Most metal oxide are thermally stable at temperature upto `1000^(@)C` but the oxide of metals below hydrogen in the electrochemical series fairly. Thus `HgO and Ag_(2)O` decomposes on heating.
Q. Correct code for following thermal decomposition reaction(s) evolving gas having equal number of `sigma- and pi-`bonds is :
(i)`BeCO_(3)overset(delta)(to)` (ii)`ZnSO_(4)overset(delta)underset(gammalt800^(@)C)(to)`
(iii)`FeSO_(4)overset(300^(@)C)(to)` (iv)`(NH_(4))_(2)Cr_(2)O_(7)overset(delta)(to)`

Options

A. i, ii, iii
B. i, iii, iv
C. i, ii, iii and IV
D. All of these

Answer

To solve the problem, we need to analyze the thermal decomposition reactions given and identify the gases produced in each reaction. Then, we will determine which of these gases have equal numbers of sigma (σ) and pi (π) bonds.

### Step 1: Analyze the Reactions

1. **Reaction (i):**
\[ \text{BeCO}_3 \xrightarrow{\Delta} \text{BeO} + \text{CO}_2 \]
- Products: Beryllium oxide (BeO) and carbon dioxide (CO₂).
- Gas produced: CO₂.

2. **Reaction (ii):**
\[ \text{ZnSO}_4 \xrightarrow{\Delta < 800^\circ C} \text{ZnO} + \text{SO}_2 + \text{O}_2 \]
- Products: Zinc oxide (ZnO), sulfur dioxide (SO₂), and oxygen (O₂).
- Gases produced: SO₂ and O₂.

3. **Reaction (iii):**
\[ \text{FeSO}_4 \xrightarrow{300^\circ C} \text{Fe}_2\text{O}_3 + \text{SO}_2 + \text{SO}_3 \]
- Products: Ferric oxide (Fe₂O₃), sulfur dioxide (SO₂), and sulfur trioxide (SO₃).
- Gases produced: SO₂ and SO₃.

4. **Reaction (iv):**
\[ (\text{NH}_4)_2\text{Cr}_2\text{O}_7 \xrightarrow{\Delta} \text{Cr}_2\text{O}_3 + \text{N}_2 + \text{H}_2\text{O} \]
- Products: Chromium oxide (Cr₂O₃), nitrogen gas (N₂), and water (H₂O).
- Gas produced: N₂.

### Step 2: Determine Sigma and Pi Bonds in Gases

1. **Carbon Dioxide (CO₂):**
- Structure: O=C=O
- Bonds: 2 σ bonds (one between C and each O) and 2 π bonds (one for each double bond).
- **Equal σ and π bonds: Yes.**

2. **Sulfur Dioxide (SO₂):**
- Structure: O=S=O
- Bonds: 2 σ bonds (one between S and each O) and 2 π bonds (one for each double bond).
- **Equal σ and π bonds: Yes.**

3. **Oxygen (O₂):**
- Structure: O=O
- Bonds: 1 σ bond and 1 π bond.
- **Equal σ and π bonds: Yes.**

4. **Sulfur Trioxide (SO₃):**
- Structure: O=S=O (with one additional O connected to S through a double bond).
- Bonds: 3 σ bonds and 3 π bonds.
- **Equal σ and π bonds: Yes.**

5. **Nitrogen (N₂):**
- Structure: N≡N
- Bonds: 1 σ bond and 2 π bonds.
- **Equal σ and π bonds: No.**

### Step 3: Conclusion

The gases produced in reactions (i), (ii), (iii), and (iv) are:
- (i) CO₂
- (ii) SO₂, O₂
- (iii) SO₂, SO₃
- (iv) N₂

The gases with equal numbers of σ and π bonds are:
- CO₂
- SO₂
- O₂
- SO₃

Thus, the correct reactions that produce gases with equal numbers of σ and π bonds are:
- Reaction (i): CO₂
- Reaction (ii): SO₂, O₂
- Reaction (iii): SO₂, SO₃

### Final Answer
The correct code for the reactions is: **(i), (ii), (iii)**.