$x & y$ are the number of moles of electrons involved respectively during oxidation of $\text{I}^-$ to $\text{I}_2$ & $\text{S}^{2-}$ to $\text{S}$ by acidified $\text{K}_2\text{Cr}_2\text{O}_7$. The value of $x+y$ is ?
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When asked for the number of electrons involved in an oxidation step catalyzed by a specific amount of oxidant, calculate the total electrons required by the oxidant ($\text{Cr}_2\text{O}_7^{2-}$ requires $6\text{e}^-$) and scale the oxidation half-reaction accordingly.
To solve the problem, we need to calculate the number of moles of electrons exchanged in the redox reactions involving the oxidation of \(\text{I}^-\\) to \(\text{I}_2\\) and \(\text{S}^{2-}\\) to \(\text{S}\\) using acidified \(\text{K}_2\text{Cr}_2\text{O}_7\\).
Step 1: Oxidation of \(\text{I}^-\\) to \(\text{I}_2\\)
The balanced half-reaction for the oxidation of iodide ions (\(\text{I}^-\\)) to iodine (\(\text{I}_2\\)) is:
In this reaction, 2 moles of electrons are released when 2 moles of \(\text{I}^-\\) are oxidized to 1 mole of \(\text{I}_2\\). Thus, \(x = 2\) moles of electrons are involved in this oxidation process.
Step 2: Oxidation of \(\text{S}^{2-}\\) to \(\text{S}\\)
The balanced half-reaction for the oxidation of sulfide ions (\(\text{S}^{2-}\\)) to sulfur (\(\text{S}\\)) is:
Here, each mole of \(\text{S}^{2-}\\) loses 2 moles of electrons to form 1 mole of sulfur. Therefore, \(y = 2\) moles of electrons are involved in this oxidation step.
Step 3: Sum of moles of electrons involved
The total moles of electrons involved, \(x + y\), is calculated by adding the moles from both reactions:
\(x + y = 2 + 2 = 4\\)
The actual reaction involves \(\text{K}_2\text{Cr}_2\text{O}_7\\), which has its own redox reactions. While the given reaction with \(\text{Cr}_2\text{O}_7^{2-}\\) in acidic medium involves 6 moles of electrons:
Considering the total reaction involving the dichromate ion (where 6 moles of electrons are exchanged), combined with both half reactions from above, the total is:
\(6 + 6 = 12\\)
Conclusion: Therefore, the value of \(x + y\\) is 12.
