Electrochemistry Notes

Electrochemistry

• Electrochemistry is the study of batteries and the conversion between chemical and electrical energy.
• Galvanic cells (Voltaic cells) are batteries that generate electricity through a spontaneous chemical reaction.
• Reactions in batteries are redox (oxidation-reduction) reactions; one substance gains electrons, and another loses electrons.
• Oxidation and reduction MUST happen together.

Oxidation Numbers

• Free elements: oxidation number = 0 (e.g., $H_2(g)$, $Hg(l)$).
• Ions in binary ionic compounds: oxidation number = charge. Example: For $Al<em>2S</em>3$, oxidation number for Al = +3, oxidation number for S = -2.
• Hydrogen: oxidation number = +1, except when H is with alkali metals, it is -1 (e.g., LiH, NaH).
• Oxygen: oxidation number = -2, except in peroxides, it is -1 (e.g., $H<em>2O</em>2$, $K<em>2O</em>2$).
• The sum of the oxidation numbers of all the atoms in a molecule = 0.
• For polyatomic ions, the sum of the oxidation numbers must equal the charge on the ion.
• The non-oxygen element in a polyatomic ion has to be determined from the other oxidation numbers.

Oxidation Number Examples

• Find oxidation numbers for all atoms in $HCO_3^-$.
  • H: oxidation number = +1, O: oxidation number = -2
  • 1
    H + 1
    C + 3
    O = -1
  • $+1 + C + 3(-2) = -1$
  • Oxidation number for C = +4
• What is the oxidation number for Cr in $Cr<em>2O</em>7^{2-}$.
  • $2Cr + 7O = -2$
  • $2Cr + 7(-2) = -2$
  • Cr = +6

Redox Reactions

• LEO the lion goes GER
  • Oxidation: Loss of electrons; oxidation number increases, more positive.
  • Reduction: Gain of electrons; oxidation number decreases, more negative.
  • Oxidizing agent: substance that is reduced; it caused the oxidation of another substance.
  • Reducing agent: substance that is oxidized; it caused the reduction of another substance.
• Example: $Zn(s) + Cu(NO<em>3)</em>2(aq) \rightarrow Zn(NO<em>3)</em>2(aq) + Cu(s)$
  • What is reduced: $Cu^{2+}$ in $Cu(NO<em>3)</em>2$
  • What is the oxidizing agent: $Cu(NO<em>3)</em>2$
  • What is the reducing agent: $Zn(s)$
  • What is oxidized: $Zn(s)$
• $Zn$ 0 to +2 oxidation number increases; $Zn$ becomes more +
• $Cu^{+2}$ to 0 oxidation number decreases; $Cu^{2+}$ becomes more -
• Reduced/oxidized – give a specific atom or ion.
• Reducing/oxidizing Agent – give the whole chemical substance (compound or element).

Half-Reactions

• $Zn(s) + Cu(NO<em>3)</em>2(aq) \rightarrow Zn(NO<em>3)</em>2(aq) + Cu(s)$
  • Oxidation half-reaction: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$ (LEO; electrons are a product) $Zn(s)$ dissolves.
  • Reduction half-reaction: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$ (GER; electrons are a reactant) $Cu$ plates on the electrode.

Balancing Redox Reactions

• Example: $Cr^{3+}(aq) + Be(s) \rightarrow Cr(s) + Be^{2+}(aq)$
  1. Break the redox reaction into two half-reactions: oxidation and reduction.
  2. Balance charges by adding electrons ($e^-$.) to the more positive side for each half-reaction.
  3. Balance electrons by multiplying each half-reaction by an integer so that the number of electrons gained = number of electrons lost.
• Write the Half reactions
  • Oxidation: $Be(s) \rightarrow Be^{2+}(aq) + 2e^-$ ($e^-$ = product)
  • Reduction: $Cr^{3+}(aq) + 3e^- \rightarrow Cr(s)$ ($e^-$ = reactant)
• Balance the electrons
  • Oxidation: $(Be(s) \rightarrow Be^{2+}(aq) + 2e^-) \times 3$
  • Reduction: $(Cr^{3+}(aq) + 3e^- \rightarrow Cr(s)) \times 2$
• Add reactions and cancel common terms:
  • $2Cr^{3+}(aq) + 3Be(s) \rightarrow 2Cr(s) + 3Be^{2+}(aq)$

Types of Cells

• Galvanic cell (also called voltaic cell):
  • Electrochemical cell in which a spontaneous reaction generates electricity (electric energy is produced).
• Electrolytic cell:
  • Electrochemical cell in which an electrical current is used to drive a nonspontaneous reaction (electric energy is consumed).

Galvanic Cells

• Oxidation occurs at the anode (both vowels).
  • Mass of anode decreases - it is dissolving as metal atoms lose electrons to form ions in solution.
• Reduction occurs at the cathode (both consonants).
  • Mass of the cathode increases as metal ions are reduced to form atoms that plate onto the cathode.
• External Circuit
  • Electrons flow from the anode to the cathode via an external wire.
• Salt bridge
  • Soluble salt solution in a bridge that connects the two half cells; ions flow through the bridge to complete the electrical circuit.
• Migration of ions maintains charge neutrality in both compartments:
  • Anions move into the anode where excess + charge builds up as metal cations are formed by oxidation.
  • Cations move into the cathode where excess (-) charge builds up as the metal cations are reduced to form neutral metal atoms.
• Mnemonic:
  • Fat red cat eats electrons!
  • Anorexic ox spits them out!
  • Cathode is reduced (gains $e^-$) & mass increases (plating)
  • Anode is oxidized (loses $e^-$) & mass decreases (dissolves)

Standard Hydrogen Electrode (SHE)

• Uses Pt as electrode.
• Inert electrodes allow electrons to transfer but don’t take part in the reaction.

Shorthand Notation for Galvanic Cells

• $Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$
  • $|$ = Phase boundary between components in the same cell
  • $||$ = Salt bridge between two half cells
  • electrodes always on 2 ends: anode on left; cathode on right
  • Inert electrodes (Pt) are used for gas phase and aqueous reactions. They allow $e^-$ transfer to occur but don’t react with cell components.
• Overall cell reaction:
  • $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$

Electromotive Force

• emf = $E_{cell}$ = cell voltage
• Electromotive force is the cell potential measured in volts. This is the driving force that pushes electrons away from the anode and towards the cathode.
• Joules = Coulombs x Volts
• $E_{cell}$ is measured in volts: $V = J/C$
  • coulomb - the quantity of charge that passes a point in 1 second when a current of 1 ampere flows.

Standard Cell Potential

• Gases at 1 atm, Solutions at 1 M, Temperature at 298 K (25°C).
• Standard potential for any galvanic cell is the sum of the half-cell potentials.
• $E<em>{cell}^o = E</em>{ox}^o + E_{red}^o$
• All cell potentials are compared to hydrogen (SHE: standard hydrogen electrode).
• SHE consists of Pt electrode in contact with 1 M $H^+$ solution and $H_2$ gas at 1 atm pressure.
• $2H^+ + 2e^- \rightarrow H<em>2(g) E</em>{red}^o = 0 V$

Reduction Potentials

• We can use the table of Standard Reduction Potentials for reduction half-reactions to determine the cell potential of a galvanic cell.
• All potentials are listed as reduction potentials.
• Oxidation potentials: reverse the reaction and change the sign.
• For the oxidation reaction at the anode, make sure you reverse the reaction and change the sign for $E_{ox}^o$, then add the reduction and oxidation potentials.
• $E^o$ is intensive; it does not depend on the number of moles involved. Don't multiply $E^o$ by a factor if coefficients of reaction are changed.

Strength of Oxidizing/Reducing Agents

• $F<em>2(g) + 2e^- \rightarrow 2F^-(aq) E</em>{red}^o = 2.866 V$
  • $F<em>2$ has the most positive $E</em>{red}^o$ value.
  • $F_2$ is the easiest to reduce (it wants electrons the most!).
  • Thus $F_2$ is the strongest oxidizing agent.
  • Active nonmetals are good oxidizing agents (oxidizing agent = reduced = gain $e^-$.
  • As $E_{red}$ increases, the strength of the oxidizing agent increases.
• $Li^+(aq) + e^- \rightarrow Li(s) E_{red}^o = -3.04 V$
  • $Li$ has the most negative $E_{red}^o$ value, so it is the easiest to oxidize.
  • $Li(s)$ is the strongest reducing agent.
  • $Li(s)$ wants to lose electrons, so the reverse reaction occurs: $Li(s) \rightarrow Li^+(aq) + e^- E_{ox}^o = +3.04 V$
  • Active metals are good reducing agents (reducing agent = oxidation = lose $e^-$.

Cell Potentials

• A positive $E_{cell}^o$ means the reaction is product-favored and spontaneous.
• A negative $E_{cell}^o$ means the reaction won’t happen in the forward direction.
• Therefore, we want two half-reactions that yield the most positive $E_{cell}^o$ value.
• Assign the reaction with the more positive $E_{red}^o$ as the cathode!
• $E<em>{cell}^o = E</em>{red}^o + E_{ox}^o$

Free Energy and EMF

• $\Delta G = -nFE$
  • n = number of moles of $e^-$ transferred
  • E = Emf of cell
  • F = Faraday's constant
• Spontaneous reaction: $\Delta G < 0$ and $E > 0$
• Nonspontaneous reaction: \Delta G > 0 and E < 0
• At equilibrium: $\Delta G = 0$ and $E = 0$

Standard EMF & K

• At equilibrium, $E = 0$ and $Q = K$ (plug these conditions into the Nernst Equation).
• At 298 K,

Cell Potentials Summary

• Positive $E_{cell}^o$ value
  • Provides energy
  • $\Delta G^o$ is negative
  • K is large
  • Reaction is product-favored
• Negative $E_{cell}^o$ value
  • Consumes energy
  • $\Delta G^o$ is positive
  • K is small
  • Reaction is reactant-favored

The Nernst Equation

• Calculate emf for nonstandard conditions
• Recall: $\Delta G = \Delta G^o + RT \ln Q$
• Plugging in $\Delta G = -nFE$ and $\Delta G^o = -nFE^o$
• At 298 K:

Electrolysis

• Electrolytic Cell
  • Electrical energy from an external source (outlet or a battery) is used to force a nonspontaneous redox reaction to proceed.
  • Water doesn’t naturally decompose into $H<em>2$ and $O</em>2$. A battery must supply energy to drive this reaction forward.
  • $2H<em>2O(l) \rightarrow 2H</em>2(g) + O<em>2(g) E</em>{cell} = -1.23 V$
  • Anode: $2H<em>2O(l) \rightarrow O</em>2(g) + 4H^+(aq) + 4e^-$
  • Cathode: $4H^+(aq) + 4e^- \rightarrow 2H_2(g)$
  • The electrodes are still the same for electrolysis (oxidation at the anode, reduction at the cathode).
  • Reactions occur in the opposite direction of the spontaneous process:
    • $O<em>2(g)$ likes to gain electrons while $H</em>2(g)$ usually loses electrons.

Electrolysis Calculations

• Used to find the mass or volume of product produced by passing current through the cell.
• Current: measured in Amps (A = C/s)
  • ampere: unit of electric current; rate of flow of electrons.
• charge = current x time
• coulombs = amps x seconds
• How many grams of $Cu$ can be collected in 1.00 hour by a current of 1.62 A from a $CuSO_4$ solution?
  • Reduction reaction: $Cu^{2+} + 2 e^- \rightarrow Cu$
  • Calculate coulombs: Current (C/s) x time (s) = C
  • C to mol $e^-$ to mol solid to g metal
  • convert time to secs: 1 hr = 3600 secs

Batteries

• Batteries are examples of Galvanic cells we use in everyday life.
• For a Galvanic cell, the voltage keeps dropping as the spontaneous reaction proceeds.
• A battery is dead when $E_{cell} = 0$ (at equilibrium the reaction no longer proceeds forward; this is the minimum point on the free energy curve).
• Bigger batteries only last longer; they don’t have more volts. Volts are determined by the chemical reaction that occurs.

Types of Batteries

• Lead Storage (Car) Batteries
  • 6 cells
  • 2 V per cell
  • 12 V total
  • Rechargeable
  • Anode: $Pb(s) + 2HSO<em>4^–(aq) \rightarrow PbSO</em>4(s) + H^+(aq) + 2e^-$
  • Cathode: $PbO<em>2 (s) + 3H^+ (aq) + HSO</em>4^–(aq) + 2e^– \rightarrow PbSO<em>4 (s) + 2H</em>2O(l)$
  • Overall: $Pb(s) + PbO<em>2 (s) + 2H</em>2SO<em>4 (aq) \rightarrow 2PbSO</em>4 (s) + 2H_2O(l)$
• Dry Cell (or Laclanche) Batteries
  • Zinc container (anode), Graphite rod (cathode), 1.5 V
  • Anode: $Zn(s) \rightarrow Zn^{2+} (aq) + 2e^–$
  • Cathode: $2 NH<em>4 ^+(aq) + 2MnO</em>2(s) + 2e^– \rightarrow Mn<em>2O</em>3(s) + 2NH<em>3(aq) + H</em>2O(l)$
  • Overall: $Zn(s) + 2NH<em>4 ^+(aq) + 2MnO</em>2(s) \rightarrow Zn^{2+}(aq)+ Mn<em>2O</em>3(s) + 2NH<em>3(aq) + H</em>2O(l)$
• Alkaline Batteries
  • Zinc container (anode), Graphite rod (cathode), 1.43 V
  • Anode: $Zn(s) + 2OH^-(aq) \rightarrow ZnO(s) + H_2O(l) + 2e^–$
  • Cathode: $2MnO<em>2(s) +H</em>2O(l) + 2e^– \rightarrow Mn<em>2O</em>3(s) + 2OH^-(aq)$
  • Overall: $Zn(s) + 2MnO<em>2(s) \rightarrow ZnO(s)+ Mn</em>2O_3(s)$
• 9 V Batteries
  • 6 x 1.5 V Dry Cell batteries connected in series
• NiCd Batteries
  • Nickel-plated cathode and cadmium-plated anode.
  • Anode: $Cd(s) + 2OH^-(aq) \rightarrow Cd(OH)_2(s) + 2e^–$
  • Cathode: $NiO<em>2(s) + 2H</em>2O(l) + 2e^– \rightarrow Ni(OH)_2(s) + 2OH^-(aq)$
  • Overall: $Cd(s) + NiO<em>2(s)+ 2H</em>2O(l) \rightarrow Cd(OH)<em>2(s)+ Ni(OH)</em>2(s)$
• Lithium-ion (Rechargeable) batteries
  • Charge flows between the electrodes as the lithium ions move between the anode and cathode.
  • Cell potential: 3.7 V
  • Anode: $Li(s) \rightarrow Li^+ + e^–$
  • Cathode: $Li^+(aq) + CoO<em>2 + e^– \rightarrow LiCoO</em>2(s)$
  • Overall: $Li^+(s) + CoO<em>2 \rightarrow LiCoO</em>2(s)$
• Fuel Cells
  • $E_{cell}^o = 1.23 V$
  • Anode: $2H<em>2(g) + 2O</em>2 ^-(aq) \rightarrow 2H_2O(l) + 4e^–$
  • Cathode: $O<em>2 (aq) + 4e^– \rightarrow 2O</em>2 ^-(aq)$
  • Overall: $2H<em>2(g) + O</em>2(g) \rightarrow 2H_2O(l)$

Corrosion

• The term corrosion generally refers to the deterioration of a metal by an electrochemical process (e.g., rusting of iron).