`K_(2)Cr_(2)O_(7) overset(Delta) to K_(2)CrO_(4)+Cr_(2)O_(3)+O_(2)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 \( K_2Cr_2O_7 \) when heated, we will analyze the products formed and the changes in oxidation states of chromium. The reaction is:

\[ K_2Cr_2O_7 \xrightarrow{\Delta} K_2CrO_4 + Cr_2O_3 + O_2 \]

### Step 1: Identify the Reactants and Products
The reactant is potassium dichromate (\( K_2Cr_2O_7 \)), and the products are potassium chromate (\( K_2CrO_4 \)), chromium(III) oxide (\( Cr_2O_3 \)), and oxygen gas (\( O_2 \)).

### Step 2: Determine the Oxidation States of Chromium
1. **In \( K_2Cr_2O_7 \)**:
- Potassium (\( K \)) has an oxidation state of \( +1 \).
- Oxygen (\( O \)) has an oxidation state of \( -2 \).
- Let the oxidation state of chromium be \( x \).
- The equation for the oxidation states is:
\[ 2(+1) + 2x + 7(-2) = 0 \implies 2 + 2x - 14 = 0 \implies 2x - 12 = 0 \implies x = +6 \]
- Therefore, the oxidation state of chromium in \( K_2Cr_2O_7 \) is \( +6 \).

2. **In \( K_2CrO_4 \)**:
- The equation for the oxidation states is:
\[ 2(+1) + x + 4(-2) = 0 \implies 2 + x - 8 = 0 \implies x - 6 = 0 \implies x = +6 \]
- The oxidation state of chromium in \( K_2CrO_4 \) is also \( +6 \).

3. **In \( Cr_2O_3 \)**:
- The equation for the oxidation states is:
\[ 2x + 3(-2) = 0 \implies 2x - 6 = 0 \implies x = +3 \]
- The oxidation state of chromium in \( Cr_2O_3 \) is \( +3 \).

### Step 3: Analyze the Changes in Oxidation States
- In \( K_2Cr_2O_7 \) and \( K_2CrO_4 \), chromium remains in the \( +6 \) oxidation state.
- In \( Cr_2O_3 \), chromium is reduced to \( +3 \).
- Thus, we see that one chromium atom is reduced (from \( +6 \) to \( +3 \)), while the other remains unchanged.

### Step 4: Classify the Reaction
Since one chromium species is reduced and the other remains unchanged, this reaction does not fit the criteria for a disproportionation reaction (where a single species undergoes both oxidation and reduction). Instead, it is a thermal decomposition reaction, where one compound decomposes into multiple products.

### Conclusion
The reaction \( K_2Cr_2O_7 \) decomposes upon heating to form \( K_2CrO_4 \), \( Cr_2O_3 \), and \( O_2 \). This is classified as a thermal decomposition reaction.

### Final Answer
The reaction is a **thermal decomposition reaction**.

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