Which of the following represents a synthetic detergent?

Options

A. `C_(15) H_(31)COOK`
B. `CH_(3)[CH_2]_(16)COONa`
C.
D. None of the above

Answer

To determine which of the given options represents a synthetic detergent, we need to understand the characteristics and general formula of synthetic detergents.

### Step-by-Step Solution:

1. **Understanding Synthetic Detergents**:
Synthetic detergents are man-made cleaning agents that typically have a complex structure. Their general formula can be represented as \( RC_6H_4SO_3Na \), where \( R \) is a hydrocarbon chain.

2. **Identifying the Components**:
- Synthetic detergents contain a hydrophilic (water-attracting) part and a hydrophobic (water-repelling) part.
- The hydrophilic part usually contains a sulfonate or sulfate group, which allows it to interact with water.

3. **Analyzing the Options**:
- **Option 1: \( C_{15}H_{31}COOK \)**: This compound has a carboxylate group (COO) and is typically classified as soap, not a synthetic detergent.
- **Option 2: \( CH_3CH_2(CH_2)_{16}COONa \)**: Similar to the first option, this also has a carboxylate group, indicating it is a soap.
- **Option 3: \( C_{12}H_{25}C_6H_5SO_3Na \)**: This option contains the sulfonate group (SO3Na) and matches the general formula for synthetic detergents.

4. **Conclusion**:
Based on the analysis, the compound that represents a synthetic detergent is **Option 3: \( C_{12}H_{25}C_6H_5SO_3Na \)**.

### Final Answer:
**The synthetic detergent is \( C_{12}H_{25}C_6H_5SO_3Na \)**.

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