ve learned, but may have forgotten

• (Electrode) (electric) potential (V or E; in units of V = J/C) is written as a reduction

This relates to Gibbs free energy as ΔG = –RT ln K = –nFEcell (electrical work per mole), and… … partial molar Gibbs free energy is the electrochemical potential (휇ҧ, in units of J/mol) Based on➢ourChemicalcurrentpotentialsign convention (휇, in units of J/, molit is) E0(Cu2+/0) = +0.34 V vs. SHE best to ➢onlyGalvani/Innerwrite reduction (electric) potentialpotentials (ϕ, in units; of V) E0(Cu0/2+) = –0.34 V vs. SHE however,… andif inwe summary,lived 휇ҧ =in휇 +an푧퐹ϕ oxidation- Also, standard state is a solvent, a solid, and a species at unit activity (~1 M… solutes, is incorrect! ~1 bar gases) potentialAlso,-centric E = IR (Ohm’sworld, law) whenwe resistancecould iswrite constant them all (i.e. everything) as oxidation You can subtract redox • Galvanic cells produce power (in units of W = A xpotentials V = C/s x J/C but = J/s)do not by spontaneous change the potentialsredox; reactionssimply put, it is best to not sign of the potential and then mix the conventions and so stick with • Electrolytic cells require a power input to drive redoxcall reactions;it an oxidation thus, the potential! reactions are reductionthermodynamicallypotentials unfavorable • A battery has an anode/anolyte and a cathode/catholyte, but these descriptors change depending on whether the battery is being discharged (galvanic) or charged (electrolytic); negative electrode/negolyte and positive electrode/posolyte are better

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79 International Union of Pure and Applied Chemistry (IUPAC)

(Accepted) Nomenclature and Terminology that you’ve learned, but may have forgotten

This relates to Gibbs free energy as ΔG = –RT ln K = –nFEcell (electrical work per mole), and… … partial molar Gibbs free energy is the electrochemical potential (휇ҧ, in units of J/mol) ➢ Chemical potential (휇, in units of J/mol) ➢ Galvani/Inner (electric) potential (ϕ, in units of V) Cannot be … and in summary, 휇ҧ = 휇 + 푧퐹ϕ measured Also, standard state is a solvent, a solid, and a species at unit activity (~1 M solutes, ~1 bar gases) Also, E = IR (Ohm’s law) when resistance is constant independently! • Galvanic cells produce power (in units of W = A x V = C/s x J/C = J/s) by spontaneous redox reactions

• Electrolytic cells require a power input to drive redox reactions; thus, the reactions are thermodynamically unfavorable

• A battery has an anode/anolyte and a cathode/catholyte, but these descriptors change depending on whether the battery is being discharged (galvanic) or charged (electrolytic); negative electrode/negolyte and positive electrode/posolyte are better

80 International Union of Pure and Applied Chemistry (IUPAC)

(Accepted) Nomenclature and Terminology that you’ve learned, but may have forgotten

This relates to Gibbs free energy as ΔG = –RT ln K = –nFEcell (electrical work per mole), and… … partial molar Gibbs free energy is the electrochemical potential (휇ҧ, in units of J/mol) ➢ Chemical potential (휇, in units of J/mol) ➢ Galvani/Inner (electric) potential (ϕ, in units of V) … and in summary, 휇ҧ = 휇 + 푧퐹ϕ Also, standard state is a solvent, a solid, and a species at unit activity (~1 M solutes, ~1 bar gases) Also, E = IR (Ohm’s law) when resistance is constant

• Galvanic cells produce power (P; in units of W = A x V = C/s x J/C = J/s) by spontaneous redox reactions opposites • Electrolytic cells require a power input to drive redox reactions; thus, the reactions are thermodynamically unfavorable • A battery has an anode/anolyte and a cathode/catholyte, but these descriptors change depending on whether the battery is being discharged (galvanic) or charged (electrolytic); negative electrode/negolyte and positive electrode/posolyte are better

For “clarity,” a brief (more rigorous) “review” of thermodynamics… 81

Electrochemical potential of species i in phase β is an energy (J/mol),

휷 흏푮 휷 휷 흁ഥ풊 = 휷 = 흁풊 + 풛풊푭흓 , where 흏풏풊 푻,풑,풏풋≠풊 G (Gibbs free energy (J))

ni (amount of species i (mol)) ퟎ 흁풊 = 흁풊 + 푹푻 풍풏 풂풊 (chemical potential (J/mol)) zi (valency of species i) F ≈ 105 (Faraday constant (C/mol) ϕβ (Galvani/inner electric potential (V))

ai (activity of species i)

β β For an uncharged species 휇ҧ푖 = 휇푖 .

Parsons, Pure & Appl. Chem., 1973, 37, 501 … more on this later… IUPAC Gold (http://goldbook.iupac.org)

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Half reactions, at non-unity activity, obey the Nernst equation… 82

Take ∆퐺 = ∆퐺0 + 푅푇 ln 푄 and use the relation ∆퐺 = −푛퐹퐸,

But first… what is Q, again? … the reaction quotient!

푣푝 푐푝 푣푝 ς푝 γ푝 0 ς푝 푎푝 푐푝 0 푄 = = 푣 , because 휇 = 휇 + 푅푇 ln 푎 ς 푎 푣푟 푐 푟 푖 푖 푖 푟 푟 ς γ 푟 푟 푟푐 0 푣푝 푟 ς푝 푐푝 푄 = 푣 , for dilute solutions… which we never have, and where ς푟 푐푟 푟 ap is the activity of product p ar is the activity of reactant r vi is the stoichiometric number of i γi is the activity coefficient of i ci is the concentration of i 0 ci is the standard state concentration of i

Half reactions, at non-unity activity, obey the Nernst equation… 83

Take ∆퐺 = ∆퐺0 + 푅푇 ln 푄 and use the relation ∆퐺 = −푛퐹퐸,

But first… what is Q, again? … the reaction quotient!

푣푝 푐푝 푣푝 ς푝 γ푝 0 ς푝 푎푝 푐푝 푄 = 푣 = 푣푟 ς푟 푎푟 푟 푐푟 ς푟 γ푟 0 푐푟

푣푝 ς푝 푐푝 푄 = 푣 , for dilute solutions… which we never have! ς푟 푐푟 푟 ap is the activity of product p ar is the activity of reactant r vi is the stoichiometric number of i γi is the activity coefficient of i ci is the concentration of i 0 ci is the standard state concentration of i

Half reactions, at non-unity activity, obey the Nernst equation… 84

Take ∆퐺 = ∆퐺0 + 푅푇 ln 푄 and use the relation ∆퐺 = −푛퐹퐸,

Reaction quotient as −푛퐹퐸 = −푛퐹퐸0 + 푅푇 ln 푄 product and quotient of 푅푇 species’ activities 퐸 = 퐸0 − ln 푄 푛퐹 Physicist 푅푇 log 푄 퐸 = 퐸0 − 푛퐹 log 푒 푅푇 퐸 = 퐸0 − log 푄 0.4343푛퐹

2.3026푅푇 Walther Hermann Nernst 퐸 = 퐸0 − log 푄 (1864–1941) 푛퐹 Nobel Prize (Chemistry, 1920) 0.05916 V from Wiki … and at 298.15 K, 퐸 = 퐸0 − log 푄 푛

Memorize ~60 mV per order in log10, but do not forget n and that this is at 25 °C!

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Looking forward… our review of Chapter “0” ● Cool applications ● Redox half-reactions ● Balancing electrochemical equations ● History of electrochemistry and Batteries

● IUPAC terminology and Ecell = Ered – Eox ● Thermodynamics and the Nernst equation ● Common reference electrodes ● Standard and Absolute potentials ● Latimer and Pourbaix diagrams

● Calculating Ecell under non-standard state conditions ● Conventions

Half reactions must be referenced to something… 86

퐸cell = 퐸red − 퐸ox Since the method of half-reactions ultimately results in us taking their difference, we can add an arbitrary constant to all half reactions… By one (somewhat arbitrary) convention, it is often assumed that Eo for the standard hydrogen electrode (SHE) is equal to zero.

Half-Reaction for Hydrogen gas (H2): + − 1 H + e → 2퐻2 푔

푝 퐸 = 퐸0 + 푅푇 ln H2 퐸0 = 0 H2 H2 퐹 H+ H2

Thus, the potentials for half-cell reactions are actually full-cell potential (difference(s)) versus SHE, or other!