Select the correct equation (s) which represent double displacement reaction?
I. `Pb+CuCl_(2)toPbCl_(2)+Cu`
II. `Na_(2)SO_(4)+BaCl_(2)toBaSO_(4)+2NaCl`
III. `C+O_(2)toCO_(2)`
IV. `CH_(4)+2O_(2)toCO_(2)+2H_(2)O`

Options

A. I and IV
B. II only
C. I and II
D. III and IV

Explanation

To determine which equations represent double displacement reactions, we first need to understand what a double displacement reaction is. In a double displacement reaction, two compounds exchange their ions to form two new compounds. The general form can be represented as:

\[ AB + CD \rightarrow AD + CB \]

where \( A \) and \( C \) are cations, and \( B \) and \( D \) are anions.

Now, let's analyze each option provided in the question:

### Step 1: Analyze the equations

1. **Equation I: \( Pb + CuCl_2 \rightarrow PbCl_2 + Cu \)**
- In this equation, lead (Pb) displaces copper (Cu) from copper(II) chloride (CuCl₂). This is a **single displacement reaction**, not a double displacement reaction.

2. **Equation II: \( Na_2SO_4 + BaCl_2 \rightarrow BaSO_4 + 2NaCl \)**
- Here, sodium (Na) and barium (Ba) exchange places with sulfate (SO₄) and chloride (Cl). This is a classic example of a **double displacement reaction**.

3. **Equation III: \( C + O_2 \rightarrow CO_2 \)**
- This reaction involves the combination of carbon (C) and oxygen (O₂) to form carbon dioxide (CO₂). This is a **combination reaction**, not a double displacement reaction.

4. **Equation IV: \( CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \)**
- This reaction represents the combustion of methane (CH₄) and is also not a double displacement reaction. It is a **combustion reaction**.

### Conclusion:
From the analysis, only **Equation II** represents a double displacement reaction.

### Final Answer:
The correct equation that represents a double displacement reaction is:
- **II. \( Na_2SO_4 + BaCl_2 \rightarrow BaSO_4 + 2NaCl \)**

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