During the titration of a mixture of `Na_(2)CO_(3)` and `NaHCO_(3)` against HCl :

Options

A. Phenolphthalein is used to detect the first end point
B. Phenolphthalein is used to detect the second end point
C. Methyl orange is used to detect the first end point
D. Phenolphthalein is used to detect the first and second end point

Answer

To solve the question regarding the titration of a mixture of sodium carbonate (Na₂CO₃) and sodium bicarbonate (NaHCO₃) against hydrochloric acid (HCl), we can break down the process step-by-step:

### Step 1: Understanding the Reaction
In the titration of Na₂CO₃ and NaHCO₃ with HCl, two distinct reactions occur.

1. **First Reaction**: Sodium carbonate reacts with hydrochloric acid to form sodium bicarbonate and sodium chloride.
\[ \text{Na}_2\text{CO}_3 + \text{HCl} \rightarrow \text{NaHCO}_3 + \text{NaCl} \]

2. **Second Reaction**: The sodium bicarbonate formed in the first reaction then reacts with another mole of hydrochloric acid to produce sodium chloride, water, and carbon dioxide.
\[ \text{NaHCO}_3 + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \]

### Step 2: Identifying the Endpoints
The titration has two endpoints:
- **First Endpoint**: This occurs when all the sodium carbonate has been converted to sodium bicarbonate.
- **Second Endpoint**: This occurs when all the sodium bicarbonate has been converted to sodium chloride.

### Step 3: Choosing Indicators
Indicators are chosen based on the pH at the endpoints:
- **For the First Endpoint**: Phenolphthalein is typically used, which changes color in the pH range of approximately 8.3 to 10. This is suitable for detecting the endpoint when Na₂CO₃ is converted to NaHCO₃.

- **For the Second Endpoint**: Methyl orange is used, which changes color in the pH range of about 3.1 to 4.4. This is appropriate for detecting the endpoint when NaHCO₃ is converted to NaCl.

### Step 4: Evaluating the Options
Now we can evaluate the options provided in the question:
1. Phenolphthalein is used to detect the first endpoint. **(True)**
2. Phenolphthalein is used to detect the second endpoint. **(False)**
3. Methyl orange is used to detect the first endpoint. **(False)**
4. Phenolphthalein is used to detect both the first and second endpoints. **(False)**

### Conclusion
The correct statement is that phenolphthalein is used to detect the first endpoint. Therefore, the correct answer is **Option 1**.

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