To solve this question, we need to determine the oxidation state of chromium in the final product formed from the reaction between potassium iodide (KI) and acidified potassium dichromate (\( K_2Cr_2O_7 \)). The reaction occurs in an acidic condition, generally using sulfuric acid.
The balanced chemical equation for the reaction is:
\[
Cr_2O_7^{2-} + 14H^+ + 6I^- \rightarrow 2Cr^{3+} + 7H_2O + 3I_2
\]
In this reaction, the dichromate ion (\( Cr_2O_7^{2-} \)) is reduced to chromium ions (\( Cr^{3+} \)). Here, the relevant oxidation state changes occur:
- In \( K_2Cr_2O_7 \), the oxidation state of chromium is +6. This is because the chemical formula of the dichromate ion, \( Cr_2O_7^{2-} \), can be analyzed: each \(\text{O}^-\) is -2 and altogether they contribute -14, hence each Cr must be +6 to balance the -2 charge.
- In the product, each chromium atom in \( Cr^{3+} \) has an oxidation state of +3.
Thus, the oxidation state of chromium in the final product is +3, which corresponds to the correct answer.
Let's analyze why the oxidation state is +3:
- The dichromate ion is reduced, and simultaneously, the iodide ions (\( I^- \)) are oxidized to iodine (\( I_2 \)). The overall process is a redox reaction.
- In a redox reaction, the oxidation state of the reduced species decreases. As \( Cr^{6+} \) is reduced to \( Cr^{3+} \), this indicates a decrease in the oxidation number, confirming the final oxidation state of chromium as +3.
Therefore, the oxidation state of chromium in the final product is +3.