Question

What is the stoichiometric coefficient of SO$_2$ in the following balanced reaction? \[ {MnO}_4^-(aq) + {SO}_2(g) \rightarrow {Mn}^{2+}(aq) + {HSO}_4^-(aq) \] (in acidic solution)

• A. 5
• B. 4
• C. 3
• D. 2

Hint:

Balancing redox reactions involves writing the oxidation and reduction half reactions, balancing the electrons, and then combining the half reactions.

Answer 1

The Correct Option is A

Step 1: {Oxidation Half Reaction}
Write the oxidation half reaction: \[ {SO}_2(g) + 2 {H}_2{O}(l) \rightarrow {HSO}_4^-(aq) + 3 {H}^+(aq) + 2e^- \] Step 2: {Reduction Half Reaction}
Write the reduction half reaction: \[ {MnO}_4^-(aq) + 8 {H}^+(aq) + 5e^- \rightarrow {Mn}^{2+}(aq) + 4 {H}_2{O}(l) \] Step 3: {Balance the Electrons}
To balance the electrons, multiply the oxidation half reaction by 5 and the reduction half reaction by 2: \[ 5 {SO}_2(g) + 10 {H}_2{O}(l) \rightarrow 5 {HSO}_4^-(aq) + 15 {H}^+(aq) + 10e^- \] \[ 2 {MnO}_4^-(aq) + 16 {H}^+(aq) + 10e^- \rightarrow 2 {Mn}^{2+}(aq) + 8 {H}_2{O}(l) \] Step 4: {Combine and Simplify}
Combine the two half reactions: \[ 2 {MnO}_4^-(aq) + 5 {SO}_2(g) + 16 {H}^+(aq) \rightarrow 2 {Mn}^{2+}(aq) + 5 {HSO}_4^-(aq) + 8 {H}_2{O}(l) \] Thus, the stoichiometric coefficient of SO$_2$ is 5.

Answer 2

Step 1: Identify the redox nature of the reaction
This is a redox reaction in an acidic medium involving:
- \( MnO_4^- \) being reduced to \( Mn^{2+} \)
- \( SO_2 \) being oxidized to \( HSO_4^- \)

Step 2: Assign oxidation states
- In \( MnO_4^- \), Mn is in +7 oxidation state
- In \( Mn^{2+} \), Mn is in +2 oxidation state
⇒ Mn gains 5 electrons (reduction)

- In \( SO_2 \), S is in +4 oxidation state
- In \( HSO_4^- \), S is in +6 oxidation state
⇒ S loses 2 electrons (oxidation)

Step 3: Balance the electron transfer
To balance the electrons, we use the LCM of 5 and 2 = 10
- 2 \( MnO_4^- \) will gain 10 electrons
- 5 \( SO_2 \) will lose 10 electrons

Step 4: Balanced redox reaction in acidic medium
The balanced reaction becomes:
\[ 2MnO_4^- + 5SO_2 + 2H_2O \rightarrow 2Mn^{2+} + 5HSO_4^- + 2H^+ \]

Step 5: Identify the stoichiometric coefficient of SO₂
From the balanced equation, the coefficient of SO₂ is 5

Final Answer: 5