`(NH_(4))_(2)Cr_(2)O_(7) overset(Delta)to N_(2)uarr+Cr_(2)O_(3)darr+H_(2)O uarr`

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 solve the given reaction `(NH_(4))_(2)Cr_(2)O_(7) → N_(2) + Cr_(2)O_(3) + H_(2)O`, we will analyze the oxidation states of the elements involved and determine the type of reaction.

### Step-by-Step Solution:

1. **Identify the Reactant and Products**:
The reactant is ammonium dichromate, \((NH_4)_2Cr_2O_7\), and the products are nitrogen gas \((N_2)\), chromium(III) oxide \((Cr_2O_3)\), and water \((H_2O)\).

2. **Determine the Oxidation States**:
- For nitrogen in \((NH_4)_2Cr_2O_7\):
- Each \(NH_4^+\) has a charge of +1. Since there are two ammonium ions, the total positive charge is +2.
- Let the oxidation state of nitrogen be \(X\). The equation for nitrogen becomes:
\[ X + 4(+1) = +1 \quad \text{(for one } NH_4^+\text{)} \]
\[ X + 4 = 1 \implies X = -3 \]
- Therefore, nitrogen in \((NH_4)_2Cr_2O_7\) is in the -3 oxidation state.

- For chromium in \((NH_4)_2Cr_2O_7\):
- The dichromate ion \((Cr_2O_7)^{2-}\) has a total charge of -2.
- Let the oxidation state of chromium be \(Y\). The equation becomes:
\[ 2Y + 7(-2) = -2 \]
\[ 2Y - 14 = -2 \implies 2Y = 12 \implies Y = +6 \]
- Therefore, chromium in \((NH_4)_2Cr_2O_7\) is in the +6 oxidation state.

- For nitrogen in \(N_2\):
- The oxidation state of nitrogen in \(N_2\) is 0.

- For chromium in \(Cr_2O_3\):
- The oxidation state of chromium can be calculated as follows:
\[ 2Z + 3(-2) = 0 \]
\[ 2Z - 6 = 0 \implies 2Z = 6 \implies Z = +3 \]
- Therefore, chromium in \(Cr_2O_3\) is in the +3 oxidation state.

3. **Analyze the Changes in Oxidation States**:
- Nitrogen changes from -3 in \((NH_4)_2Cr_2O_7\) to 0 in \(N_2\) (oxidation).
- Chromium changes from +6 in \((NH_4)_2Cr_2O_7\) to +3 in \(Cr_2O_3\) (reduction).

4. **Determine the Type of Reaction**:
- Since one element (nitrogen) is oxidized and another element (chromium) is reduced, this is a redox reaction.
- It is also a thermal decomposition reaction because a single reactant is decomposing into multiple products.

5. **Conclusion**:
The reaction is classified as a thermal decomposition redox reaction.

### Final Answer:
The reaction `(NH_(4))_(2)Cr_(2)O_(7) → N_(2) + Cr_(2)O_(3) + H_(2)O` is a thermal decomposition redox reaction.