Oxidation State Rules and Calculation Practice and Calculations

General Rule for Oxidation States

• Rule 7: Sum of Oxidation States
  • In a neutral molecule, the sum of the oxidation states of all the constituent atoms must equal $0$.
  • In an ion, the sum of the oxidation states of all constituent atoms must equal the net charge of the ion.

Introductory Formula Examples

• Calculating Oxidation State in $H_{2}SO_{4}$ (Sulfuric Acid):

  • The molecule is neutral, so the sum equals $0$.
  • Hydrogen ($H$) state: $+1$.
  • Oxygen ($O$) state: $-2$.
  • Calculation: $(2 \times (+1)) + x + (4 \times (-2)) = 0$
  • Intermediate step: $+2 + x + (-8) = 0$
  • Simplified: $x - 6 = 0$
  • Result for Sulfur ($S$): $x = +6$

• Calculating Oxidation State in $PO_{4}^{3-}$ (Phosphate Ion):

  • Note: The transcript labels this as $PO3$, but performs the calculation for the phosphate ion ($PO_{4}^{3-}$).
  • Sum equals the charge: $-3$.
  • Calculation: $x + (-8) = -3$
  • Step: $x = -3 + 8$
  • Result for Phosphorus ($P$): $x = +5$

Oxidation and Reduction in Chemical Reactions

• Reaction Example: $Na_{(s)} + \text{Cl}_{2(g)} \rightarrow NaCl_{(s)}$
  • Sodium ($Na$):
    • Initial state: $0$ (solid element).
    • Final state in $NaCl$: $+1$.
    • Process: Oxidation (increase in oxidation state).
    • Role: $Na$ is the Reducing Agent (R.A).
  • Chlorine ($Cl$):
    • Initial state: $0$ (gaseous element).
    • Final state in $NaCl$: $-1$.
    • Process: Reduction (decrease in oxidation state).
    • Role: Chlorine is the Oxidizing Agent (O.A).

Calculations for Specific Underlined Atoms

• $CO_{2}$ (Carbon Dioxide):

  • Goal: Calculate oxidation state of Carbon ($C$).
  • Equation: $x + 2(-2) = 0$
  • Step: $x - 4 = 0$
  • Result: $x = +4$

• $H_{2}S$ (Hydrogen Sulfide):

  • Goal: Calculate oxidation state of Sulfur ($S$).
  • Equation: $2(+1) + x = 0$
  • Step: $+2 + x = 0$
  • Result: $x = -2$

• $CH_{4}$ (Methane):

  • Goal: Calculate oxidation state of Carbon ($C$).
  • Equation: $x + 4(+1) = 0$
  • Step: $x + 4 = 0$
  • Result: $x = -4$

• $CH_{2}Cl_{2}$ (Dichloromethane):

  • Goal: Calculate oxidation state of Carbon ($C$).
  • Equation: $x + 2(+1) + 2(-1) = 0$
  • Step: $x + 2 - 2 = 0$
  • Result: $x = 0$

• $NH_{3}$ (Ammonia):

  • Goal: Calculate oxidation state of Nitrogen ($N$).
  • Equation: $x + 3(+1) = 0$
  • Step: $x + 3 = 0$
  • Result: $x = -3$

• $NH_{4}NO_{3}$ (Ammonium Nitrate):

  • Goal: Calculate oxidation state of Nitrogen ($N$) in the nitrate group.
  • Using the nitrate component ($NO_{3}^{-}$):
  • Equation: $x + 3(-2) = -1$
  • Step: $+1 + x + 3(-2) = 0$ (Represented in transcript as treating the neutral salt parts).
  • Step: $+1 + x - 6 = 0$
  • Result: $x = +5$

• $KAl(SO_{4})_{2} \cdot 12H_{2}O$ (Potash Alum):

  • Goal: Calculate oxidation state of Aluminum ($Al$).
  • Method: Treat the sulfate group ($SO_{4}$) as a single unit with a charge of $-2$. Water ($H_{2}O$) is a neutral ligand ($0$).
  • Potassium ($K$) state: $+1$.
  • Equation: $+1 + x + 2(-2) + 12(0) = 0$
  • Step: $+1 + x - 4 + 0 = 0$
  • Result: $x = +3$

Additional Chemical Species Identified

• Superoxide:
  • Formula: $KO_{2}$
  • The oxygen in superoxide has an oxidation state of $-\frac{1}{2}$.