`Fe^(2+)(aq.)+Cr_(2)O_(7)^(2-)+H^(+) to Fe^(3+)(aq.)+Cr^(3+)`

Options

A. For disproportionation reaction.
B. For comproportionation reaction.
C. For either intermolecular redox reaction or displacement reaction
D. For either thermal combination redox reaction or thermal decomposition redox reaction.

Answer

To analyze the given reaction \( \text{Fe}^{2+}(aq) + \text{Cr}_2\text{O}_7^{2-} + \text{H}^+ \rightarrow \text{Fe}^{3+}(aq) + \text{Cr}^{3+} \), we will break it down step by step to determine if it is a redox reaction and identify the type of reaction it represents.

### Step 1: Identify Oxidation and Reduction
1. **Oxidation**: Oxidation is defined as the loss of electrons or an increase in oxidation state.
- In this reaction, \( \text{Fe}^{2+} \) is converted to \( \text{Fe}^{3+} \).
- The oxidation state of iron increases from +2 to +3, indicating that it loses one electron:
\[ \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^- \]
- Therefore, \( \text{Fe}^{2+} \) is oxidized.

2. **Reduction**: Reduction is defined as the gain of electrons or a decrease in oxidation state.
- The dichromate ion \( \text{Cr}_2\text{O}_7^{2-} \) is reduced to \( \text{Cr}^{3+} \).
- To find the oxidation state of chromium in \( \text{Cr}_2\text{O}_7^{2-} \):
- Let the oxidation state of Cr be \( x \). The equation is:
\[ 2x + 7(-2) = -2 \implies 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
- Thus, the oxidation state of Cr in \( \text{Cr}_2\text{O}_7^{2-} \) is +6. It is reduced to +3:
\[ \text{Cr}_2\text{O}_7^{2-} + 6e^- \rightarrow 2\text{Cr}^{3+} \]
- Therefore, \( \text{Cr}^{6+} \) is reduced to \( \text{Cr}^{3+} \).

### Step 2: Confirming the Reaction is a Redox Reaction
- Since \( \text{Fe}^{2+} \) is oxidized (loses electrons) and \( \text{Cr}_2\text{O}_7^{2-} \) is reduced (gains electrons), this confirms that the reaction is indeed a redox reaction.

### Step 3: Determine the Type of Reaction
- **Disproportionation Reaction**: This type of reaction involves a single element undergoing both oxidation and reduction. In our case, different elements (Fe and Cr) are involved, so it is not a disproportionation reaction.

- **Comproportionation Reaction**: This involves two different oxidation states of the same element combining to form a single oxidation state. Again, this does not apply here as we have different elements.

- **Intermolecular Redox Reaction**: This reaction occurs between different molecules. Since \( \text{Fe}^{2+} \) and \( \text{Cr}_2\text{O}_7^{2-} \) are different species, this is indeed an intermolecular redox reaction.

- **Thermal Decomposition Redox Reaction**: This would require heat to be involved in the reaction, which is not the case here.

### Conclusion
The reaction \( \text{Fe}^{2+}(aq) + \text{Cr}_2\text{O}_7^{2-} + \text{H}^+ \rightarrow \text{Fe}^{3+}(aq) + \text{Cr}^{3+} \) is an **intermolecular redox reaction**.