Unit 6: Galvanic Cells
Harnessing chemical energy from redox reactions to generate electricity.
6.13 Electrode Potentials
When a metal is placed in a solution containing its own ions (e.g., a zinc rod in a $ZnSO_4$ solution), a dynamic equilibrium is established at the surface of the metal.
- Oxidation: Metal atoms can lose electrons and enter the solution as positive ions ($Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$). This leaves excess electrons on the metal, making it negatively charged.
- Reduction: Metal ions from the solution can gain electrons from the metal and deposit as neutral atoms ($Zn^{2+}(aq) + 2e^- \rightarrow Zn(s)$). This removes electrons from the metal, making it positively charged.
This separation of charge creates a potential difference between the metal and the solution. This is called the electrode potential. The magnitude and sign of this potential depend on the metal's tendency to be oxidised or reduced. A more reactive metal will have a greater tendency to lose electrons (be oxidised), resulting in a more negative electrode potential.
Solved Examples:
- What is an electrode potential?
Solution: The potential difference created between a metal electrode and a solution containing its ions due to the establishment of a redox equilibrium. - Write the equilibrium that occurs when a copper rod is placed in copper(II) sulphate solution.
Solution: $Cu^{2+}(aq) + 2e^- \rightleftharpoons Cu(s)$. - Which metal would you expect to have a more negative electrode potential: magnesium or silver?
Solution: Magnesium, because it is much more reactive and has a stronger tendency to lose electrons (be oxidised). - What happens to the charge on a zinc rod if the equilibrium $Zn(s) \rightleftharpoons Zn^{2+}(aq) + 2e^-$ lies to the right?
Solution: The rod will accumulate excess electrons, becoming negatively charged relative to the solution. - Can a single electrode potential be measured directly?
Solution: No, you can only measure the potential difference *between* two different electrodes. - What factors affect the value of an electrode potential?
Solution: The nature of the metal, the concentration of its ions in solution, and the temperature. - What is a half-cell?
Solution: A half-cell consists of an electrode in contact with a solution of its ions (e.g., a zinc rod in zinc sulphate solution). - If a metal has a strong tendency to be reduced, will its electrode potential be more positive or more negative?
Solution: More positive. A positive potential indicates a greater tendency for reduction to occur at that electrode. - What is the purpose of the metal ions in the solution?
Solution: They are part of the redox equilibrium, allowing for both the oxidation of the metal and the reduction of the ions to occur. - What is the term for the metal rod or plate in a half-cell?
Solution: The electrode.
6.14 Creating an Electromotive Force (EMF)
A single half-cell is in equilibrium and produces no net reaction or flow of electrons. However, if two different half-cells are connected, a spontaneous redox reaction can occur. This setup is called a galvanic cell (or voltaic cell).
The connection requires two components:
- An external wire to allow electrons to flow from the more negative electrode (where oxidation occurs) to the more positive electrode (where reduction occurs).
- A salt bridge (e.g., filter paper soaked in an inert electrolyte like $KNO_3$) to connect the two solutions. This allows ions to flow between the half-cells to maintain charge neutrality, completing the circuit.
The difference in electrode potential between the two half-cells creates a "push" on the electrons, causing them to flow. This potential difference is called the electromotive force (EMF) or cell potential ($E_{cell}$), measured in volts (V).
In a galvanic cell:
- The more negative electrode is the anode, where oxidation occurs.
- The more positive electrode is the cathode, where reduction occurs.
Solved Examples:
- What is a galvanic cell?
Solution: A device that uses a spontaneous redox reaction to generate electrical energy, composed of two connected half-cells. - What is the function of a salt bridge?
Solution: To complete the electrical circuit by allowing ions to flow between the two half-cells, maintaining charge balance in each. - In a zinc-copper cell, electrons flow from the zinc electrode to the copper electrode. Which is the anode?
Solution: The zinc electrode is the anode, as it is the site of oxidation (electron loss). - What is the electromotive force (EMF) of a cell?
Solution: It is the potential difference between the two half-cells that drives the flow of electrons. - What process occurs at the cathode of a galvanic cell?
Solution: Reduction. - Why is potassium nitrate a suitable electrolyte for a salt bridge?
Solution: It is inert and will not react with the ions in either half-cell to form a precipitate. - If the salt bridge is removed from a working galvanic cell, what happens?
Solution: The flow of electrons stops immediately. Charge would build up in each half-cell, preventing further reaction. - Which electrode is assigned a positive sign in a galvanic cell?
Solution: The cathode (where reduction occurs). - How is chemical energy converted to electrical energy in a galvanic cell?
Solution: The spontaneous redox reaction releases energy, which is used to push electrons through an external circuit. - What would happen to the mass of the copper cathode in a zinc-copper cell over time?
Solution: It would increase, as copper ions from the solution are reduced and deposited as solid copper metal onto the electrode.
6.15 Conventional Representation of Cells (Cell Notation)
Drawing a full diagram for every galvanic cell is cumbersome. A shorthand cell notation is used to represent them.
Rules for Cell Notation:
- The half-cell undergoing oxidation (anode) is written on the left.
- The half-cell undergoing reduction (cathode) is written on the right.
- A single vertical line ( | ) represents a phase boundary (e.g., between a solid electrode and an aqueous solution).
- A double vertical line ( || ) represents the salt bridge connecting the two half-cells.
- The chemical species are written with their state symbols, and concentrations are included in parentheses if not standard.
Example: The zinc-copper cell.
- Anode (Oxidation): $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
- Cathode (Reduction): $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
The cell notation is: $Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$
Solved Examples:
- What does the double vertical line (||) represent in cell notation?
Solution: The salt bridge. - Write the cell notation for a cell made from magnesium and zinc half-cells, where magnesium is oxidised.
Solution: $Mg(s) | Mg^{2+}(aq) || Zn^{2+}(aq) | Zn(s)$. - In the cell notation $Fe(s) | Fe^{2+}(aq) || Ag^{+}(aq) | Ag(s)$, which metal is the cathode?
Solution: Silver ($Ag$) is the cathode, as it is on the right side (the site of reduction). - What is the oxidation half-reaction for the cell in the previous question?
Solution: $Fe(s) \rightarrow Fe^{2+}(aq) + 2e^-$. - What does a single vertical line (|) represent?
Solution: A phase boundary. - Write the overall reaction for the cell: $Al(s) | Al^{3+}(aq) || Pb^{2+}(aq) | Pb(s)$.
Solution: Oxidation: $Al \rightarrow Al^{3+} + 3e^-$. Reduction: $Pb^{2+} + 2e^- \rightarrow Pb$. Balance electrons and combine: $2Al(s) + 3Pb^{2+}(aq) \rightarrow 2Al^{3+}(aq) + 3Pb(s)$. - Which electrode is the anode in the cell from the previous question?
Solution: Aluminium ($Al$). - Write the cell notation for a cell where nickel is oxidised and silver ions are reduced.
Solution: $Ni(s) | Ni^{2+}(aq) || Ag^{+}(aq) | Ag(s)$. - What information is typically included in parentheses next to the aqueous species?
Solution: Their concentration (e.g., 1.0 M). - In the cell notation, where is the more negative electrode written?
Solution: On the left (the anode).
6.16 & 6.17 Measuring & Standard Electrode Potentials ($E^\circ$)
As it's impossible to measure the potential of a single half-cell, a reference point is needed. The universally accepted reference is the Standard Hydrogen Electrode (SHE).
The Standard Hydrogen Electrode (SHE):
- Reaction: $2H^+(aq) + 2e^- \rightleftharpoons H_2(g)$
- Setup: A platinum electrode immersed in a 1.0 M solution of $H^+$ ions, with hydrogen gas at 1 atm pressure bubbled over it.
- By international agreement, the SHE is assigned an electrode potential of exactly 0.00 V under standard conditions.
Standard Electrode Potential ($E^\circ$):
The standard electrode potential ($E^\circ$) of a half-cell is the EMF produced when that half-cell is connected to the SHE under standard conditions (298 K, 1 atm, 1.0 M concentrations).
A list of $E^\circ$ values (the electrochemical series) allows us to predict the spontaneity of redox reactions and calculate the EMF of any galvanic cell:
$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$
(Where cathode is the more positive $E^\circ$ value and anode is the more negative $E^\circ$ value). A positive $E^\circ_{cell}$ indicates a spontaneous reaction.
Solved Examples:
- What is the standard reference electrode?
Solution: The Standard Hydrogen Electrode (SHE). - What potential is assigned to the SHE?
Solution: 0.00 V. - What are the standard conditions for measuring $E^\circ$?
Solution: 298 K (25 °C), 1 atm pressure for gases, and 1.0 M concentration for all aqueous species. - Given $E^\circ(Zn^{2+}/Zn) = -0.76 V$ and $E^\circ(Cu^{2+}/Cu) = +0.34 V$, calculate the $E^\circ_{cell}$ for a zinc-copper cell.
Solution: Copper is the cathode (more positive). Zinc is the anode. $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} = (+0.34) - (-0.76) = \textbf{+1.10 V}$. - In the cell from the previous question, which reaction is spontaneous?
Solution: Since $E^\circ_{cell}$ is positive, the reaction as written (Zn being oxidised, Cu²⁺ being reduced) is spontaneous. - The $E^\circ$ for $Ag^+/Ag$ is +0.80 V. If this half-cell is connected to the SHE, which is the cathode?
Solution: The silver half-cell is the cathode because its potential (+0.80 V) is more positive than the SHE (0.00 V). - What does a more negative $E^\circ$ value indicate about a species?
Solution: It indicates a greater tendency to be oxidised (it is a stronger reducing agent). - What does a more positive $E^\circ$ value indicate?
Solution: It indicates a greater tendency to be reduced (it is a stronger oxidising agent). - Calculate the $E^\circ_{cell}$ for a cell made of Mg ($E^\circ = -2.37 V$) and Fe ($E^\circ = -0.44 V$).
Solution: Fe is the cathode (less negative). Mg is the anode. $E^\circ_{cell} = (-0.44) - (-2.37) = \textbf{+1.93 V}$. - Why is a platinum electrode used in the SHE?
Solution: Platinum is chemically inert but provides a surface for the hydrogen/hydrogen ion equilibrium to be established and for electron transfer to occur.