Comprehensive Study Guide for Electrochemistry and Galvanic Cells

Introduction to Electrochemical Cells

• Transition from Balancing to Application: Previously, the focus was on the tedious process of balancing half-equations in acidic and basic conditions. The current objective is to move from theoretical balancing to the practical application of harnessing electron flow (electricity) to do work.

• Cell Types:

  • Galvanic or Voltaic Cells: These terms are synonymous, named after Alessandro Volta and Luigi Galvani. A galvanic cell is spontaneous, meaning the chemical reaction proceeds on its own without external intervention.

  • Electrolytic Cells: These are non-spontaneous reactions. They do not occur on their own and require an external power source, such as being "plugged into the wall," to force the reaction to proceed.

• Thermodynamic Connection: For a galvanic or voltaic cell to be spontaneous, the Gibbs Free Energy change ($\Delta G$) must be negative. Conversely, electrolytic cells have a positive $\Delta G$.

Fundamental Concepts of Electricity

• Electric Charge: The SI unit for electric charge is the Coulomb ($C$).

  • Primary charge of an electron: $-1.602 \times 10^{-19}\,C$.

  • A proton has an equal magnitude but opposite charge ($+1.602 \times 10^{-19}\,C$).

• Ampere (Amp): Defined as one Coulomb per second ($1\,C/s$). It is a measure of electron flow.

  • To calculate the number of electrons per second for one amp: $(1\,C/s) \times (1\,e^{-}/1.602 \times 10^{-19}\,C) = 6.242 \times 10^{18}$ electrons per second.

• Volt (V): Defined as Joules per Coulomb ($J/C$). It represents the energy associated with the electron flow.

• Plumbing Metaphor:

  • An Amp is analogous to the volume/rate of water flowing through a pipe.

  • A Volt is analogous to the water pressure.

  • They are directly related: more electrons (amps) usually correlate with more energy (volts). However, they are distinct; if a pipe is capped (increasing resistance $R$), flow stops (amps go to zero), but pressure (volts) remains high.

• Electromotive Force (EMF): Also known as $E_{cell}$, this is the difference in potential between two half-reactions based on their tendency to be reduced or oxidized.

Galvanic Cell Components and Functions

• Anode:

  • The site where oxidation occurs ($\text{loss of electrons}$).

  • In a galvanic/voltaic cell, the anode is considered the negative terminal because it produces electrons.

  • Electrons are written as products in the oxidation half-reaction.

• Cathode:

  • The site where reduction occurs ($\text{gain of electrons}$).

  • In a galvanic/voltaic cell, the cathode is the positive terminal because it receives electrons.

  • Electrons are written as reactants in the reduction half-reaction.

• Electron Flow: Electrons always flow through the external wire from the anode to the cathode.

• The Salt Bridge:

  • Essential for maintaining the reaction. Without it, the reaction would shut down in milliseconds because of charge buildup.

  • It contains an electrolyte solution (e.g., $MgSO_4$).

  • Function: It neutralizes counterions as they are produced or consumed. For example, in a zinc-copper cell, zinc buildup ($Zn^{2+}$) at the anode attracts sulfate ($SO_4^{2-}$) from the salt bridge to maintain neutrality. Conversely, at the cathode, as $Cu^{2+}$ is reduced to $Cu(s)$, the remaining sulfate spectators are neutralized by cations (like $Mg^{2+}$) from the salt bridge.

Standard Reduction Potentials and Spontaneity

• Standard Hydrogen Electrode (SHE/Sheet):

  • Since the voltage of a single half-reaction cannot be measured in isolation, all values are measured relative to a standard.

  • The "Sheet" serves as the reference point with a potential of exactly $0.00\,V$.

  • Reaction: $2H^{+} + 2e^{-} \rightarrow H_2$.

• Standard Reduction Table:

  • Lists half-reactions as reductions ($\text{electrons on reactant side}$).

  • Top of the Table: Strongest oxidizing agents (e.g., Fluorine, $F_2$). They have high positive reduction potentials and "want" to be reduced.

  • Bottom of the Table: Strongest reducing agents (e.g., Lithium, $Li$). They have negative reduction potentials and "want" to be oxidized.

• Intensive Properties: Standard reduction potentials ($E^0$) are intensive properties, meaning they are independent of the amount of substance.

  • Crucial Rule: When balancing a redox reaction to calculate $E_{cell}$, if you multiply the chemical equation by a coefficient (e.g., $2$ or $3$), you DO NOT multiply the voltage ($E^0$) by that number. The value remains unchanged.

Calculating Cell Potential ($E_{cell}$)

• Spontaneity Rule: For a reaction to be spontaneous (a galvanic cell), the total $E_{cell}$ must be positive (E_{cell} > 0).

• The Calculation Methods:

  1. Standard Formula: $E_{cell} = E_{cathode} - E_{anode}$. In this method, you use the numbers exactly as they appear in the reduction table and perform the subtraction.

  2. The "Flip" Method: Identify the two half-reactions. The reaction with the least positive (or most negative) value on the table is the one that will be oxidized. Flip its sign and add it to the other reduction potential.

• Example: Zinc-Copper Cell:

  • $Cu^{2+} + 2e^{-} \rightarrow Cu(s)$: $E^0 = +0.34\,V$

  • $Zn^{2+} + 2e^{-} \rightarrow Zn(s)$: $E^0 = -0.76\,V$

  • Calculation: Flip the sign of Zinc ($+0.76\,V$) because it is lower on the table. Add: $0.34\,V + 0.76\,V = 1.10\,V$.

Balancing Redox Reactions in Acidic Conditions

1. Identify the Redox Nature: Verify if oxidation states are changing.

2. Separate Half-Reactions: Divide the equation into oxidation and reduction halves.

3. Balance Mass (Non-H and O): Balance all atoms except hydrogen and oxygen.

4. Balance Oxygen: Use water ($H_2O$) to balance oxygen atoms.

5. Balance Hydrogen: Use hydrogen ions ($H^+$) to balance hydrogen atoms.

6. Balance Charge: Use electrons ($e^-$) to balance the total charge on both sides of each half-reaction.

7. Equalize Electrons: Multiply the half-reactions by integers so the number of electrons lost in oxidation equals the number gained in reduction.

8. Add and Cancel: Combine the reactions and cancel out electrons and any redundant water or hydrogen ions.

Example: Dichromate and Chlorine

• Oxidation: $2Cr^{3+}(aq) + 7H_2O(l) \rightarrow Cr_2O_7^{2-}(aq) + 14H^{+}(aq) + 6e^{-}$ ($E^0 = 1.23\,V$ on table).

• Reduction: $3Cl_2(g) + 6e^{-} \rightarrow 6Cl^{-}(aq)$ ($E^0 = 1.36\,V$ on table).

• Calculation: Chlorine is the cathode ($1.36\,V$), Dichromate is the anode ($1.23\,V$).

• Result: $E_{cell} = 1.36\,V - 1.23\,V = 0.13\,V$. (Spontaneous but low energy).

Practical Applications and Sacrificial Electrodes

• Sacrificial Anodes: Using a more reactive metal (lower on the reduction table) to prevent the corrosion of a less reactive, more valuable metal.

• Galvanization: Coating iron nails with zinc. Because zinc has a lower reduction potential ($-0.76\,V$) compared to iron ($-0.44\,V$), the zinc will oxidize (rust) first, protecting the underlying iron from degradation.

• Boating Application: Attachment of sacrificial metal blocks (anodes) to the hulls of boats. These blocks oxidize preferentially, sparing the boat's primary structure from corrosion.

Questions & Discussion

• Question: In an electrolytic cell, are the charges on the anode and cathode different?

• Answer: Yes. In a spontaneous galvanic cell, the anode is negative and the cathode is positive. If you use external electricity to force the reaction in the opposite direction (electrolytic cell), those charges are flipped.