Electrochemistry

• Electrochemical cells are contained systems where redox reactions occur
• Have electrodes where redox happens
  • Oxidation at anode
  • Reduction at cathode
  • (An-Ox and a Red-Cat)
• Electromotive force (emf) corresponds to voltage (potential difference)
  • If emf is $+$ → can release energy → spontaneous
  • If emf is $-$ → must absorb energy → nonspontaneous

Galvanic (Voltaic) cells

• Non-rechargeable batteries
• Since they supply energy, they’re spontaneous
• Free energy decreases as cell releases energy
  • $\Delta G < 0$ → $\text{emf} > 0$
• Two different electrodes placed in different compartments (half-cells), connected with conductive material
• Aqueous electrolyte solution of cations/anions surrounds electrodes
  • Cations can be same element as electrode
• Salt bridge connects the structures
• Charge flows when electrodes are connected with conductive material
• Inert salt used in the bridge
• As reaction goes toward equilibrium, movement of e⁻ converts internal energy into kinetic energy
• Can harness this energy to do work

Daniell cell

• Zinc electrode in $\text{ZnSO}_4$ solution, copper electrode in $\text{CuSO}_4$ solution
• Anode = zinc bar
  • Zinc oxidized: $\text{Zn} \rightarrow \text{Zn}^{2+} + 2 e^- \quad (E^\circ \approx -0.762\ \text{V})$
• Cathode = copper bar
  • Copper reduced: $\text{Cu}^{2+} + 2 e^- \rightarrow \text{Cu} \quad (E^\circ \approx +0.34\ \text{V})$
• If cells not separated, Cu²⁺ would directly react with Zn bar
• If wire provided for e⁻:
  • Reaction would eventually stop because excess $+$ charge builds on anode and $-$ charge on cathode
• If you provide a countercurrent large enough to prevent redox, current ceases
• Salt bridge has ions that won’t react with the solutions
  • Anions diffuse to anode side
  • Cations diffuse to cathode side
• Plating or galvanization occurs at the cathode
• e⁻ flow from zinc anode through wire to copper cathode
• Flow of ions from salt bridge depletes bridge and limits cell lifespan

Cell diagram

• Example Daniell cell:
  • $\text{Zn (s)} \;|\; \text{Zn}^{2+} (1\ \text{M}) \;||\; \text{Cu}^{2+} (1\ \text{M}) \;|\; \text{Cu (s)}$
• Listed from left to right: anode, anode solution, cathode solution, cathode
• Single vertical line = phase boundary
• Double vertical line = salt bridge/barrier

Electrolytic cells

• All have redox reactions at cathode and anode
• Opposite of galvanic cells:
  • Galvanic = spontaneous redox that generates electrical energy
  • Electrolytic = nonspontaneous redox that requires energy input
• Driven by electrolysis → chemical compounds decomposed
• Since nonspontaneous, electrode can be any material that resists high temp and corrosion

Examples of electrolytic cells

• Decomposition of water into $\text{O}_2$ and $\text{H}_2$
• Molten $\text{NaCl}$ into $\text{Cl}_2$ and Na
  • $\text{Na}^+$ goes to cathode and is reduced
  • $\text{Cl}^-$ goes to anode and is oxidized
• Since nonspontaneous, don’t need to separate into compartments
• Lets us obtain pure Na and Cl, which aren’t found in nature

Mⁿ⁺ and Faraday

• General reduction: $\text{M}^{n+} + n e^- \rightarrow \text{M (s)}$
• One mole of metal produced if $n$ moles of e⁻ are supplied to one mole of $\text{M}^{n+}$
• One e⁻ carries charge of $1.6 \times 10^{-19}\ \text{C}$
• One mole of e⁻ carries about $96{,}485\ \text{C/mol}$ (Faraday constant, $F \approx 10^5\ \text{C/mol}$)

Electrodeposition equation

• $\text{mol M} = \dfrac{I t}{n F}$
  • $\text{mol M}$ = amount of metal deposited at electrode
  • $I$ = current
  • $t$ = time (seconds)
  • $n$ = number of equivalent e⁻ per metal ion (for $\text{Cu}^{2+}$, $n = 2$)
  • $F$ = Faraday constant

Concentration cells

• Special type of galvanic cell with same electrode material in both half-cells
• Electrodes are chemically identical → same reduction potential
• Current is a function of concentration gradient
  • Current stops when concentrations are equal
  • Voltage/emf is $0$ when concentrations equal
• Use Nernst equation to calculate cell potential
• Similar to cell membrane of a neuron:
  • $\text{Na}^+$, $\text{K}^+$, $\text{Cl}^-$ exchanged to produce electrical potential
  • Resting membrane potential established

Rechargeable cells

• Can act as both galvanic and electrolytic cells

Lead–acid batteries

• Voltaic cell with Pb anode and porous $\text{PbO}_2$ cathode
• Connected by $4\ \text{M}\ \text{H}_2\text{SO}_4$ when charged
• When discharged: both electrodes become $\text{PbSO}_4$ with dilute $\text{H}_2\text{SO}_4$
• Overall discharge reaction:
  • $\text{Pb} + \text{PbO}_2 + 2\ \text{H}_2\text{SO}_4 \rightarrow 2\ \text{PbSO}_4 + 2\ \text{H}_2\text{O}$
• When charging, cell is part of an electrolytic circuit, and reaction runs in reverse
• Acid solution gets more concentrated when charging (seen with jumper cables)
• Has relatively low energy-to-weight ratio (energy density) → need more battery material for given output

Nickel–cadmium batteries

• Rechargeable cells
• Two half-cells:
  • Cadmium (anode)
  • Nickel(III) oxide-hydroxide (cathode)
• Connected by conductive material in KOH
• AA and AAA versions have layered electrodes wrapped around a cylinder

Half-reactions

• Anode:
  • $\text{Cd} + 2\ \text{OH}^- \rightarrow \text{Cd(OH)}2 + 2 e^- \quad E\text{red}^\circ = -0.86\ \text{V}$
• Cathode:
  • $2\ \text{NiO(OH)} + 2\ \text{H}_2\text{O} + 2 e^- \rightarrow 2\ \text{Ni(OH)}2 + 2\ \text{OH}^- \quad E\text{red}^\circ = +0.49\ \text{V}$
• Overall reaction:
  • $2\ \text{NiO(OH)} + \text{Cd} + 2\ \text{H}_2\text{O} \rightarrow 2\ \text{Ni(OH)}_2 + \text{Cd(OH)}_2$
• Cell potential:
  • $E_\text{cell}^\circ = 0.49\ \text{V} - (-0.86\ \text{V}) = 1.35\ \text{V}$
• Nickel–cadmium largely replaced by nickel–metal hydride (NiMH)
  • Higher energy density, more cost effective, less toxic

Electrode charge designations

• Galvanic cell:
  • Anode = source of e⁻ → negative
  • Cathode = positive
  • e⁻ move from negative to positive (low → high potential)
  • Current flows from positive to negative (high → low potential)
• Electrolytic cell:
  • Anode = positive (attached to positive pole of external source)
  • Cathode = negative, attracts cations from solution
• Always:
  • Oxidation at anode
  • Reduction at cathode
  • Cathode attracts cations
  • Anode attracts anions

Electrophoresis

• These rules apply to electrophoresis setups
• Isoelectric focusing separates amino acids or polypeptides based on isoelectric point ($pI$)
  • Positively charged amino acids migrate toward cathode
  • Negatively charged amino acids migrate toward anode

• In galvanic cells, spontaneous movement is from anode to cathode

Determining oxidation vs. reduction

• Determined experimentally and referenced to $\text{H}^+$ being reduced as the zero point

Reduction potentials

• Measured in volts (V), defined relative to the standard hydrogen electrode (SHE)
• SHE assigned potential of $0\ \text{V}$ by convention
• Species that gets reduced is chosen by comparing reduction potentials
• More positive potential → greater tendency to be reduced
• Between two half-reactions:
  • Higher $E_\text{red}^\circ$ → reduced (cathode)
  • Lower $E_\text{red}^\circ$ → oxidized (anode)
• Standard reduction potential $E_\text{red}^\circ$ measured under standard conditions
• Positive $E_\text{red}^\circ$ → tendency for reduction to occur

In galvanic cells

• More positive $E_\text{red}^\circ$ = cathode (reduction)
• Less positive $E_\text{red}^\circ$ = anode (oxidation)

In electrolytic cells

• Positive emf → spontaneous → galvanic
• Negative emf → nonspontaneous → electrolytic
• In electrolytic cells with external voltage:
  • The more positive reduction potential can be forced to be oxidized (anode)
  • The less positive can be forced to be reduced (cathode)
• To get the opposite of a reaction, flip the equation and flip the sign of $E_\text{red}^\circ$

Electromotive force

• Standard cell potential:
  • $E_\text{cell}^\circ = E_{\text{red,cathode}}^\circ - E_{\text{red,anode}}^\circ$
• Do not multiply potentials by the number of moles
  • Potential depends on identity of the species, not how many moles
• If you multiply a half-reaction to balance e⁻, you do not multiply its $E_\text{red}^\circ$

Gibbs free energy

• Change in energy available to do work depends on coulombs of charge transferred and cell potential
• $\Delta G^\circ = -n F E_\text{cell}^\circ$
  • $\Delta G^\circ$ = standard Gibbs free energy change
  • $n$ = moles of e⁻ transferred
  • $F$ = Faraday constant
  • $E_\text{cell}^\circ$ = standard emf
• If using $F$ in ${J/V·mol}$, then $\Delta G^\circ$ must be in joules, not kJ
• $\Delta G^\circ$ and $E_\text{cell}^\circ$ always have opposite signs

Reaction quotients

• Real electrochemical cells often have ionic concentrations ≠ $1\ \text{M}$
• Use Nernst equation:
  • $E_\text{cell} = E_\text{cell}^\circ - \dfrac{R T}{n F} \ln(Q)$
  • $E_\text{cell}$ = emf under nonstandard conditions
  • $E_\text{cell}^\circ$ = emf under standard conditions
  • $R$ = gas constant
  • $T$ = temperature (K)
  • $n$ = moles of e⁻
  • $Q$ = reaction quotient
• Assuming $T = 298\ \text{K}$:
  • $E_\text{cell} = E_\text{cell}^\circ - \dfrac{0.0592}{n} \log(Q)$
• Recall:
  • $Q = \dfrac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b}$
• Only species in solution are included; solids are not
• Emf can be measured with a voltmeter
• Potentiometer is a voltmeter that draws essentially no current, giving more accurate potential readings

Equilibria

• $\Delta G^\circ = -R T \ln(K_\text{eq})$
• Also:
  • $\Delta G^\circ = -n F E_\text{cell}^\circ = -R T \ln(K_\text{eq})$
• If $K_\text{eq} < 1$ (product/reactant ratio < $1$):
  • $\ln(K_\text{eq})$ is negative
  • $E_\text{cell}^\circ$ is negative → characteristic of electrolytic (nonspontaneous) cells
• If $K_\text{eq} > 1$:
  • $E_\text{cell}^\circ > 0$ → galvanic (spontaneous) cells
• Nonstandard conditions:
  • $\Delta G = \Delta G^\circ + R T \ln(Q)$