To balance the given redox reaction using the half-reaction method for an acidic solution, let’s break it down step-by-step.
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Identify the half-reactions:
- The reduction half-reaction involves \( \text{MnO}_4^- \) reducing to \( \text{Mn}^{2+} \).
- The oxidation half-reaction involves \( \text{CHCl}_3 \) oxidizing to \( \text{Cl}_2 \) and \( \text{CO}_2 \).
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Balance the reduction half-reaction: The reduction half-reaction: \[ \text{MnO}_4^- + 8 \text{H}^+ + 5 \text{e}^- \rightarrow \text{Mn}^{2+} + 4 \text{H}_2\text{O} \]
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Balance the oxidation half-reaction: The oxidation of \( \text{CHCl}_3 \) to \( \text{Cl}_2 \): \[ 2 \text{CHCl}_3 \rightarrow 3 \text{Cl}_2 + 2 \text{CO}_2 + 6 \text{H}^+ + 6 \text{e}^- \]
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Combine the half-reactions: To combine these, we need to ensure the number of electrons lost equals the number gained. We have 5 electrons gained in the reduction and 6 electrons lost in the oxidation. The least common multiple of 5 and 6 is 30. Therefore, we need to multiply the half-reactions accordingly:
- The reduction reaction must be multiplied by 6: \[ 6 \text{MnO}_4^- + 48 \text{H}^+ + 30 \text{e}^- \rightarrow 6 \text{Mn}^{2+} + 24 \text{H}_2\text{O} \]
- The oxidation reaction must be multiplied by 5: \[ 10 \text{CHCl}_3 \rightarrow 15 \text{Cl}_2 + 10 \text{CO}_2 + 30 \text{H}^+ + 30 \text{e}^- \]
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Final balanced equation: Combining these, we get: \[ 6 \text{MnO}_4^- + 10 \text{CHCl}_3 + 18 \text{H}^+ \rightarrow 6 \text{Mn}^{2+} + 15 \text{Cl}_2 + 10 \text{CO}_2 + 24 \text{H}_2\text{O} \]
From this balanced equation, we can analyze the options provided:
- Option a (4H2O on product side): This is incorrect (we have 24 H2O).
- Option b (6H^+ on the products side): This is incorrect (we have 18 H⁺ on the reactants side).
- Option c (6H2O on reactants side): This is incorrect (we have 24 H2O on the product side).
- Option d (4H^+ on the reactants side): This is incorrect (we have 18 H⁺ on the reactants side).
Ultimately: None of the given options seem correct because all descriptions from the options do not match the balanced reaction. Please verify the question or the options provided again.