Question B 2 The following redox reaction is used in acidic solution in the Breathalyzer test to determine the level of alcohol in th blood of drunk drivers: $$ \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{H}_{5} \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} $$ a) Identify the elements undergoing changes in oxidation state and indicate the initial and final oxidation numbers for theseelements.

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In the given redox reaction:

$$ \mathrm{H}^{+}(\mathrm{aq}) + \mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}(\mathrm{aq}) + \mathrm{C}_{2}\mathrm{H}_{5} \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq}) + \mathrm{C}_{2}\mathrm{H}_{4}\mathrm{O}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O} $$

**a) Identifying Elements Undergoing Changes in Oxidation State:**

Two elements undergo changes in oxidation state during this reaction:

1. **Chromium (Cr)**
2. **Carbon (C)**

**Detailed Oxidation State Changes:**

1. **Chromium (Cr):**
   - **Initial Oxidation State:** In the dichromate ion ($$\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}$$):
     - Oxygen has an oxidation state of $$-2$$.
     - For $$\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}$$:
       $$
       2 \times (\text{Oxidation state of Cr}) + 7 \times (-2) = -2 \
       2 \times (\text{Oxidation state of Cr}) - 14 = -2 \
       2 \times (\text{Oxidation state of Cr}) = +12 \
       \text{Oxidation state of Cr} = +6
       $$
   - **Final Oxidation State:** In $$\mathrm{Cr}^{3+}$$, chromium has an oxidation state of $$+3$$.

- **Change:** Chromium is **reduced** from $$+6$$ to $$+3$$.

2. **Carbon (C):**
   - **Initial Oxidation State:** In ethanol ($$\mathrm{C}_{2}\mathrm{H}_{5}$$):
     - Consider the two carbon atoms separately:
       - **First Carbon (C₁):** Attached to 3 hydrogen atoms and 1 carbon atom.
         $$
         \text{Oxidation state of C₁} = -3
         $$
       - **Second Carbon (C₂):** Attached to 2 hydrogen atoms and 1 oxygen atom.
         $$
         \text{Oxidation state of C₂} = -1
         $$
     - **Average Oxidation State:** For simplicity, considering the relevant carbon undergoing oxidation:
       $$
       \text{Carbon oxidation state increases from } -1 \text{ to } 0
       $$
   
   - **Final Oxidation State:** In acetaldehyde ($$\mathrm{C}_{2}\mathrm{H}_{4}\mathrm{O}$$):
     - **Second Carbon (C₂):** Attached to 1 hydrogen atom and 1 oxygen atom.
       $$
       \text{Oxidation state of C₂} = 0
       $$
   
   - **Change:** Carbon is **oxidized** from $$-1$$ to $$0$$.

**Summary:**

- **Chromium (Cr):** $$+6$$ in $$\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}$$ → $$+3$$ in $$\mathrm{Cr}^{3+}$$
- **Carbon (C):** $$-1$$ in $$\mathrm{C}_{2}\mathrm{H}_{5}$$ → $$0$$ in $$\mathrm{C}_{2}\mathrm{H}_{4}\mathrm{O}$$

These changes indicate that chromium is being reduced while carbon is being oxidized in the reaction.

**Final Answer:**

**a)** Chromium and carbon undergo oxidation state changes. Chromium is reduced from +6 in dichromate (Cr₂O₇²⁻) to +3 in Cr³⁺. Carbon is oxidized from –1 in ethanol (C₂H₅) to 0 in acetaldehyde (C₂H₄O).
Chromium changes from +6 to +3, and carbon changes from -1 to 0.

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