2. Is the following reaction a redox reaction? Justify your answer by showing the oxidation numbers for each element and show your work. (5 Marks)

To determine if the reaction \( S(s) + HNO_3(aq) \rightarrow SO_2(g) + NO(g) + H_2O(l) \) is a redox reaction, we can analyze the oxidation states (oxidation numbers) of the elements involved before and after the reaction.

Step 1: Assign oxidation states

1. Reactants:

   • Sulfur (\( S \)): In its elemental form, sulfur has an oxidation state of 0.
   • Hydrogen (\( H \)) in \( HNO_3 \): The oxidation state of hydrogen is +1.
   • Nitrogen (\( N \)) in \( HNO_3 \): The oxidation state of nitrogen can be calculated as follows:
     • The total charge of \( HNO_3 \) is 0.
     • \( H: +1 \)
     • \( O: -2 \times 3 = -6 \)
     • Let the oxidation state of \( N \) be \( x \).
     • Therefore: \[ +1 + x - 6 = 0 \implies x = +5 \]
   • Oxygen (\( O \)) in \( HNO_3 \): The oxidation state of oxygen is -2.

2. Products:

   • Sulfur (\( S \)) in \( SO_2 \):
     • The total charge of \( SO_2 \) is 0.
     • Let the oxidation state of \( S \) be \( y \).
     • So we have: \[ y - 2 \times 2 = 0 \implies y = +4 \]
   • Nitrogen (\( N \)) in \( NO \):
     • The total charge of \( NO \) is 0.
     • Let the oxidation state of \( N \) be \( z \).
     • Therefore: \[ z - 2 = 0 \implies z = +2 \]
   • Hydrogen (\( H \)) in \( H_2O \): The oxidation state of hydrogen is +1.
   • Oxygen (\( O \)) in \( H_2O \): The oxidation state of oxygen is -2.

Step 2: Summary of oxidation states

• Reactants:

  • \( S: 0 \)
  • \( H: +1 \) (from \( HNO_3 \))
  • \( N: +5 \) (from \( HNO_3 \))
  • \( O: -2 \) (from \( HNO_3 \))

• Products:

  • \( S: +4 \) (from \( SO_2 \))
  • \( N: +2 \) (from \( NO \))
  • \( H: +1 \) (from \( H_2O \))
  • \( O: -2 \) (from \( H_2O \))

Step 3: Determine changes in oxidation states

• Sulfur (\( S \)):

  • Changes from 0 (reactant) to +4 (product) = oxidation (loss of electrons).

• Nitrogen (\( N \)):

  • Changes from +5 (reactant) to +2 (product) = reduction (gain of electrons).

Conclusion:

Since there is a change in oxidation states for both sulfur and nitrogen, this indicates that oxidation and reduction processes are occurring. Therefore, we identify this reaction as a redox reaction.

Final Verdict: Yes, this reaction is a redox reaction due to the changes in oxidation states of sulfur (oxidation) and nitrogen (reduction).