To balance the equation for the oxidation of Fe²⁺ ions to Fe³⁺ ions by dichromate ions (Cr₂O₇²⁻) in an acidic medium, we need to follow these steps:
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Identify the Half-Reactions:
- The oxidation half-reaction: \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} \)
- The reduction half-reaction (for dichromate): \( \text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}^{3+} \)
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Balance the Half-Reactions:
- Oxidation of Fe: \[ \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^{-} \]
- Reduction of Dichromate in acidic medium: To balance Cr and O, we add water and hydrogen ions as needed: \[ \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^{-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \]
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Balance the Electrons: To combine the half-reactions, we need to balance the number of electrons transferred. Because the oxidation of one Fe²⁺ gives one electron, and the reduction of dichromate uses 6 electrons, we will multiply the oxidation half-reaction by 6: \[ 6\text{Fe}^{2+} \rightarrow 6\text{Fe}^{3+} + 6e^{-} \]
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Combine the Half-Reactions: Now we can combine the two balanced half-reactions: \[ 6\text{Fe}^{2+} + \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 6\text{Fe}^{3+} + 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \]
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Final Balanced Equation: The final balanced redox reaction in acidic medium is: \[ 6\text{Fe}^{2+} + \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 6\text{Fe}^{3+} + 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \]
This equation represents the oxidation of ferrous ions to ferric ions by dichromate ions in an acidic medium.