2.3 Cell Notation and Conventions

Galvanic cells power our world through electrochemical reactions. Cell notation provides a standardized way to represent these reactions, showing how electrons flow from the anode to the cathode through an external circuit.

Understanding ion migration and oxidation numbers is crucial for balancing redox reactions. These concepts help us track charge movement and changes in oxidation states, enabling us to harness the power of electrochemistry in batteries and more.

Cell Notation and Conventions

Cell notation for galvanic cells

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• Represents components and reactions in a galvanic cell using a standardized format (Zn | Zn$^{2+}$ || Cu$^{2+}$ | Cu)
• Anode written on the left, where oxidation occurs and electrons are released (Zn → Zn$^{2+}$ + 2e$^-$)
• Cathode written on the right, where reduction occurs and electrons are accepted (Cu$^{2+}$ + 2e$^- →$ Cu)
• Single vertical line ( | ) separates anode and cathode from their respective solutions (Zn | Zn$^{2+}$)
• Double vertical line ( || ) separates anode and cathode solutions, representing a salt bridge or porous membrane (Zn$^{2+}$ || Cu$^{2+}$)
• Electron flow occurs from anode to cathode through an external circuit, enabling the redox reactions

Ion migration in electrochemical cells

• Cations (positively charged ions) migrate towards the negatively charged cathode (Na$^+$, K$^+$, Ca$^{2+}$)
  • Attracted by the negative charge of the cathode
• Anions (negatively charged ions) migrate towards the positively charged anode (Cl$^-$, NO$_3^-$, SO$_4^{2-}$)
  • Attracted by the positive charge of the anode
• Ion migration maintains charge balance in the cell, preventing accumulation of charge in electrode compartments
  • Cations and anions move in opposite directions through the salt bridge or porous membrane
  • Equal number of positive and negative charges migrate to maintain electroneutrality

Conventions of oxidation numbers

• Oxidation number represents the degree of oxidation of an atom in a compound or ion, indicating its apparent charge
• Free elements have an oxidation number of zero (Na, Fe, O$_2$, P$_4$)
• Monatomic ions have an oxidation number equal to their charge (Na$^+$ = +1, Cl$^-$ = -1, Ca$^{2+}$ = +2)
• Oxygen usually has an oxidation number of -2, except in peroxides (H$_2$O$_2$, -1) and when bonded to fluorine (OF$_2$, +2)
• Hydrogen usually has an oxidation number of +1, except in metal hydrides (NaH, -1)
• Fluorine always has an oxidation number of -1 due to its high electronegativity (HF, NaF)
• In a neutral compound, the sum of oxidation numbers of all atoms is zero (H$_2$O: 2 × (+1) + (-2) = 0)
• In a polyatomic ion, the sum of oxidation numbers of all atoms equals the charge of the ion (SO$_4^{2-}$: (+6) + 4 × (-2) = -2)

Oxidation numbers in redox reactions

• Redox reactions involve changes in oxidation numbers of atoms, with oxidation being an increase and reduction a decrease
• To balance a redox reaction:
  1. Assign oxidation numbers to all atoms in reactants and products
  2. Identify atoms undergoing changes in oxidation number
  3. Balance atoms that are oxidized and reduced
  4. Balance remaining atoms (except H and O)
  5. Balance hydrogen and oxygen atoms by adding H$^+$ or OH$^-$ ions
  6. Verify that the sum of charges on both sides of the equation is equal
• Changes in oxidation state determined by comparing oxidation numbers of atoms in reactants and products
  • Increase in oxidation number indicates oxidation (Fe$^{2+} →$ Fe$^{3+}$)
  • Decrease in oxidation number indicates reduction (MnO$_4^- →$ Mn$^{2+}$)
• Balanced redox reactions demonstrate conservation of mass and charge, with equal numbers of atoms and charges on both sides