Which among the following is (are) double displacement reaction (s)?
(i) `Pb+CuCl_(2)rarrPbCl_(2)+Cu`
(ii) `Na_(2)SO_(4)+BaCl_(2)rarrBaSO_(4)+2NaCl`
(iii) `C+O_(2)rarrCO_(2)`
(iv) `CH_(4)+2O_(2)rarrCO_(2)+2H_(2)O`

Options

A. `(i) and (iv)`
B. Only(ii)
C. `(i) and (ii)`
D. `(iii) and (iv)`

Explanation

To determine which of the provided reactions are double displacement reactions, we will analyze each reaction step by step.

### Step 1: Understand Double Displacement Reactions
A double displacement reaction (also known as a double replacement reaction) is characterized by the exchange of ions between two compounds, resulting in the formation of two new compounds. This typically involves the swapping of cations and anions.

### Step 2: Analyze Each Reaction

1. **Reaction (i): `Pb + CuCl₂ → PbCl₂ + Cu`**
- In this reaction, lead (Pb) displaces copper (Cu) from copper(II) chloride (CuCl₂).
- Here, there is no exchange of ions between two compounds; instead, one element (lead) is replacing another (copper).
- **Conclusion**: This is a single displacement reaction, not a double displacement reaction.

2. **Reaction (ii): `Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl`**
- In this reaction, sodium (Na) ions from sodium sulfate (Na₂SO₄) exchange places with barium (Ba) ions from barium chloride (BaCl₂).
- The sulfate (SO₄²⁻) combines with barium (Ba²⁺), and sodium (Na⁺) combines with chloride (Cl⁻).
- **Conclusion**: This is a double displacement reaction because there is an exchange of ions resulting in the formation of two new compounds (BaSO₄ and NaCl).

3. **Reaction (iii): `C + O₂ → CO₂`**
- In this reaction, carbon (C) combines with oxygen (O₂) to form carbon dioxide (CO₂).
- This is a simple combination reaction where two reactants form one product.
- **Conclusion**: This is not a double displacement reaction.

4. **Reaction (iv): `CH₄ + 2O₂ → CO₂ + 2H₂O`**
- In this reaction, methane (CH₄) reacts with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O).
- This is a combustion reaction where a hydrocarbon reacts with oxygen.
- **Conclusion**: This is not a double displacement reaction.

### Final Conclusion
Among the given reactions, only **Reaction (ii)** `Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl` is a double displacement reaction.

### Summary of Results
- **Double Displacement Reaction**: (ii) `Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl`
- **Not Double Displacement Reactions**: (i), (iii), (iv)