A vessel contains a mixture of `O_(2 )and N_(2)`. The quantity of `O_(2)` is 16% of total mixture. Some quantity of mixture taken out from it and replaced by `N_(2)`. This process is repeated once more. Now the quantity of` O_(2)` is 9% of total mixture. If total quantity of mixture was 8 lt , then find the quantity of mixture which is taken out.

Answer

To solve the problem step-by-step, we will use the information provided in the question and apply the formula for mixtures.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- The total quantity of the mixture is 8 liters.
- The initial percentage of \( O_2 \) in the mixture is 16%.

2. **Calculate Initial Quantity of \( O_2 \)**:
\[ \text{Initial quantity of } O_2 = \frac{16}{100} \times 8 = 1.28 \text{ liters} \]

3. **Understand the Process**:
- A certain quantity \( X \) of the mixture is taken out and replaced with \( N_2 \).
- This process is repeated twice.

4. **Set Up the Equation After Two Replacements**:
- After the first replacement, the quantity of \( O_2 \) remaining can be expressed as:
\[ \text{Quantity of } O_2 \text{ after first replacement} = 1.28 \times \left(1 - \frac{X}{8}\right) \]
- After the second replacement, the quantity of \( O_2 \) becomes:
\[ \text{Quantity of } O_2 \text{ after second replacement} = 1.28 \times \left(1 - \frac{X}{8}\right)^2 \]

5. **Set Up the Final Condition**:
- We know that after two replacements, the percentage of \( O_2 \) is now 9%. Thus:
\[ \text{Final quantity of } O_2 = \frac{9}{100} \times 8 = 0.72 \text{ liters} \]

6. **Create the Equation**:
\[ 1.28 \times \left(1 - \frac{X}{8}\right)^2 = 0.72 \]

7. **Simplify the Equation**:
- Divide both sides by 1.28:
\[ \left(1 - \frac{X}{8}\right)^2 = \frac{0.72}{1.28} \]
- Calculate \( \frac{0.72}{1.28} = 0.5625 \).

8. **Take the Square Root**:
\[ 1 - \frac{X}{8} = \sqrt{0.5625} = 0.75 \]

9. **Solve for \( X \)**:
\[ \frac{X}{8} = 1 - 0.75 = 0.25 \]
\[ X = 0.25 \times 8 = 2 \text{ liters} \]

10. **Conclusion**:
- The quantity of the mixture that is taken out each time is \( 2 \) liters.

### Final Answer:
The quantity of mixture which is taken out is **2 liters**.